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THE 

CONTROL OF WATER 

\ 

AS APPLIED TO IRRIGATION, POWER 
AND TOWN WATER SUPPLY PURPOSES 


PHILIP A MORLEY PARKER 

* % 

A.M.I.C.E., A.M. Am. Soc. C.E., M.D.I.V., B. A. (Cantab.) 

B.C.E. (Melbourne) 


WITH FULL DIAGRAMMATIC ILLUSTRATIONS 


NEW Y b R K 

D. VAN NOSTRAND COMPANY 
TWENTY-FIVE PARK PLACE 
, 1 9 1 3 


I C.I4-S 

.P?> 


1 ..*. 








GIFT 

GOL. C. M. TOWNSEND 

OCT. ?2. 1940 


, « i 


/ 


JL 



K 






s 



This book is essentially the product of actual engineering experience, 
and is mainly based on a collection of notes and formulae accumulated 
in some eighteen years of professional work, during the major portion 
of which I was engaged in independent practice. It must therefore 
be regarded not as a text-book, but rather as a manual for engineers 
in active work. 

Although the initial knowledge assumed in the reader may be con¬ 
sidered to be somewhat unusual, many portions of the book have 
stood the test of everyday office requirements in the hands of draughts¬ 
men and assistants; and I consequently trust that on the whole it will 
prove useful to all technically trained engineers. 

The treatment of the theoretical parts is purposely cursory, and may 
even appear somewhat incomplete; but, after considerable experience 
of precise hydraulic measurements both under field and laboratory 
conditions, I have come to the conclusion that at the present date 
the results obtained from well-conducted observations are more accurate 
than the assumptions made in the most modern mathematical treat¬ 
ment of hydraulics. To illustrate my meaning, I need only refer to 
the errors introduced by the usual theoretical assumption of uniform 
velocity, and to the undoubted fact that no weir capable of practical 
construction discharges water according to the law of (head) 1,s . 

With a view to providing a bibliography an attempt has been made 
to give systematic references to original authorities; but it is as well to 
mention that in several cases the reference is not to the original 
authority, but to some later paper which contains a more useful presenta¬ 
tion of the subject. In some cases, however, search for the original 
authority has proved fruitless, and I must consequently apologise to 
all engineers who may find their work utilised without any definite 


VI 


PREFA CE 


acknowledgment on my part, and can assure them that such omission 
has been quite unintentional. 

I must further acknowledge my general indebtedness to Prof. W. C. 
Unwin, and the late Prof. Kernot of Melbourne University; also to 
Messrs. Middleton, Hunter, and Duff. 

For the facilities afforded by nearly every officer of the Punjab 
Irrigation Branch, and especially by my former superior officers, Messrs. 
Floyd and Tickell, I am greatly indebted. 

For assistance in the preparation of the book, and for much helpful 
criticism, I have also to thank Messrs. R. E. Middleton, P. H. Fish, 
R. E. Reeves, M. Mawson, H. C. Booth, and W. R. Pettit, whose 
special knowledge has been extremely useful. 


25 Victoria Street, S.W. 


CONTENTS 


CHA.P. PAGE 

Preface . . . . . . . . . v 

I. Preliminary Data . . . . . i 

II. General Theory of Hydraulics .... 5 

III. Gauging of Streams and Rivers . . . 32 

IV. Gauging by Weirs ....... 96 

V. Discharge of Orifices . . . . . .135 

VI. Collection of Water and Flood Discharge . .169 

VI1 . Dams and Reservoirs . . . . .291 

VIII. Pipes ......... 422 

IX. Open Channels ....... 469 

X. Filtration and Purification of Water . . . 497 

XI. Problems connected with Town Water Supply . . 597 

XII. Irrigation ........ 623 

XIII. Movable Dams ... . . . .771 

XIV. Hydraulic Machinery other than Turbines . . 783 

XV. Turbines and Centrifugal Pumps . . . .868 

XVI. Concrete, Ironwork, and Allied Hydraulic Construc¬ 
tion ........ 957 

Tables. ........ 997 

Graphic Diagrams ....... 1014 

Index ......... 1039 


Vll 































I II 

. 







'' • •' ’ 

v/ 


** 











1,1V.. / I ► . IHO ♦ / 











u *4 i , 































t,- ■ * 























































CHAPTER 1 
PRELIMINARY DATA 

Preliminary Data of Hydraulics.— Density and weight of a cube foot of pure water 
—Conversion tables—Rain-fall and run-off figures—Conversion from metric into 
English measure. 


PRELIMINARY DATA OF HYDRAULICS 

In most cases the figures required for conversion purposes are considered 
and tabulated on the pages where they are likely to be wanted. The following 
figures are used so frequently that they are tabulated together in order to save 
reference. The column headed “ Approximate Values ” will be found to indicate 
very rapid methods of conversion, which are liable to but small errors either 
absolutely or in arithmetical working. 


DENSITY AND WEIGHT OF A CUBE FOOT OF PURE 
WATER AT DIFFERENT TEMPERATURES 


Temperature in 
Degrees Fahr. 

Density. 

Weight of a Cube 
Foot in Lbs. 

3 2 ’° 

0*99987 

62*416 

39’3 

I -OOOOO 

62-424 

45 ‘° 

0-99992 

62*419 

5 °‘° 

°’99975 

62*408 

55 ’° 

0-99946 

62*390 

6o’o 

0-99907 

62*366 

65*0 

0-99859 

62-336 

70*0 

0*99802 

62*300 

75 '° 

0-99739 

62-261 

8o*o 

0*99669 

62-217 

85-0 

0-99592 

62*169 

90*0 

°’ 995 10 

62*118 

IOO'O 

0*99418 

62-061 

105-0 

°‘ 993 i 8 

61*998 

I IO’O 

0-99214 

6 i *933 

115-0 

°’ 99 io 5 

61-865 

120*0 

0*98870 

61-719 


I 



















2 


CONTROL OF WATER 


CONVERSION TABLE FOR QUANTITIES FREQUENTLY USED IN 

HYDRAULICS 



Accurate Values. 


Number. 

Log. 

Cube feet into imperial gallons 

6*24 

0*7952 

Cube feet into U.S. gallons 

7*49 

0-8744 

Imperial gallons into cube feet 

0*1603 

1-2048 

U.S. gallons into cube feet 

0*1336 

1-1256 

U.S. gallons into imperial gal- 

o ' 8 333 

I -9208 

Ions 



Imperial gallons into U.S. gal- 

I *200 

0*0792 

Ions 



Feet head of water into lbs. 

0*434 

i * 6 375 

per square inch 

Lbs. per square inch into feet 

2*304 

0-3625 

head of water 


Kilograms into pounds . 

2*2046 

0*3433 

Kilos per square centimetre 

14-225 

1 * I 53 ° 

into lbs. per square inch 

Kilos per square metre into 

0*2048 

i* 3 H 4 

lbs. per square foot 


Lbs. per square inch into 

0-0703 

2*8470 

kilos per square centimetre 



Lbs. per square foot into 

4*8829 

0*6886 

kilos per square metre 


Lbs. per cube foot into kilos 

16-019 

1*2046 

per cube metre 

Metres into feet. 

3-2808 

0*5160 

Square metres into square feet 

10-764 

1 *0320 

Cube metres into cube feet. . 

35 * 3 i 5 

1-5480 

Inches into centimetres 

2*54 

0-4048 

Square inches into square 

6*45 

0-8096 

centimetres 


Imperial gallons into litres 

4*544 

o *6575 

U.S. gallons into litres . 

3785 

0-5780 

Feet into metres 

0-3048 

1-4840 

Square feet into square metres 

0*0929 

2-9680 

Cube feet into cube metres 

* 

0*02832 

2-4521 


Approximate 

Values. 


6-25 


10 0 _ 2_5 
16 4 

V = 7*5 
1 6 
itr<T 

lV + irV = 0 'i333 

5 


2 +j\= 2’2 


3 + 4+tI(7=3'28 
io + i + i=io*75 
-§-+2 = 35*333 
2 + 1 = 2*5 

6 '5 
4*5 

? 3 

3 t 


In actual practice the use of systematic tables saves both time and errors. 
The following works are useful : 

Bellasis Hydraulics with Tables (Rivington’s), which contains a very com¬ 
plete set of tables usually employed in Hydraulics. In my opinion the book 

also gives the soundest general treatment of theoretical questions that exists in 
English. 































CONVERSION OF UNITS 


3 


Horton’s Weir Experiments , Coefficients , and Formulce (United States 
Geological Survey : apply to the Superintendent of Public Documents, Wash¬ 
ington, D.C., U.S.A.) is indispensable for weir work, and contains many other 
very useful tables. 

Kennedy’s Graphic Hydraulic Diagrams (apply to Thomason College, 
Roorkee, U.P., India). This volume is intended purely for irrigation purposes. 
If silty waters are considered it is indispensable. 


EQUIVALENTS FOR USE IN RAINFALL AND RUN-OFF 


Calculations .—These are calculated on the assumption that 6f gallons =i cube foot, 


and 365 days: 

1 inch of run-off in a year . 

1 inch of run-off in an hour. 

« 

1 cusec per square mile 

1 inch depth over 1 square mile . 
100,000 cube feet storage per acre 
100,000 imperial gallons per acre 
1000 imperial gallons per acre per day 


1 year. 

= 0*0736 cusecs per square mile. 
= 640 cusecs per square mile. 

= 1 cusec per acre. 

= 13*56 inches yearly run-off. 

= 31*54 million cube feet yearly. 
= 2*32 million cube feet yearly. 
= 27*5 inches depth on 1 acre. 

= 4*40 inches depth on 1 acre. 

= 16*08 inches yearly run-off. 


CONVERSION OF AN EQUATION FROM ENGLISH INTO METRIC 

UNITS, AND VICE VERSA 


The most usual form for a hydraulic equation is one or other of the two 
following : 

Q = C 1 /// 1 - 5 or, Q = Al n h m 

v — C,Srs or, v — V>r p s q 

As a rule it is necessary to transform from metric into English units. Now : 
Q is in cubic metres .... =( 3 ’ 28 o 9 ) 3 cubic feet. 

I is in metres ..... =3*2809 feet. 
h is in metres ..... =3*2809 feet. 

Thus the new value of C x (say C e ), or of A (say A e ), is given by : 

(3* 2 8o9) 3 Q = C t Y/z 1 • 5 (3 *2 809) 25 = A e /”A w (3*28o9) n + m 

Therefore C e = ^ 3*2809 =i’8iiC. 

A e = A(3*28o9) 3 -” 1 -’'. 

So also, proceeding to the second equation, 

v = C ^ rs 


v is in metres per second 
r is in metres 

j is a pure number 


= 3*2809^ feet per second. 
= 3*2809^ feet. 

_ metres _ feet 
metres feet 


So that C. = Cr8i 1. B. = BO^Sog) 1 -;*. 

The principles are now clear. 

More complicated cases are better treated by successive substitution. 

Let us consider Maxime Levy’s equation for the velocity of water in metres 
per second in cast-iron pipes with a radius of R metres. We have 

z/ = 2Q*5VRj(i + 3VR) 







4 


CONTROL OF WATER 


Let us transform this into English measure, and substitute r (the hydraulic 
mean radius) for R, i.e. we obtain : 

v= C V r.r(i-KrVr) m feet, and feet P er second. 

In metres r=—=-—R feet. 

2 2 

i +3^R= i +jV r. if r64R = 3^R, or x = =- = 2*34. 

Vi *64 

We have consequently disposed of the factor i + 3 Vr, and we get : 


C = 


v 


V' rs(i +x */ r ) 
3*287/ 


3*28 


___ — . - 20*5 =20*5 x 2*56= 52*5. 

v /r64Ri-(i + 3VR) v i*64 

Or, V = 52*5 V rs(i +2*34\/ r ) is the equation in English measure. 


i n 











,. 1 





s i 



















CHAPTER II 

GENERAL THEORY OF HYDRAULICS 

Definitions.— Pressure —Gauge and Absolute— Head —Velocity head— Viscosity— 
Theoretical equations of hydraulics. 

Velocity. —Definition of mean velocity—Velocity—Practical measurement—Resultant 
velocity—Steady and uniform motion. 

Periodic Unsteady Motion. 

Theoretical Investigation. —Mean local velocity—Irregularity of velocity—Discharge 
formula—Differences of the local velocities—Practical applications to discharge 
observations. 

Hydraulic Calculations. —Bernouilli’s equation. 

Losses by Friction. —Shock—Curves. 

Practical Equation. —Correction for influence of local velocities—Coefficient of local 
distribution—Curve losses. 

General Laws of Resistance to the Motion of Fluids. —Turbulent motion— 
Stream line motion—Distribution of velocities in a circular pipe—Reynold’s critical 
velocities—Resistance at velocities less than the critical—Practical applications to 
orifices and weirs. 

Capillary Motion or Percolation. —Capillary elevation. 

Percolation of Water through Sand or Gravel. —General laws—Effective size and 
uniformity coefficient of sand—Hazen’s formula—Effect of dirt or clayey matter. 

Curve Resistances. —Practical rules—Weisbach’s formulas —Bellasis’ table. 


UNITS 

Throughout this book, unless otherwise definitely stated, the units employed are feet, 
pounds, and seconds. Thus areas are measured in square feet, volumes in cube feet, 
velocities in feet per second, etc. 

Pressures, however, are usually measured in feet of water, so that a pressure of I foot 
of water corresponds to a pressure of 62'5 lbs. per square foot, or 0*433 lbs. per square 
inch. 

Since practical utility rather than uniformity is considered of primary importance, 
the inch unit is occasionally employed when discussing structures such as pipes, or metal 
work, which are bought and sold by this unit ; also where the adoption of a foot would 
lead to very small figures or to long strings of zeros. These cases are invariably 
indicated by the word Inch being printed opposite to the formula in which the symbol 
occurs, besides being defined in the letterpress. In the actual working of examples feet 
and decimals of a foot are almost exclusively employed. This practice is already adopted 
by many hydraulic engineers, and where quantities of water are measured accuracy can 
hardly be attained if feet and inches are employed. 

The term Cusec is used as an abbreviation for cubic feet per second. The American 
equivalent is Second-foot. 

The term acre-foot is occasionally used to denote a volume of 43,560 cube feet, which 
is obviously the content of a reservoir 1 acre in area and 1 foot deep. 

It may be noted that for all practical purposes : 1 cusec flowing for 24 hours 

delivers 2 acre-feet. 

The actual figures are—86,400 and 87,120 cubic feet respectively. 

Also I cube foot per minute = 9000 imperial gallons per day of 24 hours, and therefore 
1 cusec = 540,000 gallons per day. 


5 


6 


CONTROL OF WATER 


Definitions. —The ordinary definition of a fluid is a “ substance which 
yields continually to the slightest tangential stress. 5 ' Consequently, when the 
fluid has come to rest the stress across any surface in the fluid must be noimal 
to the surface.” 

Pressure.—In all cases considered in this book (which is exclusively devoted 
to the discussion of engineering practice) the above stress must be a pressure. 
The intensity of the pressure is measured by the number of units of force per 
unit of area. Thus if P be the force in pounds acting on an area of #, square 

p 

feet, the mean pressure over this area is p m —— lbs. per square foot, and, as usual 


in mechanics, the pressure at a given point is defined as ^ = Lt —> when a 


decreases to an indefinitely small area surrounding the point considered. The 
pressure across any surface being normal to the surface, it follows that the 
pressure at any point is the same in all directions about that point. 

As already stated, pressures are usually measured in feet of water. Thus 
the pressure at a point in a body of water at rest,^ feet below the free surface 
of the body of water, is y feet of water, 


or 62’5/ lbs. per square foot, 
or o‘433_)/ lbs. per square inch. 

This is the “pressure” usually considered by engineers, since it is that 
measured by a pressure tube open to the atmosphere, or by a pressure gauge, 
and is that which engineering structures are usually required to sustain. The 
pressure of the atmosphere, however, can be measured by a barometer, and is 
found to vary from day to day, and also to depend upon the height above the 
sea level. On the average, however, the absolute pressure of the atmosphere 
is about 2ii6*8 lbs. per square foot, or 32^9 feet of water. Thus, the height of 
the water barometer is about 33 feet, and the absolute pressure at a point 
where the gauge pressure is y feet is about y+33 feet of water. In certain 
calculations it is found that reckoning the pressure in this manner obviates all 
necessity for a consideration of “ negative pressures.” The term “ absolute 
pressure” is then employed, and “gauge pressure” signifies the pressure as 
first defined. The term pressure when used without qualification denotes gauge 
pressure. 

The term head is frequently employed by engineers, and the following 
discussion will show that head is in reality a generalised expression for the 
energy due to pressure and position, and its mechanical transformations into 
velocity. 

Head. —The term head was primarily used by millwrights in order to 
describe the differences in elevation between the water surfaces in the head 
and tail races of a mill. 

The term as at present used may be best defined as follows : 

Let a vertical tube of a size which will prevent any measurable capillary 
elevation be placed in communication with a mass of water in such a manner 
that the velocity of the water does not affect the height to which the water rises 
in this tube. Let the free water surface in this tube stand at a height H feet 
above a fixed datum plane. Then the water at the point where the tube opens 
into the mass of water considered is said to be under a head H relative to the 
fixed datum plane. It will be evident that if fi Q represent the gauge pressure 


HEAD AND ENERGY 7 

in feet of water and z the height of the mass of water considered above the 
datum plane : 

h=a+* 

and, as remarked later on, we are not concerned with the absolute magnitude 
of H, but rather with the changes in its absolute magnitude. Hence we may 
also say that: 

H=/ rt +2' 


where ft a is the absolute pressure in feet of water, provided that we adhere to 
this notation throughout the whole investigation. 

In actual practice it is found that the orifice of the tube must be somewhat 
carefully shaped and adjusted relatively to the direction of the velocity of the 
water, in order to prevent this velocity from having any influence on the height 
of the water in the tube. If the orifice is so adjusted as to permit the velocity 
to have its greatest possible effect, it will be found that the water surface rises 
a certain additional amount, which (errors and imperfections in the tube orifice 

'iA 

being neglected) is equal to — feet, where v is the velocity of the water in feet 
per second. 

It will therefore be evident that H represents the portion of the energy of a 
unit mass of the water considered, which depends on its position, and that the 


portion which depends on its 


velocity is represented by H„ = 



As a matter of fact, it is well known that the total energy of a body cannot 
be measured, and all that engineers are really concerned with is the measure¬ 
ment of the change of energy. Thus, if strict accuracy be desired the variation 
of H represents the variation of that portion of the energy which is due to 
the position and pressure of the unit mass considered, and similarly the varia¬ 
tion of H„ represents the variation of the energy due to the velocity of the 
unit mass. 

Water being a highly incompressible fluid, and the alterations in temperature 
which occur in practical hydraulics being small, we can usually regard the 
changes in its energy due to compression and changes of temperature as 
negligible. Hence it can be stated that the whole energy of a unit mass of 
water relative to the datum plane is represented by H + Hy. If the matter is re¬ 
garded in this manner, and the above definitions are accepted, we see that H + Hy, 
is constant for the mass of water considered, and that Bernouilli’s equation : 


iA 

H H— =z+/>(,-1 -= a constant 

2 g 2 g 


follows at once. It must, however, be understood that this is no proof, as the 
definition of the velocity cannot be regarded as complete. Still less is it a 
proof of Bernouilli’s equation as applied to two unit masses of water, which at 
the same instant of time are at different points in a stream of water in motion. 

When thus applied we find in practice that 

v 2 

For the first point.H x + —= say 

2 <^" 
v 2 

For the second point .... H 2 + - 2 - = A 2 . 


8 CONTROL OF IVATER 

The difference A,-A, (which is positive if the first point be upstream of 
the second) is defined as the head lost by friction or shock. The definition 
must be regarded merely as a statement of observational fact. A profound 
ignorance exists as to the precise manner in which this energy is d ' s ='P^ te ' 
All that can really be said is that in certain cases the lost energy has been 
accounted for by an observed rise in the temperature of the water. This loss 




A 


T 


5? 

r 


V 

U .V 


is. Velocity = U ft/sec. 


Pressure brittle ImpacT'iOrifice 


K1 


4 

Plane with reference to which the Head /s measured 


dote . 1 is observable with a level 

• a pressure gauge 
- a Pitot or Jarcy tube 


* 

% - 


Sketch No. i. —Relations between Head, Pressure, and Position, and between 

Velocity Head and Velocity. 

of energy is believed to be produced by the internal motion of the water, which 
gradually dies out, and is transformed into heat energy. In the majority of 
cases the observed rise of temperature does not fully account for the loss in 
energy. This may be explained either by imperfections in the experimental 
arrangements, or by the internal motions which still exist but are not observed. 

Viscosity.—The term Viscosity is employed for that property of fluids in 
virtue of which the change in form of the fluid under the action of a continued 





















VELOCITY 


stress proceeds gradually, and is opposed by a resistance which increases as 
the relative velocity of adjacent particles of the fluid increase. While it is 
probable that the whole series of experimental coefficients discussed in this 
book are in reality caused by the fact that water is a viscous fluid, viscosity 
per se does not generally obtrude itself upon the notice of engineers, and is 
therefore discussed only in connection with critical velocities. 

In treatises on Hydraulics certain proofs concerning such relations as the 
connection between the pressure at an orifice and the velocity with which water 
flows through the orifice are usually given. The mathematical demonstration 
of these proofs invariably rests on Bernouilli’s equation (see p. 13). As this 
book is largely concerned with a discussion of the corrections that must in 
practice be applied to these theoretical equations, I have thought it best to 
assume the theoretical equations and to at once consider the experimental 
corrections. The process has practical advantages, as the theoretical relations 
are almost invariably so masked by experimental coefficients that their applica¬ 
tion in an uncorrected form would usually lead to highly erroneous results. 

VELOCITY. —The velocity of water at any time /, and at any point P, and 
in any direction, is defined as follows : 

Consider a small plane area, denoted by a. Let the quantity of water that 
passes through this area in the interval between the times / and /+T seconds 
after a fixed epoch be given by Q = av T. Then, if Q is expressed in cube, 
and a in square feet, v is defined as the mean velocity in feet per second over 
the area <2, during the time interval T, in a direction normal to the plane of a. 

Following the usual rules of mechanics, the velocity at the time / at a point 
P in this direction is 


the limit of 


a T 


when a and T become indefinitely small, and P is the centre of the indefinitely 
small area a. 

This definition is an ideal one. In practice a is a measurable area (the 
smallest value occurring when a Pitot tube is employed in order to measure 
the velocity, and a is then the area of the pressure orifice, which is at least 
^Vnd of an inch in diameter). So also, except in Pitot tube observations, T 
is an appreciable interval of time, say twenty seconds at least. We therefore in 
reality measure mean velocities only. This, as will be seen later, produces a 
closer relation between observation and practical results ; but the difference 
must be borne in mind, since all theoretical equations are concerned not with 
mean velocities as measured, but with the ideal limits of mean velocities as 
above defined. 

We can similarly define the resultant mean velocity (usually termed the 
velocity) at P, as the value of the mean velocity obtained when the area a is 
so oriented that the velocity through it is greater than that through any equal 
area which is not similarly oriented ; or, more precisely, when the velocity 
through all areas in planes which are perpendicular to the plane of a is 
zero. The direction of this resultant mean velocity is obviously normal to the 
plane of a as thus defined. Similarly, the resultant velocity at the time / is 
the maximum limit of the mean velocity when the interval T and the area a 
become indefinitely small. 

We may also define the motion of water as steady when the magnitude 
and direction of this resultant velocity is independent of /. 


10 


CONTROL OF WATER 

In uniform motion the magnitude of the resultant velocity is the same for 
the same particle of water at every point of its path during the motion. 

In practical hydraulics (with the possible exception of motion in capillaiy 
tubes) the motion is always unsteady and non-uniform. Engineers aie, however, 
accustomed to consider the motion of water as steady or uniform when the 
above definitions are fulfilled, if we consider the motion of the entiie stream 
of water as a whole. The unsteadiness or non-uniformity of the motion of 
individual particles is thus ignored, provided that the motion of the whole body 


8 





Average Velocity*6 t5 ft/sec. NiBX ! Rm~ = ' IK 


£. -Average Velocity -S-OKt/sec —~ ' - 049 

V- 


Mean 

Average Velocity-545ft/sec. ' m 


A. 


\ 


/v. 

/ \ 


N 


y 






X \ 
Y \ 


A- 


/ 




Irregularities ofVeiocitiesas observedby Unwin mth a Current Meter 

so —Velociiiesat i&4 below Surface 

average of too revs. of.Meter say Usees, run. 

—-Bo BoMaverage of50b do. do. say 55secs. run. 

—Vetocitfesat MS below Surface 

average of 100 revs, ofMeter say 22secs run. 


Tune 


in 


Minute 


o 


2 4 6 8 10 I? 14 

Sketch No. 2.— Diagram of Irregularities of Velocity. 


/6 


of water is steady or uniform. The phraseology cannot be regarded as 
incorrect, as it is precisely similar to the use of the term “ homogeneous,” as 
applied to concrete or brickwork, or even to steel, if the results of microscopic 
investigations are considered. 

The assumption that these substances are homogeneous permits certain 
mathematical deductions to be obtained, which are found to agree very well 
with the results of observations conducted by the ordinary commercial methods. 
If, however, the observations are conducted with the utmost possible refinement, 
differences between the results of the approximate theory and the observations 





































MEAN LOCAL VELOCLTY 


11 


are disclosed, which are found to be explicable by mathematical investigations 
based on the assumption that the substances are not perfectly homogeneous. 
The difference between the tensile strength of steel plates when measured along 
and perpendicular to the direction of rolling forms a very pronounced example. 

Similarly, the assumption that the motion of water in a pipe or channel of 
constant cross-section is uniform and steady may be made, and will lead to 
results which agree fairly closely with observation so long as the motion of 
large masses of water only is considered. If, however, the motion of individual 
particles of water is investigated by accurate methods, the assumption is not 
sufficiently in accordance with the real physical facts, and the divergence 
between the approximate theory and observation will be found to be more and 
more marked the greater the accuracy of the observations. 

When the distinction between the instantaneous -values of the velocity at 
a point in a given direction, and the mean value of the same velocity over a 
period of time which is sufficiently long to eliminate the effect of the accidental 
irregularities is of importance, the term mean local velocity (see p. 12) will 
be used for the latter quantity, and the differences positive or negative between 
the mean local velocity and the instantaneous values of the velocity will be 
termed the irregularities. 

Thus in symbols : Mean local velocity — where a is very small, when T 
is sufficiently large to eliminate irregularities, and the irregularity at the time 


/is given by Jj,-Limit ( 5 ). 

As a rule, we wish to observe the mean 
term velocity to denote its value. 

Periodic Unsteady Motion.—In ordinary 


local velocity, and employ the 
channels with rough boundaries 


the velocity at any given point is found to vary from moment to moment both 
in magnitude and direction. On the other hand, the resultant mean velocity 
during a sufficiently long period (say i to 5 minutes) varies but little either 
in magnitude or direction. Hence the time variations of the direction and 
magnitude of the velocity are, in a certain sense, periodic. Consequently, if 
at each point of the stream the resultant mean velocities, as defined above, 
are regarded as being the velocities which actually exist at every moment, 
this average of the actual motions may be considered as steady, and calcula¬ 
tions based on this assumption will prove to be fairly reliable. 

Theoretical Investigation. —The definitions given above suffice for 


practical purposes, and the following distinctions need only be considered 
if extreme precision is desired. They are, however, fundamental, and although 
complicated must be taken into account if any advance in the accuracy of 
hydraulic measurements is desired. The use of mathematical symbols is 
therefore legitimate. 

Let any point in the body of water considered be denoted by its co¬ 
ordinates (x,jk, -s'). 

In considering a motion which is steady in the broad sense already defined, 
the velocity in any direction, say Oz, for clearness, is a function of /, due to the 
irregularities of the motion only, and v , the resultant velocity, is given by 


the equation : 


w = <K-r, J, z, t ) 


so that v depends on t as well as on x, y, and z. In piactical cases the 


12 


CONTROL OF WATER 


motion of the water is such that the mean value of v over a sufficiently long 
period is independent of /, or : 



V = 


T 


and V, the resultant mean velocity normal to the plane x, y, is independent 

of t or T. , 

Boussinesq terms V the mean local velocity at the point (x, y, z) in t e 
direction O z. Thus v may be regarded as a quantity which fluctuates 
irregularly about its mean value V. The meaning of the teim periodic 
steady motion is now obvious. 

Certain opinions (they possess no firmer foundation) concerning the length 
of the period T are given'later. 

In practice, engineers are almost entirely concerned with V, and do not 
wish to measure v. The difference V— v is termed the irregularity of the 
velocity, and in all practical measurements the smaller the influence which V — v 
(which may include not only variations in absolute magnitude, but also in 
direction, i.e. \—v, is a vector quantity) has on the indications of the instrument 
used to observe V, the better. The importance of this condition is best lealised 
by the statement that V — v may amount to ± 5 ° P er cent, of V. (See Sketch 2.) 

Now, considering Q, the discharge through any area in the plane z — o, 
which is supposed to be perpendicular to the direction of V, 



v dx dy dt 


where the integration is performed over the whole area, gives the mean dis¬ 
charge during the period t to /+T ; but any element of the discharge is 
represented by dQ = v dx dy dt. Thus, any instrument which is really accurate 
for the purpose of discharge measurement must measure V, and not v. 

Assuming that the instrument measures V, we can in practice only measure 
V at definite points. Thus, in place of Q—ffV dx dy, we really have : 

Q = 2 V m a, where V m is the mean value of V over the area represented by a. 

Now, the practical assumption is that, if V be measured at a point P, 
the value thus obtained represents V m for practical purposes over a certain 
area. Thus we have to consider not only the possible variations of v, for a 
fixed point {x, y) as t varies, but the possible variations of V, as x and y, 
vary over the area represented by a. These we may shortly term the 
permanent differences of the local velocities at adjacent points. 

The various formulae used in practice when calculating O, from a series 
of observations of V, are discussed later. Mathematically speaking, the most 
complicated of these formulae leads to a correct value of the discharge if the 
local velocities over the whole of each partial area a can be represented by : 

V=a 0 + a l x+b 1 yAa 2 x 2 +t>2xy+c 2 y 2 

Thus, any very marked difference between the values of V, at three 
adjacent points of observation, may be regarded as indicating a possibility of 
an error in Q due to insufficiently close spacing of the points at which V 
is observed. The question therefore at once arises,—how closely should 
the points of observation be spaced, and is it better to observe some quantity 



many points, taking the risk that T x is not sufficiently long to 





13 


BERNOUILLPS EQUATION 


eliminate the effect of irregularities typified by V — tv, or to observe the velocity 
at fewer points, and take every possible means by repetition of observations 
to secure that the mean local velocity is determined ? The alternative is 
fundamental in all hydraulic work, unless the discharge is obtained by weir or 
volumetric methods. 

A general answer cannot be given. My own experience is mainly confined 
to the gauging of large quantities of water (50 cusecs and over), flowing in 
earthen channels. In such cases irregularities in motion and differences 
between the observed velocities at consecutive points are both very pronounced. 
A mathematical study of the observations, conducted by Pearson’s curve¬ 
fitting methods, has led me to believe that a close spacing of the points at 
which the velocities are observed is preferable to a repetition of observations at 
a few selected points. 

The question, however, deserves careful study, especially when a station for 
systematic gauging observations is being selected. It is probable that in some 
cases irregularities are more marked than differences, and then fewer points 
and repeated observations at these points should produce better results. 

Hydraulic Calculations. —The equation usually employed by hydraulic 
engineers is that known as Bernouilli’s. Using feet, the weight of a cube foot of 
water, and seconds, as our foundamental units, this equation in the case of water 
can be written as follows : 

v 2 

hA-zA -— a constant 

2 % 

where v is the velocity'in feet per second, 2g= 64*4 approximately, but 
varies with the latitude and height above sea level, and h is the pressure 

at any point measured in feet of water, i.e. 

7 v . lbs* per square foot 

/z = lbs. per square inch x 2*34= — 


when the weight of water is taken as 62*5 lbs. per cube foot, and z is the height 
in feet of the point considered above a fixed plane. 

This equation can be proved mathematically for a perfect fluid moving 
under gravity. The proof extends to fluid motion, whether vortices exist or 
not, provided that the motion is steady, i.e. is the same at a fixed point at all 
instants of time, and that points in the same stream line alone are considered. 
It is somewhat doubtful whether a rigid proof can be given for such motion as 
usually takes place in cases considered in practical hydraulics. This doubt, 
however, is not a matter of great practical importance, as the form actually em¬ 
ployed in hydraulics is: 

/ l j rZ J r ' l> -—plosses by friction, etc.— a constant. 

These “ losses by friction,” etc. are calculated from the results of actual 
experiments under the assumption that Bernouilli’s equation in the above 

corrected form holds during the motion. 

The general form of the equation can consequently be regarded as valid, 

and we may proceed to investigate its practical applications. 

Losses by Friction, etc.—The friction losses {i.e. those which occur when 
the velocity remains unchanged both in magnitude and direction) are usually 
assumed to be proportional to v\ although there is ample experimental 
evidence to show that this assumption is only true under exceptional cir¬ 
cumstances The correct law is that the losses by friction (excluding those 



CONTROL OF WATER 


14 

in tubes where v is less than the critical value) vary as vn, where n langes 
from about VJ to 2 ‘i according to the smoothness of the sides of the channel 
and its size, the lower values corresponding to small smooth channels, and 
the higher to rough channels, and probably also to large channels, whether 
smooth or rough. 

For losses by shock (i.e. more or less sudden changes in velocity, or in the 
direction of velocity) the evidence that the losses vary as v 2 is fai moie con¬ 
clusive ; although, in certain cases (usually concerned more with a change in the 
direction of the velocity than with a change in its magnitude), the divergence 
from the v 2 law is greater than the possible errors in the measurements. 

Practical Equation.—For practical convenience, however, it is usual to 
express the motion of water from one cross-section of the channel (defined by 
the suffix 1) to another cross-section lower down the channel (defined by the 
suffix 2) by an equation of the following form : 

^1+*1+7^. - (^2 +*2 + jgr) = (Cf+ C + Ci)~ 

where v is a velocity which is some fraction of v l or v 2 , and is determined by 
the geometrical form of the channel between the cross-sections denoted by 
suffixes 1 and 2. 

0 is a coefficient determining the loss by friction during the intermediate 
motion. 

Co is a coefficient determining the loss by obstructions, or alterations of 
cross-sections during the intermediate motion. 

Ci is a coefficient determining the loss caused by changes in the direction of 
the velocity during the intermediate motion. 

Now, these three coefficients depend upon the hydraulic character of the 
boundaries of the channel, and also upon such geometrical quantities as the 
length and hydraulic mean radius of the channel between 1 and 2, the angle of 
deflection and radius of the bends, and the magnitude and position of the 
various alterations in its cross-section. The most important question is : How 
closely do these losses follow the law of proportionality to v 2 ? Assuming that 
the channel is completely defined in its geometrical and physical condition, 
we have to investigate the variations in the values of which depend solely 
upon variations in the quantity of water passing along the channel. That is to 
say, the question becomes : How does each C vary as v or v x varies ? 

We find experimentally that Cf is usually a variable coefficient, depending 
on the magnitude of v x or v 2} and this portion of the question is fully discussed 
later under the headings Pipes and Open Channels (see pp. 422 and 469). 

Co is usually fairly constant compared with Cf and the available information 
is given under the heading Contractions and Enlargements (see p. 796). 

As regards Ch we have little definite information. The older experimenters 
considered it to be constant, but the bulk of later evidence tends to show that 
it varies quite as much as Cf and probably follows the same laws. 

Engineers are also accustomed to write : 

v 1 A 1 = vA = v 2 h 2 

where A x and A 2 are the areas of the cross-sections of the channel at the 
points 1 and 2, and A is any intermediate area, and v is the corresponding 
velocity, and to express v and v 2 in terms of v x by these relations. 

When such a substitution is made in the above equation we really assume 



MEAN ENERG Y 


!5 


that the sum of the kinetic energies (vis viva) of all the particles of water 
(which at a given instant are found in any cross-section) is equal to the energy 
of a quantity of water equal to that which passes through this cross-section 
in unit time, moving with a velocity equal to the mean velocity of the water 
across this cross-section. For example, if v+q, be the actual velocity 
occurring over a small element da of the area A of the cross-section, we 
assume that: wAw t =f{ v+v fda 

provided that, fq da — o, 


so that v is the mean velocity over the whole cross-section A. 

The discussion already given concerning the irregularities of velocity will 
suffice to show that if we consider the momentary values of the quantity v-\-q 
this assumption is untrue. If, however, v-\-q represents a mean local velocity, 
so that q represents the difference between the mean local velocity at the point 
considered and the mean velocity over the whole cross-section, the conditions 
are not only more favourable, but also more closely represent the quantities we 
actually observe in practice. We have : 

f(v+q) 3 da = vAv 2 + yvfq 2 da -f fq 3 da. 

Now, vfq 2 da is always positive, and fq 3 da may be either positive or negative. 

The matter has been experimentally investigated by Darcy and Bazin and 
others. The results are conflicting ; but, as a general rule, we may assume that 
f(v+q) 3 da = Av . v 2 (i a), where a is positive, and is usually not far removed 
from o'o6. For definiteness we may call a the coefficient of local distribution. 

We thus see that if v 1 and v 2 differ, the usual assumption may introduce an 
error in the values deduced for the losses equal to about 6 per cent, of the head 
corresponding to the change in the mean velocity. 

In the experiments above referred to the flow was not markedly obstructed, 
and the losses corresponding to the terms'; £ 0 v 2 , and Civ 2 were small. When 
these terms are large, the values of a are quite unknown, but it is possible that 
not only does a markedly exceed o’o6, but that it varies from cross-section to 
cross-section. 

The errors thus shown to be possible are not usually allowed for, and since 
measurements are usually taken at sections where v l and v 2 are fairly equal, 
they may not be very great unless the coefficient a varies considerably. Bazin’s 
values of a are tabulated on page 481. 

Summing up the available evidence, it would appear that the present 
methods of calculating frictional and other losses are liable to certain errors due 
to the assumption that the energy corresponding to the mean velocity properly 
represents the whole velocity energy of the fluid. These errors may amount 
to 6 per cent, (possibly more) of the velocity head, and wherever the nature of 
the motion is considerably changed errors of this character may be suspected. 

For instance, let us consider the heads lost at curves, bends, or elbows in 
pipes. The present experimental values are widely divergent, although each 
experimenter’s results agree very fairly well i?iter se, and the laws may be 
considered as entirely unknown. Actual errors (in the ordinary sense) in experi¬ 
menting may be considered as unlikely, but no experimenter has as yet (with a 
few exceptions due to Saph and Schrodei, Trans. Am. Soc. oJ~ C.E ., 'vol. xlvii. 
p. 301) investigated the distribution of the velocities over the cross-section of 
the pipe before and after passing the bend. The losses of head observed aie 


j 6 CONTROL OF WATER 


(in pipes of large diameter, at any rate) only small fractionsfof the velocity 
head. We may conclude that what has been observed is not so much the 
curve resistance typified by as a combination of this and the terms : 


«i— 
2F 


«2 


^2 


where owing to the disturbance produced by the curve, rq and a 2 are probably 
not the same, so that even if i)y — v 2 we have a possible error of: 


*/ 2 


2P- 


r( a i~ a 2)- 


This quantity may be either positive or negative, and there is evidence to 

show that it may amount to as much as 0-15 J, although it is believed that so 

large a value can only be obtained when special care is taken to produce con¬ 
ditions favouring irregular motion. 

In some cases experimenters have endeavoured to correct for this source of 
error by observing the loss of head at four points, two above the curve and 
two below, and considered Cci as correctly determined when, the points being 
equidistant, it was found that : 

Loss from 1 to 2 = Loss from 3 to 4. 


And then assumed—- 

£rz/ 2 = Loss from 2 to 3 —Loss from 1 to 2 (or 3 to 4). 


It will, however, be obvious that all that is really proved is that the value 
of the quantity cq —a 2 above the curve is equal to that of the similar quantity 
a 3 — a 4 below the curve, and that a 3 does not differ so markedly from cq as to 
materially influence the friction losses in the straight lengths of pipe. These 
facts do not at all prove that a 2 and a 3 are equal, or that the disturbances 
produced by the curve have died out. The assumption that a 2 = a 3 is probably 
correct in small pipes, provided that the length 12, or 34, exceeds 100 diameters. 
In large pipes (say over 12 inches in diameter) we have no knowledge which 
enables us to say how great a length of straight pipe is required in order to wipe 
out the curve disturbances. The impression left on my mind is that, unless the 
character of the motion above and below the curve is fixed in some manner, 
errors of the character now discussed do occur, and, being constant, are not 
disclosed by mean square calculations. As a practical matter, where the 
observations are applied in order to calculate losses in pipes of the same size 
as those experimented on, the results are probably worthy of confidence. If we 
endeavour to extend the formulae thus obtained outside the limits of existing 
observations we are liable to very great errors, and I regard all calculations 
concerning curve losses in pipes 12 inches or more in diameter as waste of time 
and paper. 

The question is referred to under the heading of Backwater Calculations, 
and it may be stated that a comparison of observed and calculated backwater 
curves leads to similar results. The practical importance of the matter is best 
illustrated by a case which actually occurs on the Upper Swat Canal (Punjab). 
Here 3' 1 feet per second, v 2 — 14 feet per second, and the change occurs in 

2 _ rjj 2 

a length of 70 feet. - 2 1 • =2*89 feet, and all calculations regarding the 

o 

drop in the water surface required to produce this change in velocity are 





DISTRIBUTION OF VEIOCITIES 


i7 


plainly uncertain to about 0*06 x 2'89 feet = o'i8 foot. The question is compli¬ 
cated by the fact that occurs in an earth channel (Bazin’s y=r6 about), and 
v 2 in a masonry channel (Bazin’s 7 = 07 about). 

My final views on the question were arrived at after studying individual 
rod float velocity observations in similar channels, and I believe that the 
actual drop in the water surface, after all allowances for friction in the 
intermediate length have been made, will be found to be 3‘15+0*10 feet. The 
value calculated by the designer, after very careful investigation, is 3’40 feet. 
Since the various coefficients other than a x and a 2 are very accurately 
known, and were used in both calculations, the difference in opinion 
regarding what is theoretically a fairly simple case admirably illustrates the 
real uncertainties affecting the work. The rod float observations were 
only employed since current meter (point) velocity observations were not 
available. 

General Laws of Resistance to the Motion of Fluids.— 
The object of the present section is to discuss the changes in the 
mathematical laws expressing the physical characteristics of the resist¬ 
ance to fluid motion that are produced by variations in the velocity of the 
fluid. 

The matter has only been fully investigated in connection with the motion 
of fluids in pipes, and the distinction between the laws of motion in a capillary 
tube and those holding for a pipe of ordinary dimensions are discussed 
on page 20. 

It will, however, be shown that there are well-marked indications that 
similar changes in the mathematical expression of the laws of resistance occur 
in other cases of fluid motion. 

It may at once be stated that the whole question is at present of but little 
practical importance, and were it not for the fact that engineers are accustomed 
to apply the results of small scale laboratory experiments to the calculation of 
the dimensions of large works it could be entirely ignored. 

It is, nevertheless, necessary to discuss the general laws, and to make 
allowance for the results thus obtained when small scale laboratory experiments 
(especially those relating to bends and constrictions in pipes) are used, in order 
to deduce rules for practical calculations. 

It is also probable that no radical advance in the theory or practice of 
experimental hydraulics will be made until similar questions concerning the 
motion of water in open channels, and over sharp edges (as in weirs or orifices), 
are thoroughly investigated. 

Broadly speaking, the whole matter is included in the question of stream 
line and turbulent motion. The ordinary methods of mathematical hydro¬ 
dynamics lead to solutions of problems regarding the movement of fluids which 
are characterised by the existence of stream lines. Physically regarded, in a 
steady stream line motion, if at a time /, we find a particle of water at a point 
P, and later on at a time /+T, we find this same particle at Q, we can rest 
assured that the particle now at 1 , will ariive at Q, at a time /4-2T. The 
water particles, in fact, move through the channel in regular order, just as 
soldiers in files, where no man quits the ranks. In turbulent motion, on the 
other hand, this regularity does not exist, and the motion may be compared to 
that of a disorderly crowd, where there are no regular files and where each 
man leaves his position as he chooses. 


2 


18 CONTROL OF WATER 

In a straight circular pipe of uniform section the stream line theory shows 
that the particles of water move with velocities which entirely depend upon 
their distance from the sides of the pipe, and are parallel to the axis of the 
pipe. Pursuing the simile of a regiment, the files close to the sides of the pipe 
move slowly and the central files very much more rapidly, the graduation 
being quite regular and represented by the equation : 

Consequently, V 0 , the maximum (central) velocity, is twice the mean 
velocity, it being assumed that there is no “ slip ” at the walls of the pipe, i.e. 



Sketch No. 3. —Relations between the Mean Local Velocities over the 

Cross-sections of Pipe. 


u a — o, where a , is the radius of the pipe and v r , is the velocity of a particle of 
water at a distance r, from the axis of the pipe (Sketch No. 3). 

Now, in turbulent motion the facts are quite different. The velocities are 
no doubt greater near the centre of a pipe than close to its sides, but a particle 
which at one moment is near the walls, an instant later is close to the axis, and 
vice versa. 

Each individual particle therefore moves not only parallel to the axis of the 
pipe, but can also move in a plane perpendicular to the axis. These minor 
velocities perpendicular to the axis are entirely accidental in their nature, cannot 
be calculated, and have not as yet been studied observationally with any degree 
of accuracy. In consequence, the following discussion is solely devoted to a 
consideration of the velocities parallel to the axis of the pipe. 






























CRITICAL VELOCITIES 


19 


The law of the velocities parallel to the axis of the pipe is approximately 
(see Bazin’s discussion, Trans. A?n. Soc. of C.E., vol. 47, p. 258, or Mem. 
Sav. Etrangers, tome 32. p. 258) : 


V 0 -v r = aV l 1 -^/I-/ 3 Q } 


where V 0 , is the central and maximum velocity, V, the mean velocity, 
and v r , the^velocity at a distance r, from the centre, in a pipe of radius 

a, whilst a and /3 are constants, where a is about for English measure, and 

where C is the constant in the equation V = C — and /3 is 0*95. 

When the velocities are mean local velocities, defined as on page 12, the 
agreement with observation is very close, as is shown by Bazin’s diagram 
(Sketch No. 3). But it must always be realised that each particle in addition 
possesses irregular and constantly changing velocities, in all directions in space, 
which can be considered as super-imposed on v r , as given by the above equation. 

Still following out the military analogy, it is plain that if we clothe one file 
of soldiers in a different uniform, this file will preserve its individuality, and 
will persist as a coloured^ streak ; while if we colour each individual of the 
crowd that passes a fixed point, the coloured units will rapidly become mixed 
up with the remainder of the crowd, and will finally be equally distributed 
throughout the mass. 

The actual conditions determining whether the motion of water in a pipe is 
stream line or turbulent were first systematically investigated by Osborne 
Reynolds {Phil. Trans., 1883), who introduced colouring matter into water by 
means of a fine tube. 

I give Reynolds’ results with the remark that they cannot be considered as 
exact, since Coker {Proc. Roy. Soc., vol. 174) and other experimenters have 
found that his figures are not absolutely accurate. The causes of these 
divergencies are obscure, but can probably be explained by the previous history 
of the motion of the water. 

Reynolds found as follows : 

(i) If the mean velocity of water does not exceed 

•0388P 


Vc = 


D 


where D, is the diameter of the pipe in feet, and 


P = 


(Poisseuille’s ratio) 


I + 'O337T + '000221T 2 

where T, is the temperature of the water in degrees Centigrade, the move¬ 
ment is always stream line in character ; and even if eddies (i.e. turbulent 
motion) are artificially produced, they rapidly disappear, and the motion again 
becomes stream line. The motion being regular and ordered, the resistance is 

h 

but small, and varies as v , i.e. v = k x ^ where h is the head in feet lost in a pipe 
l feet long. 

The value of k x may be expressed by 

r cd 1 

“i—'v' . 


[Inches] 






/ 


CONTROL OF WATER 


where Reynolds gives ^r=361, when d is in inches and P is the temperature 
correction given above. 

Hazen (Trans. Am. Soc. of C.E., vol. 51, p. 317) uses the formula : 

,(/+io) 


k x — c x d 2 - 


60 


Af 
3 *1 


[Inches] 

Hazen also 


where t is in degrees Fahr. ; so that, roughly, c 1 = cx 1*339, or 

obtains for brass pipes : 

with d=o’ioy to 0*631 inch, ^ = 462 to 584, or ^=347 to 438 

Average, 495 Average, 372 

and for another series of Hazen’s, with d= 0*11 inch, average ^ = 450, or ^=338. 

It may incidentally be remarked that if we apply the mean value in Hazen’s 
formula for percolation through sand (p. 25) we find that the effective size of 
the grains of a layer of sand is about 3*0 times the mean diameter of the 
capillary passages through the layer, assuming that their length is equal to the 
thickness of the sand. 

(ii) Above this first critical velocity we have a transition stage w'here 
stream line motion can exist, but if turbulent motion is artificially produced it 
may continue. 

Thus, in any given case, the occurrence of streahr line, or turbulent motion, 
is a more or less accidental matter. The resistance is therefore also fortuitous, 
and no rule can be given. 

The transition stage ends when : 


V d " 


feet per second. D being expressed in feet. 


(iii) Above this velocity the motion is always turbulent. (Although Coker, 
nt supra , has procured stream line motion at velocities 50 per cent, above 
those given by Reynolds’ formula.) 

All velocities usually occurring in practical engineering fall into this class, 
and we have : 

i = kv- 
1 / 

where n lies between 1*70 and 2*10. 

The motion being irregular and disorderly, the resistance is usually in¬ 
creased, and, as Unwin (Hydraulics, p. 39) states : 


“Take a pipe of 12 inches diameter, with a virtual slope of 1 in 1000. If in 
such a pipe non-sinuous (i.e. stream line) motion were possible, the velocity 
would be 72 feet per second. But the actual velocity, the motion being 
turbulent, is only if foot per second.” 


Actual values of the critical velocities at o degrees Cent, are as follows : 


Diameter of Pipe 

\ 

0*0417 

1 

0*0833 

0*125 

2 inches. 

0*1667 feet. 

First critical vel- 





ocity, v c . . 

Second critical 

0*928 

0*465 

0*310 

0*232 feet per second. 

velocity, v d . 

5 ‘ 9 ° 

2 ‘95 

r 97 

r 47 


1 
















CRITICAL VELOCITIES 


21 


Sketch No. 4, a logarithmic plot of /;://, and v, taken from Reynolds’ experi¬ 
ments on a lead pipe o’242 inch in diameter, shows the conditions. I have 
added v c , and va, as given by equations No. (i), in order to show the theoretical 
turning-points more closely. 



in 

<D 


U 

> 

I 

o 


O 

ID 


)-> 

ciS 

ID 

G 

T3 

G 

a 

£ 

'aj 

, a 

in 

ID 


o 

o 

V < 

<v 

> 

1 —I 

ciS 

<D 

CD 

£ 

ciS 

G 

• 

T 3 

CIS 

ID 


1/3 

ID 

C/3 

03 

O 


o 

52; 

K 

O 

w 

W 

C/i 


As already stated, for practical calculations of pipe sizes, motion of class (iii) 
alone is of importance. If, however, we consider such small scale experiments 
as Fliegner’s (Civil IngSnieur , 1875, p. 98) on constrictions in pipes, we find 
in many cases that the velocities at some point of the pipe fall below v c or Va- 









































22 CONTROL OF WATER 

Such experiments should be rejected, as they do not fulfil the conditions 
existing in the larger scale examples to which engineers usually wish to apply 
the results obtained. It is perhaps permissible to state that, so far as can be 
gathered from a study of such cases, we may assume that Cokers value 

for v ( i {i.e. approximately —) is more correct than Reynolds. This 

may be considered as merely indicating that Coker’s precautions for securing 
a regular flow were of a more usual type than those of Reynolds. 

The difference probably arises from the fact that Reynolds worked with 
pipes with bell-mouthed inlets and without obstructions ; whereas, m the case 
of experiments by Coker and others, the water passed over sharp edges or 

through constrictions. 

I believe that the above is a complete summing up of our present know¬ 
ledge on the matter, in so far as it can be reduced to mathematical 

calculation. 

It seems advisable to state that Thrupp {Trans. Am. Soc. of C.E ., 
vol. 47. p. 234) and Bilton {Proc. of Victorian Soc. of C.E ., 1908) both 
appear to consider that a critical velocity exists for pipes more than ii inch 
in diameter, which is represented by : 

v = o' 14 foot per second for a 12-inch pipe 
rising to v—o’jo foot per second for a 30*inch pipe. But the evidence 

seems to me very doubtful. 

It will, however, be plain that the condition that the motion of water during 
the whole path traversed in any experiment should always remain in one of 
the three classes, or the effect of the change be allowed for, should be borne in 
mind by all experimenters who wish to be more than empiricists. 

Now, as a matter of visual observation, the movement of water when 
passing close to a sharp edge, as in an orifice or standard weir, is far less 
turbulent than in the approach channel, and it may be inferred that this fact 
explains certain peculiarities in weir observations. 

For example, Bazin was unable to determine any satisfactory discharge 
coefficients for heads less than 0*16 or 0*15 foot, and it is fairly well known 
that a sudden change in the coefficients occurs as the head passes from 0*35 to 
o*45 foot. 

I am therefore inclined to believe that the effect of a sharp edge is to 
temporarily cause the motion to be similar to Class (i), or stream line at a 
distance not exceeding o'15 foot, and similar to Class (ii) for an additional 
distance comparable to 0*40 foot. So also we must, for the present, regard all 
observations where the whole body of water is passed through sieves (to still 
oscillations) as not necessarily exactly comparable with those where this 
precaution is omitted. 

Similarly, we may expect to find a marked change in the coefficient of 
discharge of sharp-edged orifices as their size passes through a value 
approximately equal to 0*30 foot ( = 2x0*15), and this is known to be fairly 
correct. 

It may therefore be hoped that, as knowledge accumulates, we shall be 
able to distinguish between other hydraulic observations in a manner similar 
to that in which Reynolds has (approximately at any rate) classified pipe 
observations. 

Fortunately, the question is more of theoretical than practical interest, 



CAPILLAR Y ELE VA TION 


23 


since the differences in cases other than pipes appear to be of the order of 
2 to 3 per cent. only. In this connection it seems advisable to mention 
Thrupp’s pioneer work on open channels. Here, according to Thrupp, the 
surface slope, and not the dimensions of the channel, is of importance 
(■ P.I.C.E ., vol. 171, p. 346). Speaking from the point of view of pure theory, 
this is somewhat improbable, but there is no doubt that some change in the 
law of resistance occurs at low velocities (see p. 477). 

Similarly, consideration of these principles makes the otherwise peculiar 
observations of Bazin on depressed and adhering nappes somewhat less 
puzzling. Here it would appear that the form of the nappe is far more 
dependent upon the pressure observed as existing on the sill of the weir than 
on the actual head over the sill, i.e. on a factor observed at a point where 
presumably the change in the class of motion has occurred (see p. 124). 
Hamilton Smith’s observations on the form of a jet as influenced by the 
irregularity of supply, i.e. the turbulence of the water before it reaches the jet 
( Hydraulics , p. 51), are probably explained by similar considerations. 

The foregoing may possibly raise visions of a hydraulic engineer loaded 
with colour tubes and pressure gauges, which is as alien to the present 
generation as the current meter was to the last. But this cannot be avoided, 
and if we realise that the ultimate effect is the abolition of tables of co¬ 
efficients, and personal judgment, combined with economy in construction, 
the change may be regarded not only with equanimity, but even with favour. 

Capillary Motion or Percolation.—The general laws of the motion of water 
in capillary tubes have already been discussed, since capillary motion is merely 
motion at velocities less than Osborne Reynolds’ first critical velocity. The 
general subject of capillary tubes has a certain importance in observational 
hydraulics, since a pressure gauge may be rendered erroneous by capillary 
elevation or depression. 

CORRECTION FOR CAPILLARY ELEVATION IN A MERCURY 

GLASS PRESSURE GAUGE. 


Diameter of Tube. 

Add. 

0*08 inch. 
o’i6 „ 

0*32 „ 

0-40 „ 

0*18 inch. 
o - o8 „ 

0*027 „ 

0*016 „ 


In practical engineering, however, the question of motion in capillary tubes 
arises only in the case of percolation through sand or gravel. 







24 


CONTROL OF WATER 


Formulae. 

Poisseuille's Ratio. 

--L—-— where T, is in degrees Cent. 

i +o , c> 337T -f~o’ooo22 iT 2 

Or, if t is expressed in degrees Fahr., 

/ =I=i+o-oi87(/-32)+o*oooo682(/-32) 2 = o-4736 + o > oi43/+o-oooo682/ 2 

. / 4 -io 

Hazen’s approximate form f— ^ - 


First, v c 


Critical Velocities . 


o - o388P 


Second, v d = 


o*2458P 

~AF~ 


Resistance Formulae for Velocities less than v c . 


52ioo/'D 2 
v— 360 to 370 
= 480 to 490 


h 

j ; D, in feet, and f— 1 at 32 degrees Fahr. 

70 7 

— - ; d, in inches. P = 1 at 32 degrees Fahr. or o degree Cent. 

JL t 


(/+ io)d 2 h ' 


60 


; d, in inches, at t, degrees Fahr. 


Hazed s Values for Sand. 

v = 2\od~ ~ f or sand of an effective size equal to d, hundredths of an 

l 60 

inch, where 77, is the effective velocity (see p. 25) in feet per day. 
v^yiZod 11 ^ if d, is in millimetres. 

Percolation of Water through Sand or Gravel. —The passage of water 
through a layer of sand or fine gravel is effected by capillary flow through the 
small irregular tubes that are formed by the void spaces in the sand. It is 
therefore necessary to consider the laws of capillary flow. 

The capillary motion of water is essentially the motion of water through 
pipes at velocities, which are less than the critical velocity. 

Let be the pressure in feet of water producing such a flow through a 
pipe / l5 feet long, and d 1 , feet in diameter. The velocity of the water in feet 
per second is given by : 

v 1 — 52,100 fdf y feet per second. 

*1 

where f= 1 +o , o2(/— 32)+0*00007 (l~ 3 2 ) 2 
where t, is the temperature in degrees Fahr. ; v ly must not exceed 


°"°39 r 
—rj feet 
fd\ 

per second, or the flow may cease to be capillary (see p. 20). 

Now, in sand or gravel the length l ly cannot be measured, but, on the 
average, it is a certain multiple of /, the length of the path of percolation 
through the sand. Similarly, d lt cannot be measured, but bears, on the 
average, a certain ratio to the mean diameter of the grains of sand. Con¬ 
sequently, the expression of the quantities contained in the above formula in 
terms of quantities which are easily measurable, can only be effected by 









VELOCITY OF PERCOLATION 


2 5 


/ d 

certain assumptions concerning the average values of the ratios 7 -,and -% , where 

n «i 

/, and d, represent the length of the path through which percolation occurs, 
and d, represents some measurable quantity (say, the mean diameter of the 
sand grains), which is proportional to d the average diameter of the inter¬ 
stitial passages through the sand. 

The percolation properties of sand or gravel are best defined by the 
quantities known as the effective size and the uniformity coefficient. The 
sand can be separated into grades by sifting through sieves, and if the sizes of 
the holes in the successive sieves are sufficiently close together the diameters 
of all the particles in a grade will be approximately equal. 

The effective size is defined as the mean diameter of a grain such that 
io per cent, (by weight) of the sand is composed of smaller particles, and 90 per 
cent, of larger particles. 

The uniformity coefficient is the ratio which the mean diameter of a grain 
such that 60 per cent, (by weight) of the sand is composed of smaller particles 
bears to the effective size of the sand (see Sketch No. 264, p. 962). 

It is plain that the effective size is an approximate measure of the mean 
size of the smaller grains of the sand, and that the uniformity coefficient is an 
indication of the ratio between the sizes of the larger and smaller particles of 
the sand. 

It is also plain that these two quantities cannot be regarded as rigidly 
specifying the properties of the sand, and that their practical importance is 
solely due to the fact that sands and gravels as they occur in Nature are 
approximately similar substances, so that a coarse sand may be regarded 
either as a magnified small sand, or as a fine gravel on a diminished scale. 

Subject to these remarks, Hazen (Filtration of Water) has found experi¬ 
mentally that the effective velocity of percolation is given by : 


z/=C d 2 


(t+ 10) Jt 

~6o~7 


where z/, is the equivalent velocity at which the water passes through the sand, 
i.e. v, is not the velocity of the water in the pores of the sand (which is 
denoted by zq), but is the velocity of a solid column of water of the same area 
as that through which the percolation occurs which would deliver the quantity 
of water which actually percolates through the sand. 

/, is the length of the path along which the percolation occurs, and is the 
head producing percolation, measured in feet. 
d, is the effective size of the sand. 

The expression is an approximate representation of the factor denoted 

by f a theoretically more accurate expression for which has already been given 
(see p. 24). 

C, is a constant depending on the units employed. 

If v , is expressed in feet per 24 hours, and d in millimetres, 0 = 3280. 

If d, be expressed in hundredths of an inch, C = 2io. 

v, could also be expressed in feet per second, but C would then become an 
inconveniently small fraction. 

The equation is subject to exceptions. For example, if p be the percentage 

of voids in the sand, it is plain that v= ioo^~, where zq depends on d and - r Now, 

P L 




26 


CONTROL OF WATER 


on page 970 figures are given which show that the form of the sand grains may 
cause ft to vary from 25*6 to 34*6. Thus we may infer that the general form of 
the grains alone may cause v to vary as much as 20 per cent, eithei way. 
In practice, however, the equation is found to apply with fair accuracy to sands 
occurring in Nature, in which d lies between o’lomm. (0*004 inch) and 3 00 mm. 
(0*12 inch), and with a uniformity coefficient less than 5* The equation also 
applies with equal accuracy in gravels up to 5 or 7 nim. (0*20 to 0*28 inch) 

effective size, so long as t/ 1 = ioo^ is not too large. In this last case the limit 

at which the equation ceases to hold is fairly accurately ascertained by estim¬ 


ating the critical velocity, v c , in a tube of a diameter equal to 


4 d. 
7 


(See p. 19.) 


In most cases we can take /= 50 degrees, and then the bracketed expression 
becomes unity. 

We can also express this formula in terms of d m , the mean diameter of the 
sand grains, with a very small degree of error, by changing the value of C in 

the ratio (—-) in ordinary sand. Since d m — d\! 3, we have C m = —, and actual 
\ Cirri 3 


values as given by Seelheim, Hazen, and Krober, are as follows : 


dm, in millimetres : 


0*16 0*23 0*28 0*48 0*54 o*68 0*70 

C m , in feet per 24 hours : 

0*90 

i*35 

2*1 

1060 1047 1016 1076 1205 1063 1158 

so that the above relation is quite close to the truth. 

1395 

1030 

II65 


All these experiments were conducted on clean sand, such as is used in 
filters. The following results show the influence of a small quantity of clayey or 
dirty matter in diminishing percolation ( Trans. Am. Soc. of C.E., vol/48, p. 302). 


The experiments being recorded in terms of the effective size, we get: 


d in 
Milli¬ 
metres. 

Value of v in Feet per 
Day as ascertained ex¬ 
perimentally when 

Value for v for Sand of 
same effective Size 
according to Hazen’s 
Rule. 

Percentage of Flow 
with dirty instead of 
clean Sand. 

°*55 

758 

99 1 

76 

0*46 

*54 

695 

22 

°'45 

3° 

663 

5 

°'45 

92 

663 

14 

0*40 


525 

25 

0*38 

49 

472 

10 

o’37 

3 6 

449 

8 


Although the information is incomplete, it seems as well to record the values 


of C d 2 , or Qmd m 2 , obtained when - = 0*036, in the alluvial deposits at: 


Lyons. Strassburg. Gladbach. Augsburg. Vienna. Bucharest. 

545 I 5 11 701 n 8 o 273 403 













VELOCITY OF PERCOLATION 


27 


The value of d , not being given, C cannot be calculated. 

These values are obtained on strata of a markedly water-bearing character, 
and should consequently be considered as maxima, and as unlikely to occur in 
strata suitable for dam foundations. 

The Hazen formula has been very severely criticised of late years by many 
experimenters, especially by Baldwin Wiseman ( P.LC.E ., vol. 181, p. 29). 
As I have based many designs on the results of the formula, I consider that the 
following remarks are not out of place. 

The correction for temperature is probably somewhat faulty, and the 
Poisseuille ratio used in investigations of critical velocities in pipes is a more 
accurate method of allowing for the influence of temperature. I consider that 
Hazen’s results are approximately correct for a range of 50 to 70 degrees Fahr. 

Formula of the type suggested by Slichter or Baldwin Wiseman are 
certainly more accurate in the case of small-scale experiments. Their weak 
point, however, is that the work necessary in order to ascertain the coefficients 
is more laborious than a series of determinations of the actual flow under vary¬ 
ing heads. 

In large scale experiments the porosity, surface area per unit volume, and 
other qualities determined by Baldwin Wiseman vary from point to point. In 
view of these variations any formula more accurate than that given by Hazen 
is unnecessary. The following is a table of the velocities in feet per 24 hours 
when t= 50 degrees Fahr. : 


EFFECTIVE SIZE OF THE SAND GRAINS IN MILLIMETRES. 


h 

l 

0*10 

0*20 

0*30 

°’35 

0*40 

0*50 

I -OO 

3-00 

0*001 

0*033 

0*13 

0*30 

0*41 

0*524 

0*82 

3*28 

29*5 

O'O °5 

0*164 

o*66 

1 *48 

2*06 

2*62 

4*10 

16*40 

147*6 

O'OIO 

0*328 

J' 3 1 

2*96 

4*12 

5‘ 2 4 

8*2 

32*8 

295*0 

0*050 

1*64 

6-56 

14*8 

20*6 

26*2 

41*0 

164*0 

• • • 

0*100 

3*28 

I 3 ‘ I 

2 9’5 

41*2 

5 2 '5 

82*0 

328*0 

• • • 

1*000 

32*80 

13 1 ' 2 

2 95 * 2 

411*8 

5 2 4*8 

820*0 

• • • 

• • • 


Hazen states that a similar law holds for the motion of water in beds of 
gravel (see p. 525). There is a very fair amount of experimental evidence (sup¬ 
ported by experiments on flow in pipes) which shows that the law is really more 
complex, and that 

-j=av J rbv <1 

better represents the results. Fortunately, such large grained beds are not 
likely to form a dam foundation, so that the theory (which is obviously very 
complex) need not be investigated. 

Additional information concerning this subject will be found under the heads 
of Wells (see p. 258) and Percolation under a Dam (see p. 293). 

h 

In these cases the formula employed is 

so that K = CP 

60 
























2 8 CONTROL OF WATER 

A table of values of K, when /= 50° Fahr., in terms of the number of meshes 
per lineal inch of a sieve that retains 10 per cent, by weight of the sand (i.e. Cd 2 
expressed in terms of the mesh of the sieve), is given on page 269. 

Curve Resistance. —The experiments of Saph and Schroder (Tra?is. Am. 
Soc. of C.E., vol. 47, p. 301), and Brightmore (. P.I.C.E ., vol. 169, p. 31 S), 
show very clearly that curve resistance is caused by a redistribution of the 

velocities over the cross-section of the pipe. 

The maximum velocity in the case of motion in a straight pipe is found at, 
or close to, the centre of the pipe. Whereas, when the water has passed 
through a sufficient length of curved pipe, the maximum velocity is found close 
to (about fths of the radius away from) the concave side of the pipe. 

It may be stated in general terms that the velocities in a straight pipe tend 
to be uniform over the cross-section, but owing to the resistance of the sides of 


Velocity Contour L ines 

F/hures oive Velocity in ft/sec. 

7 Concave 



SFranoJit Pipe 



Convex 

Curved Pipe 2"Did. 

Saph & Schroder. 


Sketch No. 5.— Distribution of Velocities in Straight and Curved Pipes. 

the pipe the actual distribution is as already discussed. Likewise, in a curved 
pipe, the velocities tend to arrange themselves as in a free vortex, where 7/, 
being the velocity at a distance x, from the centre of the circle formed by the 
curve of the pipe, vx = constant. Owing to the influence of the sides of the 
pipe the final distribution is of the form shown in Sketch No. 5 (which is an 
example given by Saph and Schroder). 

Experimentally it would appear that the change from the form of motion 
appropriate to straight pipes to that occurring in curved pipes does not entail 
any marked loss of head. The head is lost in a gradual wiping out of the curve 
distribution of velocities by the friction of the sides of the straight portion of the 
pipe which succeeds the curve. 

The head lost at a curve is therefore in a certain sense a species of head 
lost by skin friction, and is subject to the same laws. Consequently, it cannot 














CURVE RESISTANCE 


29 


be considered as being accurately proportional to v 2 . This has been amply 
proved by Alexander ( P.I.C.E ., vol. 159, p. 341), who found that for smooth 

h 

wooden tubes, ij inch in diameter, in which the friction loss was -^—kv 1 ' 777 

the resistance of all curves was given by 

hcl = kl v ^ 77 

For a knee (z.e. a curve of radius = radius of the pipe), and an elbow where 
the loss is mostly due to shock, Alexander found that: 

h d =k^v l 

Now, it will be evident that the problem is complicated. In the first place, 
the length of the curve must be considered, since it determines the amount of 
redistribution of velocities that takes place. 



Secondly, the length of straight pipe below the curve must be sufficient to 
eliminate this redistribution. 

Thus if / be the length of the curve which is sufficient to entirely effect the 
redistribution of velocities, and / 2 , be the length of straight pipe in which this 
distribution is wiped out, we see that: 

(i) All curves of a length greater than /, produce the same curve resistance. 

(ii) If any other curves or obstructions occur before the water has traversed 
a length / 2 , downstream of the end of the curve, another redistribution of 
velocities takes place, and the observed resistance is then affected by this 
factor, and is therefore not completely determined by the circumstances of the 
original curve. 

Sketch No. 6 shows Brightmore’s and Davis’ observations on the loss of head 





















































30 


CONTROL OF WATER 


in curves of 90 degrees, in pipes, 3, 4, and 6 inches in diameter. They are 
interesting as showing that the bend with least resistance has a radius of about 
four times the diameter of the pipe. This fact is confirmed by the experiments 
of Schoder and Davis {Trans. Am. Soc. of C.E ., vol. 62, p. 67) on pipes 6 
and 2^ inches in diameter. 

A study of Schroder’s paper will show the extreme complexity of the 
question. 

I consider that the whole subject is useless from a practical point of view. 

For bends of 90 degrees with radii such as are found in practical work, the 


v £ 


loss of head caused by the bend rarely, if ever, exceeds ^ In pipes of 

diameters greater than 6 inches this figure is probably never reached. 

Now, in ordinary motion the loss of head by skin friction in a length of pipe 

iT 

equal to the diameter of the pipe is approximately equal to 3^ —, (C is assumed 

as 100). Thus, at the worst, a bend produces a loss equal to that caused by a 
length equal to 13 diameters of the pipe. This loss is not fully experienced 
(i.e. the distortion of the velocities is not fully wiped out), even in a smooth tube 
2 inches in diameter, until more than 120 diameters of straight pipe have 
succeeded the curve. 

In larger pipes we may assume that the requisite number of diameters is 
certainly not less than in the case of smaller ones. Thus at the most the curve 
loss amounts to an increase of 10 per cent, in the total friction of the whole 
length of pipe over which it is distributed, and it is probably a far smaller 
fraction. 

Hence, we may reason as follows : 

If the curves in a line of pipes form a large fraction of its total length, the 
full loss of head caused by each curve is not experienced. If the curves form 
so small a fraction of the total length that the full loss of head caused by each 
curve is experienced, the loss of head due to the curves constitutes so small a 
fraction of the total loss that the usual allowances made for uncertainties as to 
the exact value of skin friction will amply cover the extra loss which is 
occasioned by curves and bends. 

Schroder {ut supra , vol. 62, p. 89) measured the resistance of an iron pipe 
8 inches in diameter, and found that the loss of head per 1000 feet in four 
different straight lengths of the same pipe varied as much as 15 per cent., and 
that while the four portions containing curves gave more variable results, yet 
only one of these four lengths showed a loss of head per 1000 feet which ex¬ 
ceeded the mean loss per 1000 feet for the four straight portions. 

The only exception to the above rule is where a series of curves follow one 
another in reverse directions. A considerable loss of head may then occur in 
a short length of pipe, since the reverse curve very rapidly wipes out the 
distortion of the velocity which is produced by the preceding curve. Such 
arrangements of piping are not likely to occur in practice, except in the case of 
turbines, when the available installation space is small. Here, owing to the 
disturbances produced by the turbine, it is doubtful what influence the curves 
really have. A study of tests of turbines under such circumstances suggests 
that any curve action will be amply allowed for by assuming a loss of head 

1 V<1 

equal to o*io —• 

2 g 


CURVE RESISTANCE 


3 1 


For elbows in small pipes the formula h e = nj — is given by Brightmore 

{tit supra), and probably holds good for all sizes of pipes in which elbows 
occur in practice. 

The formulae of Weisbach (Die Experimental Hydraulik) for the head 
lost by curves, and angular deflections in pipes, have been frequently quoted. 
They refer to small pipes i j inch in diameter, and are as follows : 

(i) For an angular deflection with a deflection angle represented by cf) ; 

hd—id ", where £*=0*9457 sin 2 ^ + 2*o47 sin 4 ^ 

(ii) For a curve with radius equal to p, in a pipe with a diameter equal to d, 
we have : 

^=0-131+ 1-847 (I)” 

In a pipe of rectangular section, with a side parallel to p, represented by s, 
Weisbach finds that: 


£*=0*124 + 3*104 


d) 


3.5 


The circumstances under which these results were obtained are not known. 
If they were similar to those discussed when referring to Weisbach’s experi¬ 
ments on valves (p. 781) it is probable that these formulae are not applicable 
to the cases which are usually met with in practice. The results obtained when 
these formulae are applied in order to calculate the resistance of bends in large 
pipes, confirm this view. I therefore merely quote the formulae, and believe 
that they should only be applied to small pipes. 

Bellasis (. Engineering , May 26, I9ii)has recently discussed all recorded 

ii 

experiments on the loss of head at bends in pipes. Putting /i c i = Cd — he finds 

2 g, 

the following approximate values of £*: 



Diameter 
of Pipe in 
Inches 
= D. 


Value of tel when the Radius of Bend is 


Authority. 

Elbow 
Radius 
= 0 

2*5 D 

3'5 F> 

5 D 

7 D 

10 D 

14 D 

15D 

20 D 

Weisbach . 

• • • 

0*89 

0*14 

o*i 35 

0*13 





• • • 

Brightmore 

3 

1*17 

• • • 

0*29 

• • • 

0*39 

... 

o-i 5 

... 

• • • 

Schroder . 

6 


0*12 

0*1 1 

• • • 

0*14 

0*08 

0*25 

0*015 

0*14 

Williams, 

H ubbell 

12 

• • • 

• • • 

°'35 

• • • 

• • • 

• • • 

... 

... 

• • • 

andFenkell 

3 ° 

• • • 

• • • 

0*40 

• • • 

• • • 

• • * 

• • • 

• • • 

• • • 


Having attempted to prepare a similar table, I am of the opinion that these 
values are most unreliable. They form, however, useful indications of the order 
of magnitude of ha. 





























CHAPTER III 

GAUGING OF STREAMS AND RIVERS 


Measurement of Quantities of Water. 

Gravimetric or Volumetric Methods.—Accuracy. 

Stream Gauging Methods.—General description. 

Soundings.—Pole—Hemp cord—Wire—Rapid streams—Position of soundings. 

Irregularity of Motion in Water. —Practical rules for observations— Irregularities 
and permanent differences. 

Calibration. —Effect of irregularities—Methods of calibration—Effect of irregularities 
on current meters—Rod floats—Surface floats—Pitot tubes. 

Calculation of the Discharge. —Harlacher’s method—Method of mean velocities 
on verticals—Formulae. 

Current Meters. —Description—Types. 

Rating. —Equations—Correction for motion of water—Waves—Special equations for 
Price & Fteley meters. 

Accuracy of Results. 

Mean Velocity over a Vertical.—Spacing of observations—Vertical velocity curves— 
Twin floats—One point—Two point—Three point—Surface velocity method—Mid 
depth—Summation methods. 

Comparison with Weir Observations. 

Rod Floats. —Velocity of rod and mean velocity. 

Francis Correction Formula. —Comparison with weir observations. 

Accuracy of Observations. 

Types of Floats. —Correction formula in rough channels. 

Surface Floats.—Harlacher’s factor—Reduction factor. 

Special Gauging Methods. —Central vertical velocity—Maximum velocity— Surface 
velocity—Central surface velocity—Bottom velocity. 

Pitot Tubes. —Formula—Theory—Pressure orifice—Practical construction. 

Practical Details. —Differential gauge calibration—Fixed tubes in pipes— Pitot 
tubes for use in jets. 

Chemical Gauging. —Practical rules—Table of chemicals—Gulp method— Application 
to weirs. 

Practical Details. —Apparatus—Chemical methods. 

\ enturi Meters. —Approximate theory—\ alues of C—Corrected theory— Changes in 
coefficient—Practical limits—Gauge for meter. 

Measurement by Travelling Screen. 

Discharge Curves. —Relation between discharge and height of gauge— Theory of 
logarithmic plotting—Rising and falling stages—Influence of a tributary. 

Rivers with Shifting Beds. —Deeps and shallows—Sheaf of discharge curves— 
Practical methods—Application to studies of silt transport—Tavernier’s studies— 
United States method. 


The following chapter is devoted to a consideration of the methods usually 
employed in the measurement of large quantities of water. Measurement by 
weirs or orifices will be considered separately, as these methods are generally 
employed for smaller volumes, and are less subject to errors caused by irregu¬ 
larities in the motion of the water. 


32 



GA UGING OF STREAMS AND RIVERS 


33 


The standard method of determining a quantity of water is by actual 
measurement of its volume or weight. Very accurate results can be obtained 
by this method, and all other methods are directly or indirectly tested by a 
comparison with a volumetric or gravimetric measurement. 

The precautions required are enumerated in most text-books of physics. 

From the point of view of an engineer the volumetric method alone is of 
importance. The most accurate results are obtained by observing the time 
which the stream of water which it is desired to measure takes to fill the 
portion of the volume of a measured vessel contained between two horizontal 
planes. The precautions required to accurately determine the level of the 
water surface are discussed under the heading Weirs. 

My own experience leads me to believe that, under favourable circumstances, 
field observations can be secured which are subject to an error of 0*4 or 0*5 
per cent. only. The main source of error is the difficulty in accurately observing 
the rise of the water. The level of a moving surface of water can hardly be 
observed with an accuracy exceeding 0^005 foot. Thus, if the water rises 1 
foot during the observations, errors of 1 per cent, from this source alone are 
possible. Whereas, if the water rises 10 feet during the observation, this error 
is reduced to o'l per cent. The volumetric method, however, is usually only 
applicable to small quantities of water, and can rarely be employed in the field. 

Methods of Stream Gauging.—These are as follow : 

(i) By Current Meter. —This method is applicable to all streams, and is the 
only possible method in large rivers, with the doubtful exception of the chemical 
system. 

(ii) By Rod Floats. —This method is especially adapted to regular canals, 
and is only approximate if the bed of the stream is at all irregular. 

(iii) By Surface Floats. —This method is only approximate, but is very 
rapid ; and when it is occasionally, but systematically, checked by more 
accurate methods, is very useful. 

(iv) By Pitot Tubes. —This method is most applicable to pipes, or to very 
regular channels ; but it is useful in the case of streams which are either too 
rapid for current meters, or where the beds of the streams are too irregular in 
cross-section for rod floats. 

Special methods requiring more or less permanent installations of measuring 
apparatus are : 

(v) Gauging by Chemical Means. 

(vi) Gauging by Weirs (see Chap. iv.). 

(vii) By Venturi, or other Meter. 

(viii) By a Travelling Screen. 

The best system in any case depends upon the character of the stream, and 
to a smaller extent upon the skill of the observer, and upon the intelligence of 
the available labour. 

(i) Gauging by current meters requires a considerable amount of skill on 
the part of the observer, but little extra apparatus beyond a boat is 
necessary. 

(ii) Gauging by rod floats demands less skill on the observer’s part, but at 
least two men are necessary for wading, or two boats when wading is impossible. 
A complete set of rod floats is less portable than a current meter. 

(iii) Gauging by surface floats is the simplest and quickest method, and can 
be carried out by a single observer ; but in order to obtain any real degree of 

3 


34 


CONTROL OF WATER 


accuracy the ratio between the surface and mean velocities must be previously 
determined by more accurate methods. 

(iv) Gauging by Pitot tubes is extremely accurate, and the method can be 
employed under conditions where a current meter would be destroyed, and 
rod floats would prove inaccurate. 

As a rule, the discharge can be obtained far more rapidly by means of rod 
floats, or by a current meter, than by a Pitot tube. This latter instrument is 
only necessary when more detailed information is wanted than is required for 
the determination of the discharge, and is not well adapted for gauging streams 
the flow of which is irregular. 

In very regular channels, lined with smooth masonry, or in pipes, where the 
geometrical distribution of the velocities over a cross-section can be accurately 
estimated, a fixed Pitot tube will record the momentary discharge with an 
accuracy which is only surpassed by a weir or Venturi meter ; but the necessary 
preliminary studies are tedious. 

The following methods require certain fixtures to be installed at each 
gauging site. 

(v) The necessary apparatus for carrying out the chemical method is easily 
installed, and is portable ; but the observations require special knowledge 
which is not usually possessed by engineers, although it can be fairly rapidly 
acquired. 

(vi) Gauging by a weir necessitates a somewhat expensive permanent con¬ 
struction, and the sacrifice of a certain head, which may be a disadvantage. 

Engineers are, I think, inclined to somewhat overestimate the accuracy of 
the weir method ; and if it is applied to measure the flow of a natural stream 
throughout the year, difficulties occur, since, a weir which correctly measures 
the low-water discharge, is quite unfit for gauging the flood discharge, and vice 
versa. 

It is, however, one of the few systems with pretensions to extreme accuracy, 
which permits the observations to be taken by an untrained man, and after¬ 
wards calculated at leisure. 

(vn) The Venturi meter is only adapted for measuring volumes of water 
which are capable of being passed through a pipe. The apparatus is relatively 
more costly than either the chemical, or weir, or screen systems. The method 
is very accurate, and no great sacrifice of head is entailed. Further, the 
method adapts itself more readily than any other to continuous recording, al¬ 
though weirs are not far inferior in this respect. 

(viii) Measurement by a screen is new, and experimental. Consequently, a 
definite statement should be made with caution. Nevertheless, it is promising, 
and has advantages which will be later discussed. 

Soundings.—With the exception of chemical and weir gaugings, all methods 
of measuring the discharges of streams require a previous knowledge of the 
cross-section of the stream channel. 

A cross-section of the river is obtained by soundings, and the mean local 
velocity perpendicular to the cross-section is observed at as many points as 
possible. The discharge is then calculated by multiplying each of these 
velocities by the area over which it is supposed to occur, so that the dis¬ 
charge is : _ 

6 Q = 2 va 

where v, is the observed velocity at any point, and a, is the corresponding 


SO UN DINGS 


35 

partial area of the cross-section of the stream over which v , is assumed to 
represent the mean velocity. 

The process for obtaining the areas is comparatively simple. The only 
difficulty lies in observing the depths. 

So long as the depth does not exceed about io feet (more or less according 
to the velocity of the current), a sounding pole is used, which is best divided 
into feet and tenths (or even hundredths), and is provided with a flat base so 
as to prevent it from sinking into the softer parts of the bottom. 

In the case of depths exceeding io feet, a sounding-line with a weight has 
generally to be employed. 

The sounding-line is usually a hemp cord, graduated into feet, or fathoms, 
by tags of leather, or cloth, inserted between the strands of the cord. A hemp 
cord is very easily handled, but errors can arise owing to alterations in the 
length of the cord caused by soaking in the water. In really accurate work 
it will be found that this alteration is not uniform over the whole length of the 
cord, and that frequent checking is essential. In some cases this has led to 
the use of piano wire, in place of hemp cord. The greater accuracy thus 
obtained is undeniable. Wire should always be employed in swift rivers where 
the velocity is sufficiently high to require a heavy weight. If a hemp cord is 
then used, the thick rope is caught by the water, and the depth observed 
exceeds the truth. 

In ordinary cases, however, the fact that a comparatively unskilled man can 
handle the cord is of great advantage ; and although the varying corrections 
entail somewhat greater labour on the part of the observer, I believe that the 
cord is really the more practical method, except possibly in a very rapid 
stream. 

The weight used'for carrying the sounding-line to the bottom is a very 
important portion of the apparatus, especially in the case of swift streams. 
The most common form adopted is a frustrum of a cone, weighing about three 
pounds. This is easily handled, and may be used in streams with a current 
not exceeding 3 to 4 feet per second. 

For more rapid streams, soundings made with such a weight usually over¬ 
estimate the depth, and the torpedo-shaped sinker shown in Sketch No. 7 should 
consequently be employed. This is by no means easy to use, but the greater 
accuracy obtained justifies the time expended in training the leadsman. 

In very rapid and deep streams, even 40-lb. weights of the above form 
are insufficient, and some device in the nature of a pulley fixed in the bows of 
the observer’s launch becomes necessary. The problem is a difficult one, and 
as yet it has not been satisfactorily solved. 

In sounding a rapid river some difficulty may be experienced through the 
water banking up against the pole. The best method is to put the pole on 
the bottom, and then withdraw it until its lower end just dips in and out of 
the waves. The distance which the pole is raised in order to effect this, as 
measured against a fixed point on the bridge, or against the support from 
which the sounding is taken, gives the depth unaffected by any banking up 
of the water, due to currents. 

The determination of the position of each sounding, and its correction for 
the rise or fall of the river during survey, is the business of a surveyor, and 
will not be discussed. 

In small streams, it is usual to stretch a cord across from bank to bank and 


36 


CONTROL OF WATER 


to determine the depth at equal intervals along the cord. The mean of three 
such cross-sections at intervals of say 50, or 100, feet along the course of the 
stream is taken as the cross-section. In large rivers, the points at which the 
depths are observed are usually fixed by observations taken with a theodolite, 
and two observers are then required. 

I may, however, remark that very accurate determinations may be made 
even in wide rivers, by the use of a sextant, and the two angle method. Only 
one skilled observer is then required. In my own practice I have found that 
this nautical system is most convenient. 



Tor pah Sinker . 

Sketch No. 7.—Torpedo-shaped Sinker. 

Irregularity in the Flow of Water. —The flow of water in Nature 
is always irregular, or turbulent, as defined on page 11. Such irregularities 
affect the indications of all instruments us.ed to observe the velocity of the 
water to a greater or less degree. Thus, except in laboratory observations, 
where special precautions are taken to regularise the flow, it is necessary to 
consider the errors which may thus be introduced. The following discussion 
is only approximate, and the figures given are in reality only relative, since it 
is believed that the matter is fundamental in all hydraulic measurements, other 
than those of a gravimetric or volumetric nature. 
















DURA TION OF INDIVID UAL OBSER VA TIO NS 37 

If we merely consider the forward velocity (i.e. the component parallel to 
the main direction of the stream), momentary variations amounting to 20 per 
cent, of the mean velocity will be found at those points where the motion is 
steadiest; and near the bottom the variations exceed 50 per cent, (see Sketch 
No. 2). These figures are less than the true values, since, the inertia and friction 
of whatever instrument is employed to observe the velocities must tend to 
diminish the irregularities. It is therefore plain that the forward velocity at 
any given point (which in future will be termed the velocity at that point), can 
nevei be ascertained by one observation only, and its mean value must be 
obtained by averaging a large number of the momentary values. 

This averaging can be effected mechanically, as in the case of the current 
meter, which indicates the mean velocity over the whole filament that passes 
thiough the vanes during its run (i.e. a cylinder say 3 inches in diameter, 
and over 100 feet long); or by means of the rod float which moves with a 
velocity nearly equal to the mean of the velocities existing in the column of 
water surrounding it (which is probably not a circular cylinder, but a more or 
less elongated elliptical cylinder). The mean velocity can also be obtained 
arithmetically, as when the average of the velocities of a certain number of 
surface floats is taken. The problem is, in fact, of exactly the same character 
as that discussed in connection with rainfall (see p. 176). 

If the forward velocity at one point in the cross-section of a large stream be 
required, the observations of Cunningham (Roorkee Hydraulic Experiments') 
indicate that the difference between the means of the velocities of 25 and 
50 consecutive floats is not likely to exceed o‘05 foot per second. Thus, at 
least 25 float observations, or Pitot tube readings, would be required to ascer¬ 
tain the velocity with an accuracy of 1 per cent. In cases where the instrument 
itself effects a certain amount of averaging, a smaller number of separate 
observations will suffice. 

In discharge observations, however, the velocity at any one point is not a 
very important factor, and such tedious repetitions are not required. The 
following rules are adopted in practice : 

For Current Meters .—For all practical purposes a run of three minutes 
gives the velocity at the point. 

For Rod Floats .—The mean of the velocities of five floats, which, during 
their path through the length over which the velocity is observed, move in a 
direction which is approximately parallel to the general direction of the 
stream, is assumed to be the mean velocity over the depth occupied by the 
float. 

A good deal of doubt exists in the case of surface floats. The results of 
some systematic observations are given on page 42. 

In view of the fact that the method of surface floats requires the selection 
of a multiplier in order to reduce the observed velocity to the mean, the mean 
velocity obtained by five float observations per point is probably sufficiently 
accurate for practical purposes. 

These rules have no very great observational basis, and in reality they 
represent the amount of time which experience shows can be devoted to 
ascertaining the velocity at any one point. They should not therefore be 
blindly applied. Unless some special reason exists which renders the accurate 
determination of the velocities desirable, it is probably better to obtain a value 
of the average velocity during a short period at each individual point as rapidly 


3 8 CONTROL OF WATER 

as possible, and to devote the time thus saved to observing the shoit period 
average velocities at more numerous points. 

The matter can be best illustrated by an example. Consider a channel 
60 feet wide. The usual process of measuring the discharge would be to take 
io soundings, 6 feet apart, across the canal, and to observe the depths at 
intermediate points wherever the io original soundings indicate irregularities 
in the bed. The mean velocities over the io original verticals would then be 
determined by one or other of the methods given later. In ordinary work, 
whether by current meter or by float, the velocities thus obtained would usually 
be averages over periods of 3 to 5 minutes ; or averages over a larger area 
(due to the floats not running in exactly the same paths) for a somewhat shorter 
period, as in rod float work. If the work is accurately carried out, it is probable 
that the individual mean velocities obtained by repeating the work over the 
same verticals will differ by 5 or 6 per cent, from those previously obtained. On 
the whole, however, some differences being positive and others negative, the 
discharges calculated from the two sets of observations should not differ by 
more than 1 or 2 per cent. Now, the mean velocities on two consecutive 
verticals may differ by as much as 10 per cent, even when these means are 
long-period averages. It is therefore probable that better results could be 
attained in either set of observations by observing the mean velocities during 
half the period of 3 to 5 minutes over 12 verticals ; since the two discharges 
would probably agree quite as accurately as when the velocities on 6 verticals 
only were observed, and the chances of missing a marked irregularity in the 
flow of the stream would be greatly minimised. Such practical tests as I have 
been able to effect confirm this view. The experiments were carried out with 
rod floats in fairly regular channels (Bazin’s y— 1*5, or Kiitter’s n = o’02o). 

The real question is whether it is more important, to eliminate the effects of 
the momentary irregularities in the velocity at individual points, or to discover 
permanent differences between the mean velocities which prevail over adjacent 
portions of the cross-section of the stream (see p. 12). The matter deserves 
careful consideration whenever a permanent gauging station is installed ; and 
in such cases the velocities and depths obtained in the early observations 
should be plotted, and the graphs should be studied for indications of 
sudden and permanent differences in the velocities at points close to one 
another. 

My own studies indicate that while it is desirable to observe the point 
velocities with great accuracy in this preliminary work, routine gaugings are 
best effected by quick determinations of the velocities at as many points as 
possible, the points being selected so as to represent the areas in which the 
preliminary studies show that permanent differences are most likely to exist. 

I believe that this principle is applicable to all discharge observations 
without exception, and there is little doubt that no engineer accustomed to 
gauge earthen channels or natural streams will dispute it. Exceptions may 
occur in laboratory work, or when observers of great skill are gauging extremely 
smooth and regular channels. For example, Francis (see p. 58) appears to 
have been satisfied with far less closely spaced rod float observations in smooth 
channels than I should be disposed to make. 

Calibration of Instruments (General Principles).—The term calibration is 
used to denote the process of comparing the indications of an instrument with 
the true values of the quantity which it is proposed to observe. 


RATING OF INSTRUMENTS 


39 

In discussing the calibration of the instruments for observing the velocity 
of water, the precautions which are necessary in order to eliminate the 
effect of irregularities in the flow of the water as it occurs in Nature require 
consideration. 

The indications given by any instrument are (to a greater or less degree) 
dependent on its construction, and on the irregularity of the flow of the 
water. 

Calibration is usually effected by moving the instrument through still water, 
at a measured velocity. Thus, the calibration takes place under circumstances 
which are probably equivalent to a water motion which is entirely devoid of 
noticeable irregularities of velocity ; hence, a consideration of the probable 
effects of the irregularity of the motion of running water in which the instru* 
ments are used is necessary. 

The irregularities of velocity distribution, both as regards the momentary 
variations of velocity at a fixed point, and as regards the permanent differences 
between the mean velocities at points close to one another, increase in pro¬ 
portion to the size of the cross-section of the channel and the roughness of 
its sides and bed. It is probable that each stream has its own peculiar 
constitution which governs the degree and] character of the irregularity of 
the flow. 

We do not, except in very rare circumstances, wish to measure the 
momentary variations of the velocity. We require to ascertain the mean 
result ( i.e . the mean local velocity, as defined on p. u, or its direction) as 
quickly as possible, apart from variations ; and all methods of calibration 
essentially consist in comparing the indications of the instrument with this 
mean value as obtained by some other process. In a well designed 
instrument momentary oscillations are prevented, or the indications are so 
damped that, as a rule, the irregularities in the quantity observed do not 
produce visible fluctuations in the reading, and an average result is alone 
indicated. 

We cannot, however, ignore the fact that it is quite possible that the 
total effect of the irregularities may influence this average reading of the 
instrument. 

So far, it must be confessed, our knowledge of hydraulics is not sufficiently 
precise to allow other than general statements to be made on the question. 
For instance, it is permissible to state that the present method of calibrating 
current meters by moving them through still water, is, theoretically speaking, 
defective ; but the method is justified by the fact that the results obtained are 
sufficiently accurate for practical purposes. 

As our knowledge of hydraulics advances, many of the uncertainties which 
at present exist will undoubtedly be recognised as caused by a lack of sufficient 
care in calibrating instruments under conditions similar to those existing during 
their practical use. 

The matter is probably of most importance in the case of Pitot tubes, 
where we can at present state that the coefficients obtained by motion through 
still water may differ by as much as 5 per cent, from those obtained by observing 
the mean velocities at different points in the cross-section of a stream, and 
comparing the discharge thus obtained with the discharge determined by a 
weir, or volumetric observation. 

This class of error is difficult to discover, for the irregularities in flow are 


40 


CONTROL OF WATER 


most marked in streams of large volume, and the greatest discharge that has 
ever been measured volumetrically, or over an accurate weir, does not at 
present exceed 300 cusecs. Hence, a careful observer is quite justified in going 
to some extra trouble and expense in attempting to carry out the calibration 
observations under circumstances as closely resembling practical conditions as 
possible. 

Thus, instruments for use in pipes should be calibrated in water moving 
through a pipe, or in a smooth channel (even although of a different size from 
those in which they are to be used), in preference to still water. 

If, for lack of the necessary opportunities, calibration must be carried out in 
still water, it is plainly advisable to calibrate instruments intended for shallow 
streams in shallow water,—and vice versa ; while any opportunity of checking 
an actual gauging in moving water volumetrically, or by standard weir 
measurements, should be taken. 

A careful comparison between a current meter and a weir, or other accurate 
gauging of a large river, is one of the most urgent requirements of the 
present day. 

The following figures show the errors which are likely to occur in good work 
when large streams, or small rivers, are gauged. 

So far as is possible only the effects of irregularities in motion are now 
referred to, and the question of the errors caused by imperfections in the 
instruments themselves is discussed separately. 

Current Meters .—Murphy {Trans. Am. Soc. of C.E ., vol. 47, p. 370) finds 
that 50 current meter gaugings (where the velocities were taken at one point 
per 2*3 square feet of cross-section) when compared with simultaneous weir 
gaugings, give : 


Maximum difference 
Minimum difference 
Mean difference . 


• 473 P er cent. 

• °'*3 

• + °'93 „ 


The observed discharges ranged from 197 to 225 cusecs ; and one of the 
meters was obviously less accurate than the others, since, if only the two most 
reliable instruments are considered, the mean difference is 074 per cent. 

Allen {ibid., vol. 66, p. 131), gives six observations of a similar character, as 
follows : 

Maximum difference .... 3 per cent. 

Minimum difference.0*5 „ 

Mean difference .... Under 2 


A theoretical estimate of the effects of irregularities in the absolute magnitude 
of the velocity can be made as follows : 

Let v = an-\-b , be the rating formula of the current meter (see p. 49). 

Let the water flow with a velocity equal to v x , for t x seconds, and then at 
a velocity v 2 , tor / 2 seconds. The total number of turns recorded on the dial 
of the meter is 


;q/ 1 + 7Z 2 / 2 = 


vfi + vfj __ bff+fA. 

a 


The true mean velocity is 7 ~~~^ = v m say, 


a 





4i 


EFFECT OF IRREGULARITIES 


and the velocity deduced from the readings is : 


v c v 


-f- 


+ b — a 


v x t x +v4o b ) 
/ 


a 


Ab 


*i+4 ^ «(4+4) 

/ b \ 

— -— h + <? = v m 

l. a a ) 

So that, assuming the rating curve is of the above form, variations in the 
absolute magnitude of the velocities do not affect the results. 

For rating curves of any other form, the effect of similar irregularities may 
be calculated for any given case ; but, since a rating curve of the form v = aii-\-b , 
represents the results of calibration with sufficient accuracy, it appears unneces¬ 
sary to go through the work. 

The question is somewhat more complicated when irregularities or variations 
in the direction of the velocity are considered. If the axis of meter makes an 
angle 6 with the true direction of the velocity, it records a velocity which is 
approximately equal to v cos 0 , and for 0 = 20 degrees, this would be 94 per cent, 
of the true velocity. Actually, the meter swings to and fro with the current, 
and may be assumed to follow the momentary direction of the current fairly 
closely, since its inertia is but small. Thus, we may assume that the meter 
records slightly less than the average of the velocities at the point of observation 
(without respect to direction). As we usually wish to observe only the forward 
velocity (since that is the important factor in discharge observations), it is possible 
that the meter will record slightly more than the forward velocity. The meters 
used by Murphy (ut supra) recorded more than the weir discharge in 34 cases, 
with an average error of +i'94 per cent. ; and less than the weir discharge in 
16 cases, with an average error of —0*91 per cent., so that, so far as these 
observations go, the above theory is confirmed. 

As these observations were taken in a very regular channel, they are likely 
to be less affected by variations in the direction of velocity than those obtained 
by a current meter in natural streams. 

The angle through which the meter swings may be considered to roughly 
indicate the [possibilities of error. So far as I have been able to observe, 
swings in excess of 30 degrees, i.e. 15 degrees on either side, corresponding to 
a possible maximum error of 3'5 per cent., are unusual. It must be noted that 
a study of the variation of absolute] velocities shows (eg. the curves given in 
Sketch No. 2) that the greater irregularities occur near the bottom of the 
stream, where it is hard to see what the meter is doing. 

While the above investigations appear to confirm the general accuracy of 
current meters, they are certainly defective in one respect, and possibly in 
several. They take no account of the probability of velocities varying both 
in magnitude and direction at different points on the vanes of the meter. 
If the motion of a stream which bears so little silt that individual particles 
are visible, is observed, the possibility of such differences is evident; and, as 
already stated, we can usually only investigate the surface portion of the stream, 
which is known to be least subject to irregularities. 

Rod Floats .—The effect of irregularities in motion is probably quite as 
marked on rod floats as in the case of a current meter. In actual practice, 
however, those observations which are most influenced by irregularities in 
direction are rejected, since floats the paths of which markedly diverge from the 
general direction of the current, are condemned, and only the results obtained 
by “fair runs” are recorded. 




42 


CONTROL OF WATER 

It should be noted that the percentage of floats which make fair runs is far 
less in large rivers than in small streams. 

We may therefore consider that the automatic averaging obtained in deeper 
channels, where the longer rod floats are affected by a greater volume of water, 
does not entirely compensate for the increased irregularity of the motion of the 
water. The probable errors of gaugings by rod floats are tabulated on page 59. 

Since, in really first class work, the probable error caused by incorrect timing 
of the runs, and sounding of the stream, does not greatly exceed 1 per cent., we 
may consider that a large fraction of the excess above 1 per cent, which occurs in 
the larger streams is due to the increased irregularity in the motion. The figures 
given are applicable to very regular canals, rather than to natural streams ; so 
that the effect of irregularities is generally greater than is indicated in the table. 

Surface Floats .—Surface floats are considerably affected by irregularities, 
and in the case of a large river it is often almost impossible to obtain fair runs. 
Such figures as 10 or 15 per cent, of fair runs only, are by no means unusually 
poor results. 

I have usually been content with the mean of 5 fair runs ; but, where time 
permits, I have endeavoured to secure 10 fair runs. In 92 examples (where 
I was able to secure 10 runs satisfactorily) I have worked out the mean 
surface velocity for the first 5, and also for the first 10 runs, and have 
expressed the difference as a percentage. As might be expected, the larger 
percentages are found where the total number of floats observed was least. 
When 5 points were selected for observation, the mean of the surface velocities 
as obtained from 25 floats shows a maximum difference of 6 per cent, from 
that obtained from 50 floats, and the mean difference is 2’i per cent. 

For 50 floats and 100 floats ( i.e . 10 points observed), the maximum difference 
between the mean velocities is 4 per cent, and the mean difference is r6 per cent. 

For the few 75 and 150 float observations which I have been able to secure, 
the maximum difference between the mean velocities is 7 per cent, (probably 
due to a slight change in the discharge of the canal), and the mean difference 
is 2*4 per cent. ; or, if the doubtful observation is rejected, r8 per cent. 

Pitot Tubes .—In Pitot tube work, the effect of the irregularity of motion is 
of primary importance ; and it may be stated that calibration in still water is, 
owing to this cause, subject to an inaccuracy which may exceed 10 per cent., 
and which is rarely less than 2 to 3 per cent. 

Even this statement does not fully disclose the possibilities of error when the 
discharge of earthen channels is observed. Working with a Pitot tube, I 
obtained the following results : 

{a) Calibration in moving water by traversing a semicircular galvanised 
iron channel, and checking against a triangular weir, gave : 

v = 1 ‘02 V 2 gh 

This calibration was the result of 7 discharge observations, and the tube 
was read at 12 points per square foot of area. The mean of 3 readings per point 
was taken as the velocity at that point. 

(b) Calibration in a small earth channel with a bed of fine sand, checked 
against a Cippoletti weir, gave : 

v = o‘9 7 \l 2gh 

This was the result of 7 discharge observations, and the tube was read at 
6 points (3 readings per point) per square foot of area. 




DISCHARGE 43 

(V) Calibration in a channel with a bed 20 feet wide, consisting of fine sand, 
carrying up to 60 cusecs, checked against chemical methods, and rod floats, 

gave: _ 

v=o’97 \J 2 gh 

as the result of 18 discharge observations ; the tube being read at 1 point per 
square foot, with 3 readings at each point. 

The system of checking was very complete, the triangular weir being 
volumetrically verified, and the Cippoletti weir being checked against a series 
of triangular weirs. In the case of the chemical and rod float determinations, 
a portion of the discharge was diverted over the Cippoletti weir, and the 
difference as indicated by chemical or float methods was compared with the 
weir readings. 

The Pitot tube was badly designed,—but by no means more so than those 
used by several other experimenters,—and it would appear that whenever a 
Pitot tube is employed to measure velocities in natural channels, very careful and 
systematic calibration in moving water under similar conditions must be made. 

Summing up, and bearing the possible errors in timing and sounding 
carefully in mind, we may state as follows : 

1 he current meter and rod float are probably not affected by the irregul¬ 
arities of the flow to such an extent as to materially influence the results. The 
present evidence suggests that the discharge obtained by a current meter is 
likely to be slightly greater than the truth. The rod float also, as will be seen 
later, usually overestimates the discharge. 

The surface float is only useful when the observations at each point are 
systematically averaged ; and, where possible, 10, rather than 5, fair runs should 
be obtained at each point, or, still better, the points at which the velocities are 
observed should be very closely spaced. 

The Pitot tube is liable to appreciable errors, which can probably be 
diminished by careful design, but which at present cause it to be unreliable 
when used in any channels except those which are very regular and smooth. 

The possible errors indicated above will evidently affect all measurements 
to much the same degree, and will only be discovered by weir or volumetric 
checking. When considering their importance, it should be remembered that 
an engineer is probably more concerned with the relative than with the 
absolute accuracy of his various results. Hence, a constant error will seldom 
lead to confusion, even if its existence is undetected. 

Calculation of the Discharge. —The velocity at any point has been 
defined on page 9. 

Assuming that the observations have been taken, and that the calibration 
of the instrument] is carried out in such a manner as to eliminate the effects of 
irregularities both in the absolute magnitude, and in the direction of the velocity, 
the quantity of water passing through a small element of the area of the cross- 
section of the stream is given by the equation : 

q = va cusecs 

where a , is the elementary area in square feet, and v, is the velocity normal to 
the area in feet per second. 

The total discharge of the stream is given by the equation : 

Q = 2va cusecs 

A study of the rate at which the observed values of v, vary from point to 



44 


CONTROL OF WATER 

point will, in any given case, permit a selection to be made of the size of the 
partial areas typified by <2, which will render this equation sufficiently collect 
for practical purposes. The usual practical rules are given on page 5 2 \ and, 
as already indicated, it is probable that in most cases too much attention is 
devoted to eliminating the momentary variations in v, and consequently the 
partial areas are larger than they should be. 

If short intervals of time, such as one-tenth of a second, are considered, so 
that v, is a momentary velocity, and irregularities are not eliminated, the 
elementary discharge given by the first expression may vary between o'5o^ and 
i’5oy. Even in the case of such periods as 20 seconds, it is probable that q 
varies as much as 10 per cent., if a , be a small fraction of the total cross-section 
of the stream. 

The equation: Q = AV m 

where A, is the total area of the cross-section, and Q, is the total discharge of the 
stream, averaged over a period of sufficient length to eliminate the effect of 
irregularities, may be considered as defining V m , the mean velocity of the stream. 
A similar equation defines v m , the mean velocity over any portion of the whole 
area A. 

This expression “sufficiently long,” as applied to intervals of time in the 
above definitions, cannot be exactly defined. I believe that in small streams it 
may be as small as 5 seconds ; while in large rivers, there is a certain amount 
of evidence to show that it may be as many minutes. The question, however, 
is not of practical importance, since no method of gauging in which the 
velocities are measured is so rapid as to permit of Q, being ascertained in an 
interval less than at least ten times the “ sufficiently long period.” It is also 
quite possible that my estimates of 5 seconds and 5 minutes are excessive. 

Actual observations on the distribution of velocity, as defined on p. 11, over a 
cross-section, show that it varies from point to point, in accordance with more or 
less regular laws. The discharge of a stream may be geometrically represented 
by a solid with no marked irregularities, constructed on the cross-section of 
the stream as base, the height at each point being proportional to the velocity. 

The obvious method of determining the discharge is therefore to plot curves 
of equal velocity at frequent intervals over the cross-section, to ascertain the 
areas contained by these curves, and to multiply each area by the velocity that 
exists across it. We thus get a series of terms, the sum of which represents 
the total discharge of a stream. 

Such methods were actually employed by Harlacher and others, and Sketch 
No. 8 shows an example. 

T he labour entailed is obvious, and it is plain that unless the points at which 
the velocity observations are taken are very closely spaced, the curves of equal 
velocity may differ greatly from the truth. In fact, the process is almost as 
subject to error as contour lines, drawn by a draughtsman who had not seen 
the natural ground, would be. 

Thus, for ordinary discharge observations, some method which is less 
dependent upon personal opinion must be employed. The method usually 
adopted in practice is that of “ mean velocities over verticals.” This is a con¬ 
venient process, and is liable to but small errors. Theoretically, it is as 
accurate as the accuracy of the individual observations justify. It may, how¬ 
ever, be stated that the same observations can be made to produce results 


DISCHARGE FORMULAE 


45 


which differ to the extent of 5 per cent., or more, by selecting one or other of 
the formulae given. Thus, when working up observations the underlying as¬ 
sumptions must be carefully borne in mind, and the information obtained by 
determining the discharge from the same set of observations by all four formulae, 
and comparing the results, forms a very valuable check on the methods 
adopted in selecting the points at which the velocities were observed. If 
differences much in excess of 2 per cent, exist, the points have not been 
sufficiently closely spaced. 

The velocity observations are taken in sets arranged in vertical lines ; and 
the mean velocity in each of these verticals is obtained either graphically or 
arithmetically, and is termed the mean velocity over that vertical (see p. 52). 



Assuming then a series of soundings, so that d\, d 2 , d$, etc., are the depths 
of the water at a series of points spaced at a distance / feet apait along a line 
perpendicular to the general flow of the river, and that v 2) ^3 mean 

velocities over the verticals d\, d 2 , d$, any one of the following formulae may be 

employed : 

(i) Q = 2 d i v 1 / 

Q = S ^ +6 f 2 ±^ 3 7/ 2 / 


(ii) 

(iii) 

(iv) 


8 


_ , , Vi -\-v 2 j d\ T d 2 % 

Calculate 7/ 1 =•—-—, and d> = —-— . 

Q = 2 d l z/V = J 2 (v 1 +v 2 ) (d 1 + d 2 ) l 

„ , , . ^i+4^2 + ^3 j _ di+4d 2 +d s . 

Calculate v n — -^-> ana ttn 5 

Q = 2 v n d n il 










46 


CONTROL OF WATER 


It will be plain that /, need not necessarily be constant, the only modification 

/ 4 -/ 

required being that 12 ^ 23 is substituted for /, where / 12 and / 23 are the 

distances from d 2 , to d u and d s respectively. So also, if the direction of the 
line of soundings is not perpendicular to the general direction of the river, we 
must put Zi2 = Li2 si n where L 12 , is the distance between two consecutive 
points, and L 12 , makes an angle with the direction of the flow of the water. 

The formulae are deduced under various assumptions as to the manner in 
which the mean velocities and depths vary across the stream (see Sketch No. 9). 

In (i) we assume that the velocities and depths vary by sudden steps, the 
change occurring half-way between the verticals where the observations are 


Cross-Sections of Stream 



Assumed in Formula If MX. 



Curves of Mean Velocities over Vertical s 



Assumed in Formulaic!. 
_____*_ 




>" 

> w 

——1— 

_ 


Assumed in Formula N°IL 



Sketch No. 9.— Diagram illustrating the Assumptions made in deducing Discharge 

Formulae. 

taken. This assumption is no doubt open to criticism, but I believe that in 
practice the error introduced is inappreciable. 

In (11) we assume that the velocities vary by steps, the chang'e occurring 
half-way between the verticals as before, but that the stream bed is composed 
of straight lines, joining the bottom of d 2 , to the bottom of d u and d 3 . I cannot 
see that this assumption possesses sufficient theoretical advantages to justify 
the additional labour entailed. 

In (iii) the adjacent velocities and depths are averaged, the assumption 
being that both the depths and velocities vary as ordinates to straight lines. 
So fat as theoiy can assist, the results are neither better nor worse than those 
of (i). It is, however, a very convenient method of obtaining the discharge 
through areas of the channel near the banks where the soundings are not 
equally spaced. Personally, I have been accustomed to use the equation in 































CURRENT METERS 




47 


cases where the depths or velocities at consecutive points vary rapidly, but I 
do not pretend that this practice has the slightest theoretical foundation. 

In (iv) the bed of the stream and the mean velocity curves are assumed 
to be composed of parabolic arcs ; and in contrast with the other formulae, 
each term of the summation expresses the discharge over a length 2/, in place 
of l. This assumption agrees fairly closely with actual observations. This 
formula, therefore, may be regarded as standard, and in considering the 
labour involved in its application, notice should be taken of the fact that 
only half the number of multiplications occurring in the other formulae are 
now required. 

In any given case, a study of the observations of velocity and depth, 
enables us to determine the assumption that most closely coincides with the 
facts, and so to select the best formula. 

As a rule, (i), with an application of (iii), or (iv), near any marked irregul¬ 
arities, leads to satisfactory results. It is as well to bear in mind that the 
usual observations for discharge are not so accurate as to justify any great 
refinement in mathematical treatment by an over-laborious formula, which 
may give rise to arithmetical errors of far greater magnitude. 

A skilled computer will probably select formula (iv) as standard, but he 
must remember that systematic gaugings necessitate computations being 
performed on the spot, by men who are but little accustomed to other than 
the usual arithmetical processes. Such men can rarely do more than handle 
formula (i), and if other formulae are used in important gaugings, I believe 
that it is best to permit the observer to select the type which appears to 
most closely fit the actual observations. The methods of obtaining the values 
of z/ 1} v 2 , Vfr etc., are discussed under the headings Current Meters, Rod 
Floats, etc. 

Current Meters. —The essential portions of a current meter consist of a 
wheel, or screw, which is set in rotation when the meter is immersed in moving 
water, and a counting apparatus which records the number of revolutions 
produced. 

The whole apparatus is usually mounted on pivots, and is provided with 
a tail vane. The rotating portion of the apparatus is thus directed so as 
always to be influenced by the maximum velocity at the point where the 
observations are made. 

In modern forms of current meters many complications are introduced in 
order to secure sensitiveness and accuracy. The rotating parts are made 
hollow, and their weight is adjusted so that it is water-borne, and the recording 
apparatus is electrical. Thus, the bearing friction is greatly reduced. So 
also, shields and guides are placed so as to protect the wheel from the impact 
of drift; and, in some cases, to prevent oblique currents in the water from 
affecting the records. 

It is not proposed to describe these details. As a general rule, most 
current meters are somewhat too sensitive for engineers field work, and as 
a personal expression of opinion I am accustomed to select the simplest 
possible form, to calibrate it carefully, and to use it roughly, but frequently, 
in the field ; on the principle that twenty fairly concordant gaugings are 
more useful than five taken with extreme accuracy. In all cases, however, 
it is desirable to systematically test every current meter for errors produced 
by oblique currents. Thus, a meter should not only be calibrated when moved 


4 s CONTROL OF WATER 

. straight ahead through the water, but comparative tests should be made at 
the same speed while moving the meter up and down, or to the right or 
left of its general direction. The best meter for field work is that which is 
least affected by such handling ; for in large rivers, at any rate, these vibratory 
motions represent the circumstances under which the meter works far more 
closely than the ordinary straight ahead motion does. 

The meters which are most usually employed in practice are those of Price, 
Haskell, and Fteley. Of these, the Fteley is probably the most accurate, and 
is best adapted for the registration of low velocities. Price’s type permits 
of the registration of all velocities usually met with in river gauging, and is 
the pattern which is almost universally employed by the American, Egyptian, 
and Indian Governments. The general adoption of the Price current meter 
is due to the fact that it combines a sufficient degree of accuracy for practical 
gaugings, with adequate constructional strength to guard against damage by 
the unavoidable incidents of field work, provided that leasonable care is 
taken of it. 

A current meter must be considered as an instrument liable to a fair 
amount of rough usage, and in the Price meter a certain degree of accuracy 
and sensitiveness has been sacrificed in order to obtain the necessary strength 
and reliability for practical operations. For laboratory work, with skilled 
and careful observers, the Fteley, or the Warren, are a little more accurate ; 
but, personally, I should be reluctant to expose either to ordinary engineering 
handling. 

As regards their adaptation to local conditions, both the Price and Haskell 
meter can be suspended on a weighted sounding-line, and are consequently 
suitable for rivers of all sizes, although the Haskell is probably somewhat 
better fitted for use in very large streams. 

The Fteley and the Harlacher meters must be fixed to rigid rods, and 
are therefore only applicable to rivers that can either be waded, or are 
spanned by bridges, and do not greatly exceed io feet in depth at the 
bridges. 

Rating.—All meters require a preliminary rating, or calibration. This is 
accomplished by moving them through still, or nearly still, water at a definite 
velocity ; and is usually effected by fixing the meter in a frame, either hung 
from a vehicle which travels along the bank, or installed well forward of a 
boat or steam launch, travelling at a known speed. 

In selecting the method of rating, it is as well, where possible, to be guided 
by the use to which the meter is to be put. For example, were I rating meters 
which would afterwards be employed in gauging small streams, I should 
prefer the system of a vehicle on the bank, since the possible retardation due 
to the proximity of the bank would also be present in actual work. Whereas, 
for meters intended for determining the discharge of large rivers, the method 
of a boat on a wide and deep canal is preferable. 

Similarly, the general effects of irregularities in the motion of the water 
can be investigated as indicated on page 41 ; and the method of allowing for 
possible currents in the “ still” water is dealt with on page 49. 

In discussing the rating of a meter, let : 
v, represent the observed velocity through still water, in feet per second, 
represent the number of revolutions per second indicated on the meter 
dial or counter. 


CURRENT METERS: RATING FORMULAE 


49 


A preliminary graphical plot shows that the relation between v and n may 
take the forms : (i ) v = an + 6 

(ii) v 2 = cn 2 + d 

(iii) 7 > = e-\-fngn 2 

Each of these relations may be discussed by the methods of least squares ; 
and on the usual assumptions of that method, we can (for any individual case) 
select that which leads to the most accurate results by calculating the probable 
errors of the constants a , b , etc. 

If this work is carried out, it will usually be found that formula (i) fits slightly 
less well than either (ii) or (iii), but in no case that I am aware of, is this differ¬ 
ence of such a magnitude as to introduce appreciable errors. 

Hence, although formula (ii), probably best represents the actual relation, 
I see no reason for abandoning the comparative simplicity of formula (i). 

Dowson (. Measurement of Volumes discharged by the Nile in 1905 and 1906) 


also discusses the formula 


v = an-\-b±u 


where zz, represents a possible current in the apparently still water used for 
rating. The effect is that for runs in one direction : 

v=an-\-b—u 

and for runs in the reverse direction : 


v = an -f b-\-u 

and by the method of mean squares he gets for his observations : 

u^— 0x1092 foot per second 
with <2 = 4-4521 b = o'i 086 foot per second 

so that the rating formula when applied to river gaugings is really represented by : 

‘ z / = 4'452 i ^ + o , io 85 

whereas, if u were ignored : 

7y = 4 , 4405;z+o , i 105 

which shows that such a velocity has practically no effect on the rating curve. 

So also, Dowson investigated the effect on a “ small Price” meter, of motion 
not in a horizontal line, but in a curve with vertical sinuosities. He demon¬ 
strates mathematically that in rough water (waves about 6-5 feet long, and 
16 inches high) the velocities deduced may be too high by 10 per cent, when 
compared with calm water calibrations ; and cites experimental results that 
confirm his calculations. 

The error introduced varies as the square of the height of the waves, and 
inversely as the square of their length, and may be by no means inappreciable 
in turbulent streams. This error may occur in all meters which rotate when 
moved up and down in a vertical direction in still water. So far as I am aware, 
the Fteley meter is the only type in which this does not take place ; although, 
in the Haskell meter {Trans. Am. Soc. of CE ., vol. 47, p. 380), wave motion 
will lead to an underestimation of the velocity. 

An investigation of the probable errors of the constants a , and b , as ascer¬ 
tained by skilled observers, for 14 different Price current meters, leads me 
to believe that the velocities deduced from readings taken with a carefully 
rated current meter are rarely subject to a greater error than 1 per cent, so long 
as the velocity exceeds o - 8 foot per second, unless the motion of the water in 
which the observations are made is far more irregular than that in which the 


4 


5o 


CONTROL OF WATER 


calibration is effected. When the velocity is less than o’5 loot per second, 
current meters are not usually employed. 

As will be shown later, irregularities in the water motion certainly induce 
errors of 5 per cent, in the velocities, and errors of 10 per cent, probably occur. 
These errors are, however, almost as likely to be positive as negative, so that 
the nett effect on the discharge is usually by no means as great as 5 per cent. 
The available evidence is given on page 56. 

Meters, when carefully handled, can be used to determine velocities as high 
as 10, or 12, feet per second, provided that the stream carries no drift or sub¬ 
merged bodies. The rating curves indicate (when the water is not turbulent) 
that the accuracy is as great, or greater than, that for low velocities. 

In a Fteley meter the general accuracy is greater, but the limits of use range 
from o - 3 foot per second, to 5*5 or 6 feet per second. 

In discussing the calibration observations of Price meters, it is as well to 
note that while the form v—an+b 

represents the observed values with sufficient accuracy for all velocities from 
o’8 to 6 feet per second, a better result can be obtained when the velocities 
range from 0*3 to 10, or 12, feet per second, by taking 

v=a l n+b 1 up to v = y$ to 4 feet per second 
and, v—atfi+bz for greater velocities. 

The tables given by Hoyt {Trans. Am. Soc. of C.E ., vol. 66, p. 90) show 
that the manufacturers’ rating, even when not specially determined for individual 
instruments, might be accepted if constant errors of 1 per cent, are permissible. 

Hoyt also states that the rating of meters is but slightly affected by use. 
My own observations, however, lead me to believe that rough handling should 
be avoided at all costs, and that where a river carries silt, the pivots and bearings 
of the instrument should be scrutinised before each observation, as a particle 
of silt in the mechanism may entirely change the rating. 

In the case of the Fteley meter, it appears that the relation 

v — a?i+b 

holds very fairly well for velocities greater than V2 foot per second, but for 
lower speeds a curve such as 

is more accurate (see Diamant, Trans. Am. Soc. of C.E., vol. 66, p. 107). 

I shall not discuss the electrical recording apparatus, but would refer to 
Hoyt’s paper as giving a very practical and reliable resume. 

Many other forms of meter are used in Europe, such as the Harlacher, 
Amsler, etc., but, having no practical experience of these instruments, I do not 
propose to discuss them. 

Accuracy of Results.—When, besides the imperfections in a current meter, 
we also take into account those due to errors in soundings, and the other 
measurements necessary to ascertain the cross-section of a river, such as those 
caused by the measured velocities not being perpendicular to the cross-section 
and finally the fact that a gauge reading alone does not necessarily completely 
determine the condition of a river (so that the discharge on a falling stage may 
differ from that at the same gauge in a rising flood), we obtain the following 
results. 


ACCURACY OF GAUGINGS 5I 

Dowson (ut supra), for the Nile at Sarras, indicates a probable error of 
4*3 per cent., as given by the discharge curve and the 126 discharge observa¬ 
tions taken to secure it. In this case the mean velocities were actually observed, 

so that errors only arise from uncertainties as to the depth and actual defects 
in the meter. 

The experiments of Prasil {Schweizerische Bauzeitung, 1906) and Barrows 
{Proc. Am. Soc. of C.E., vol. 59, p. 501), indicate that systematic current meter 
measurements, where the area of the stream section can be exactly determined, 
and the mean velocity is obtained by actual observation (no assumptions as to 
its position, or ratio, to selected velocities, being made), are probably quite as 
accurate as the weir measurements usually made by engineers, the probable 
error being o'9 per cent, in careful laboratory experiments, and 3 per cent, in 
field work. 

Where, however, the quicker methods of gauging, later discussed, are 
employed, errors of 5 per cent, are possible, and if, in addition, the velocity of 
the stream, or its depth, is so great that the area is uncertain, mistakes of 
10 per cent, seem probable. 

Murphy’s experiments (see p. 40) seem to indicate that somewhat better 
results (0*93 per cent, average error) than the 3 per cent, mentioned, can be ob¬ 
tained. The experimenters were apparently very skilful, and the conditions 
more favourable than those usually met with in field work. 

It will be evident that while the results of any one observation (especially 
flood discharges) may be open to criticism, it is unlikely that the total of, say, a 
month’s flow of a river (when obtained by careful current meter gaugings) is 
seriously in error, unless the month is one of continued high floods, or the bed 
of the stream is shifting, and the movement is not allowed for. 

Summing up these results, it seems fair to infer that errors in current meter 
gaugings are principally due to : 

(i) Irregularities in the motion of the water. 

(ii) Errors in the partial areas caused either by actual errors in the observed 
depths (such as occur in rapid streams) ; or by the soundings being too widely 
spaced, so that irregularities in the bed are overlooked. 

(iii) Errors in the mean velocities caused by the points where the velocities 
are observed being too widely distributed. 

Errors due to the first of these causes can be minimised by careful calibra¬ 
tion under circumstances which imitate irregular motion. 

The second and third class of errors are less easily avoided. 

In my own practice I am accustomed to personally observe the soundings, 
and during the velocity observations employ an assistant to systematically 
search for irregularities in the bed. If any marked irregularities are discovered, 
special velocity observations are taken round them, in order to discover if they 
produce notable differences in the velocities. Dowson’s results, however, show 
how hard it is to obtain accurate flood discharges ; and my own observations in 
the Thames when in flood, indicate errors of 7 and 8 per cent, under more 
favourable circumstances, but with less skilful observers. 

Observation of the Mean Velocity over a Vertical.—The accurate determina¬ 
tion of the discharge of a river requires velocity observations to be taken at 
many points distributed over its cross-section. 

For example, in Dowson’s Nile gaugings, there was a velocity observation for 
every 200 to 550 square feet of cross-section, according to the height of the flood. 


5 2 


CONTROL OF WATER 


In the Sudbury culvert gaugings, one observation for every 0*5 square foot. 

In Harlacher’s work, one observation for every 2 square feet in small, up to 
20 square feet in larger streams. 

The method of obtaining the discharge from velocity observations has 
already been indicated (see p. 44). 

(a) Harlacher’s graphical method may be considered to be the most 
accurate. It is so laborious, that it is only adopted in cases where the velocity 
observations are very closely distributed over the cross-section of the stream, 
and where the bed is hard and free from deposits, so that the area of the cross- 
section can be accurately measured. 

(d) Considering the method by mean velocities over verticals, and for the 
future denoting the mean velocity over the vertical by v m we find in actual 
practice that each v my is usually the mean of, say’-, 10 observations at 0*05 depth, 
o'i5 depth, etc. up to 0^95 depth ; and if 8 verticals are dealt with, there are 80 
observations in all, and 8 partial areas a. 

Sometimes this work is reduced by first observing 10 velocities on 3 repre¬ 
sentative verticals, and assuming that the mean velocity v m , for the other 5, occurs 
at the same fraction of the depth as it does on the 3 representative verticals. 
We then only take 3 x 10+5 = 35 observations. 

Either method necessitates the observation of velocities at from 4 to 10 
points on each vertical, or say 80 to 100 points in the cross-section of the 
stream ; and in large rivers even this number does not give a very close 
distribution of the verticals. 

Also, the time required to make such a series of observations is not only a 
disadvantage (as being costly and tending to discourage frequent observations), 
but may lead to errors due to the discharge of the river altering materially 
during the time taken to complete the gauging. 

Thus, methods requiring a smaller number of observations per vertical are 
needed, and should be employed even if only approximately correct. 

The general discussions on the irregularity of the motion of water will have 
made it plain that, for the same number of observations, the best distribution is 
probably secured by approximately determining the mean velocity over as many 
verticals as possible, rather than by accurately determining the mean velocity 
over a few widely spaced verticals. So far as either theory or experiment can 
be applied to what is essentially a series of accidents, it would appear that no 
advantage is gained by multiplying the point velocity observations on a vertical 
until the horizontal spacing of the verticals is less than the mean depth of the 
river. 

The most effective method of selecting the appropriate points is to examine 
the vertical velocity curves, as determined by velocity observations taken at 
regular intervals, usually 1 foot (or one-tenth the depth) apart, in a vertical 
from the surface to the bottom of the stream. 

When these velocities are plotted as abscissae, and the depths as ordinates, 
a vertical velocity curve is obtained ; and it is found that under the most varied 
conditions of depth, velocity, surface slope, and roughness of bed, these curves 
approximately assume the form of a parabola the axis of which is parallel to 
the water surface (see Sketch No. 10). 

If the curve was an accurate parabola, it would be possible to ascertain the 
mean velocity over the vertical by observations at comparatively few points. 
As a matter of observation, founded on long and careful studies, the velocities 


VERTICAL VELOCITY CURVES 53 

taken at certain points geometrically selected on a vertical, are so intimately 
connected with the mean velocity over that vertical that the mean velocity can 
be obtained from these velocities with very fair accuracy. 

A very excellent resume of the general principles will be found in Cunningham’s 

£ 


0 -! 


o-z 


Ob 


04 


06 


06 


07 


06 


09 


05 06 07 OS 09 70 H 72 73 

Ratio of Observed Velocity to Mean Velocity oyer Hie vertical. 

Sketch No. io.— Typical Curves showing the Ratios of the Velocities at various 

Depths in a Vertical. 

Roorkee Observations. The methods employed by Cunningham deserve careful 
study, and will be found very useful when abnormal circumstances are met 
with in gauging observations. 

The following rules, however, are entirely based on the results of modern 


Surface 


I 

— 

Rverage 

inflmen 

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54 


CONTROL OF WATER 


current meter work ; for the figures given by Cunningham are now known to 
be subject to errors which are greatly minimised in modern practice. For 
example, Cunningham’s twin float observations, although very accordant 
relatively to each other, are inaccurate ; and in consequence the twin float is 
now entirely abandoned. This is probably an error, as in shallow and not 
highly turbulent streams, twin float results are probably quite as accurate as 
any point velocity observations, except those which are taken by a 'current 
meter. The method was unfortunately applied to circumstances to which it 
was unsuited, and it has consequently suffered far more than it deserved. 

We define the velocity at any fraction (say ’n) of the depth of the stream, 
in the vertical considered, as the velocity observed at * n depth below the 
surface of the stream, and denote it by v. n . 

Then, we have as follows : 

I. One Point Methods. —(i) The mean velocity is equal to the velocity that 
occurs between 077 and 073 depth ; and, as a matter of observation ; 

the velocity at o'6 depth = mean velocity, or, 7/ 0 . 6 = 7/ ni . 

According to Hoyt and Grover {River Discharge ), the average result is 
^0-61 =v>n, the extremes being 073 and 078, and the error resulting from 
taking o*6 depth varies in 90 cases from —6 to +4 per cent., with a mean of 
o per cent, (see Sketch No. 10). 

The method is inapplicable to very deep (say, 40 feet and over) or decidedly 
shallow streams, although the mean for 210 examples of the latter is only 
*Vc=i*oi v m . 

If a stream is covered with ice, the o'6 depth method does not hold, v m 
occurring at about 07 depth. Barrows {Trans. Am. Soc. of C.E., vol. 66, 
p. 110), states that: 

Vm^O‘%2 tO 0*92 V 0 . 5 , 

with o'SBT/Q.g as a mean 

and Hoyt and Grover’s curves {tit supra) appear to confirm this. 

II. Two Point Method. —If the vertical velocity curve is a parabola, we 
obtain the following equation with rigid mathematical accuracy : 

2 Z/ m = 7/0.21 + ^ 0*79 

In actual practice, it is found that even if we cannot represent the velocities 
as a quadratic function of the depth, i.e. v. n , is not equal to a-\-b (* n) pc (vz) 2 , we 
find that: 

^ 0*2 T ^0-8 == 27/jjt 

Hoyt {nt supra), in 478 examples, finds maximum errors of +2'6, and —3 
per cent., and a mean error of +ot per cent., and for 219 curves in shallow 
streams, with rough beds, +1 *6, and — o*o, with a mean of -fo*5 per cent. 

The method holds for ice-covered streams, although errors of 4 per cent, 
may then occur, and may be regarded as universally applicable. 

This rule was first stated by Gordon, and his demonstration permits of 
extension. I fa, b, c, are quadratic functions of the horizontal distance from 
the centie of the stream, i.e. a = a 1 pb 1 xpc 1 x 2 , etc., where x, is the distance 
of the vertical from the centre of the stream, the mean of the mean velocities 
on the verticals at points 0*21, and 079 across the stream, is the mean velocity 
ovei the whole cross-section of the stream if the depth be uniform ; so that on 

this assumption observations at 4 points would give the mean velocity for the 
whole stream. 


POINT METHODS 


55 


The old method was : 

--—--— Vm 

2 

I do not presume to indicate how the velocity at the bottom, can be 
observed ; but since errors of 20 to 30 per cent, may occur, the question is not 
of very great interest. 

III. Three Poi?it Method. —Theory and experiment both indicate that : 

_' z / 0-2 + 2 ' z / 0-6 + ^ / 0*8 

I'm — 

4 

The error is a mean of the error of the one point and two point methods ; 
and in cases where the two point method is correct, and the o’6 depth 
method is inaccurate, we may actually increase the error by the third 
observation. 

An examination of Hoyt’s results leads me to believe that the extra 
accuracy secured is not worth the expenditure of time, and that a better 
distribution is obtained for the same number of observations by increasing the 
number of verticals. 

The old rule : y in — 2 Z/ o*b +^i-o 

4 

is open to the usual objections, and errors of 6 to 9 per cent, occur. 

IV. Special Methods. — {a) Surface Observations.—Here the meter is held 
o'5 to i*o foot below the surface, according to the depth of the stream. This 
is most useful in the case of floods. Hoyt and Grover give : 

^1 = 078 to o* 987 W ace 

and state that the deeper the stream, and the greater the velocity, the larger 
is the coefficient. 

For average American streams, in moderate freshet, we have : 

V m = O 90 ^surface 

For floods: 

Vm — Q 90 tO 0*95^surface 

But Harlacher’s rule (see p. 61) is better. 

(h) Mid Depth Method. —This is a relic of old practice, and should not be 
used, but I give the figures in the hope that the information will prevent 

further observations of this character. 

/ 

v m =o’g6 to 0*90 v 0 . 5 As a mean v m =o'giv 0 . 5 

V. Stimulation Method. —Here the meter is lowered to the bottom, and is 
raised again at a uniform rate. The reading of the meter (which is evidently 
a mechanical average of the rates at which it turns during its journey up and 
down the vertical) is assumed to correspond to the average velocity over the 
vertical. The results of the ordinary rating curve are used to obtain this 
average velocity from the observed reading. 

This method is therefore only applicable in the case of meters (such as the 
Fteley), Avhich are unaffected by lateral currents. 

The above figures give the errors produced by adopting any of the shorter 
methods of determining v m , when compared with the results obtained when 
v rn , is ascertained by 6 or 10 observations per vertical. Now, it is known 
that the discharge thus obtained may differ by 3 per cent, from the results of 
a weir gauging. We may, therefore, infer that either the 0*6 depth method, 
or the 0*24-0*8 depth method, will produce a result which probably does 





CONTROL OF WATER 


5 6 

not differ more from a weir gauging than would the theoretically more accuiate 
6 or io points per vertical methods. 

Nevertheless, comparisons of the results obtained by the shorter methods 
with weir observations are greatly to be desired, since it is plain that the 
agreement between all good current meter methods is too close to peimit 
comparisons between them to disclose any systematic errors. 

The only systematic investigation of the above question appears to be that 
undertaken at Cornell Hydraulic Laboratory (see Report on Barge Canal of the 
State of New York , p. 932). 

An abstract of the results is as follows : 


Mean Depth 
in Feet. 

^ t . Weir discharge 

Discharge by 0*6 depth method’ 

on 6 verticals 

Remarks. 

Observations worked 
up graphically. 

Observations worked 
up analytically. 

9'5 to 8*9 . 

8-5 „ 8*4 . 

7*7 „ 7*5 • 
6*3 „ 6-o . 

0*962 

0*961 

o *973 

0*964 

0 *956 ) 

0*970 q 

0*972 c 

0*962 ) 

Mean of 4 tests. 


Depth in Feet. 


Weir discharge 


Discharge by summation method on 6 verticals 

9*5 to 8*9 . 

0*994 

0*949 

0*986 

0*861 

8*5 „ 8*4 . 

0*937 

0-913 

0-973 

o* 7 i 9 

7*7 „ 7*5 • 

o* 95 1 

0*951 

0*961 

0*819 

6*4 „ 6*o . 

0*956 

1 

0-959 

0*971 

0*929 

• r ' 


In the first three cases of the last column the velocities were less than 0*5 
foot per second, so that the large errors are readily explained. 

The “ ordinary ” method consisted of velocity observations at 6 points on each 
of 6 verticals, and the results obtained were as shown in table on top of page 57. 

There is a certain amount of evidence to show that the weir discharges were 
subject to constant errors (see Horton, Weir Experiments Coefficients and 
Formula , p. 96). 

Making all possible allowance for such errors, the results are far worse 
than might be expected, and contrast markedly with those obtained with rod 
floats as given on page 59. I am inclined to consider that the whole set is 
affected by the smoothness of the channel and the slow velocities, and conse¬ 
quently the figures are of but slight importance in discussions concerning the 
discharge of rough channels such as occur in Nature. Errors in the actual 
observations are extremely improbable, so that the figures are of value if a 
smooth channel is gauged by such methods. 




















































ROD FLOATS 


57 


Depth in 

Ratio : 

Weir discharge 



Feet. 

Current meter discharge by’ 

“ ordinary ” method 

Remarks. 

9*5 to 8-9 

°’974 

0*982 

1*002 

i*i 49 

These are affected by 


0*980 

0*981 

0*994 

1*080 

velocities being less 
than 0*5 feet per 
second. 

8*5 „ S *4 

r°56 

1*012 

1*094 

1*072 

T *080 
0*999 

1*236 

I *979 

jj 

77 ,> 7*5 

1 *022 

i *°37 

0*999 

1*072 

5 ) 

6*4 ,, 6*o 

1 *°43 
1*023 

I *069 

1 *040 

1 *086 

I ‘°43 

1*083 

1 *048 



Summing up,—it may be inferred that the o*6 depth, or the o*2 + o*8 depth 
methods will probably, under favourable circumstances, agree with weir 
observations within 2 per cent., although individual observations may differ by 
5 per cent. Some portion of these differences can probably be attributed to 
errors in the weir observations. 

I consider that it is extremely doubtful whether any additional accuracy can 
be attained by such preliminary work as observing the velocities at 10 or more 
points per vertical, and then selecting the depth at which the mean velocity is 
found to occur, for all future observations. This method, however, was employed 
by Dowson, and may be useful in large rivers where, as already indicated, the 
o*6 depth method may possibly lead to errors. 

Rod Floats. —It is obvious that the velocity of a rod float, extending in a 
vertical line from the surface to the bottom of a stream, must be a fairly close 
approximation to the mean velocity over that vertical. 

The matter has been investigated by Cunningham ( Roorkee Hydraulic 
Experiments ) under the following assumptions : 

(i) The force acting on any small element of the rod is proportional to the 
square of the difference between the velocity of the rod and the velocity of the 
water in contact with the element. 

(ii) The vertical velocity curve is a parabola. 

Cunningham finds mathematically that v r , the velocity of the rod, is equal 
to v m when 4, the immersed length of the rod is from 0*950 to 0*927 the depth 
of the water ; the exact value depending upon the position of the maximum 
velocity in the vertical velocity curve. 

He takes as a mean : v m = v r , when the immersed length of the rod is 
equal to o'94 depth, i.e. 4 = 0*94^. 

An arithmetical study of 38 vertical velocity curves obtained by current 
meters leads me to believe that if Cunningham’s first principle is accepted as 
correct, the fact that a vertical velocity curve is not an exact parabola is of 
small importance. The mean result obtained was : 

Vr — 'Vm 1 when 4=0*952*4 

and the maximum value was 4 = 0*97*4 and the minimum 4 = 0*91*/. 






























5» 


CONTROL OF WATER 


The adoption of h — o’^/\d led to a mean error of-j- i per cent., and maximum 
errors of+4 per cent, and —3 per cent 

When practically tested, the rod float does not compare quite so well with 
the current meter, as the above figures indicate. 

As already stated, this must mainly be ascribed to the irregularity in flow, 
which affects all floats more markedly than current meters, since a float 
practically at rest in relation to the water, and is therefore mostly influenced by 
the irregularities of a small volume of water ; while a current meter is acted on 
by a fresh volume of water at every instant. 

Thus, taking Cunningham’s observations : 

In a current meter the mean of 6 observations gave v = 4* 13 feet per second. 

The mean of the next 6, v—/y\\ „ „ 

the maximum and minimum individual values being 4*36 and 3*84. 

While, for 50 floats the mean was v— 3*95 feet per second. 

The mean of the next 50, v = y%6 „ „ 

and the maximum and minimum individual values were 4*44, and 3*33. 

The figures do not allow of an exact comparison being made, since the 
current meter observed the velocity at 5 feet depth, while the rod floats deter¬ 
mined the mean over a depth of 10 feet. But it will be plain that 6 observa¬ 
tions of a current meter are more effective in the elimination of irregularities, 
than 50 floats. 

So also, Cunningham’s investigation of the relation between v r , and v m , does 
not appear to hold good in practice ; and, as a rule, rod float gaugings are 
found to give too high a result when checked by weir or current meter 
methods. 

I he only systematic comparison of rod float gaugings and weir measure¬ 
ments was undertaken by Francis (Lowell Hydraulic Experiments). The dis¬ 
charge was measured by rod floats in a smooth, timber-lined channel, and also 
over a weir. Putting Q r for the rod float discharge, and Q w for the weir dis¬ 
charge, Francis finds that : 

Qiv=Qr { 1 — o*ii 6 (VD— o*i)} 

where D = —That is to say, D, is the ratio of the portion of the depth 

which is not covered by the rod, to the total depth. 

Francis assumes that v m = v r {1 —o*n6(V , D — o*i)}, and his experiments 
cover the range D = 0*004 to D =0*129. The circumstances are in no way 
comparable to those under which rod floats are usually employed. Francis is 
known to have been a most careful experimenter, and there is not the least 
doubt that he observed the velocity on a sufficient number of verticals to secure 
substantially accurate values of Q r . Nevertheless, if his observations re¬ 
presented a rod float gauging of an earthen channel, they would be rejected in 
accurate work on the ground that the verticals were too widely spaced. Thus, 
the relatively smoother gauging channel in which Francis’ observations were 
made has evidently caused the horizontal distribution of the velocities to differ 
widely from that which obtains in earthen channels ; and it is therefore probable 
that the vertical distribution of velocities (and consequently the relation between 
v r and z/ m ) is also altered. 

The following results were obtained at the Cornell Hydraulic Laboratory 
(see State of New York Barge Canal Report , p. 923): 



GAUGING OF STREAMS AND RIVERS 


59 


Average Depth of 
Channel. 

. Weir measurement 

Mean of 5 rod floats per vertical 


4 = 075 depth. 

4 = 0*90 depth. 

Feet. 



9*3 

0*989 

I * 00 3 

8*3 

°'955 

°*97 3 

7*5 

0*962 

0*980 

6*3 

0*960 

0*971 


It will be seen that Francis’ statements are generally confirmed, and that 
the accuracy is somewhat better than I later indicate. 

The experiments appear to have been made in a smooth, concrete lined 
channel, and are therefore not rigidly comparable with the results obtained 
under the more irregular conditions occurring in earth channels (even if 
smoother than usual). Certain special experiments of my own indicate that 
the results obtained with floats immersed to only 75 per cent, of the depth 
would, in the case of regular earth channels (where Bazin’s y=i*5, and Kiitter’s 
^ = 0*020), usually be some 5 per cent, greater than the values obtained with 
a 90 per cent, immersion of the floats. In rougher channels (where Bazin’s 
7 = 2*3, and Kiitter’s 11 — 0*027) the difference is even greater, but these last 
observations were taken under circumstances which were not at all favourable 
to accurate work. 

In actual work, the errors which specially affect rod float gaugings are 
mainly caused by the fact that the irregularities which exist in the beds of 
natural streams are usually sufficiently marked to prevent a rod of a length 
equal to 0*90 or 0*94 of the mean depth being used to observe the velocities. 

In the Punjab Irrigation Branch the rod float is the standard gauging 
instrument, and the conditions existing are those to which the method is 
best adapted. 

The gaugings are taken in channels of regular section, usually specially 
trimmed, or lined with brick-work ; so that it is possible to run a float only 
3 inches, or at the most 6 inches, shorter than the depth of the water. It is 
always possible to select a site with a straight stretch of canal up-stream, so 
that cross currents are infrequent. The labour available is cheap, but is 
unskilled, and gaugings are frequently taken by comparatively untrained 
observers. 

When a good site is selected, the method is a very excellent one ; and so 
far as can be judged from results (checked where possible by other methods) 
I believe that a good gauging rarely errs by more than : 


i per cent, for discharges up to 

60 cusecs 

2 

jj 

3 °° „ 

3 55 


5 °° 

4 

)> 

1000 „ 

5 

>> 

2000 ,, 


/'The more or less con¬ 
stant error hereafter 
discussed being ne¬ 
glected, so that the 
comparison is really 
with other rod float 
l gaugings. 





















6o 


CONTROL OF WATER 


Above 2000 cusecs it appears that the method is not very accurate ; but 
this, I believe, is owing to the fact that it is almost impossible to find a 
gauging length where the bed is sufficiently uniform to permit a rod being run 
which is only 6 inches less than the depth. If this were possible, I consider 
that the method would prove equally satisfactory. 

It is not customary in the Punjab to correct the velocities by Francis’ 
formula (p. 58). 

I think that this is a mistake. My own experiments, and those of at least 
two other officers, lead me to consider that this correction is a very valuable 
one, and it should certainly be employed wherever justified by the accuracy of 
the rest of the work. If it is applied to a series of gaugings, I believe that the 
relative errors, above tabulated, may be reduced by one half. 

Rod floats are usually of wood, f inch, or in the larger lengths 1 inch 
square, weighted so as to show only 1 to inch above water. A useful set 
starts at 1 foot immersion, and proceeds by steps of 3 inches up to 4 feet; and 
then by steps of 6 inches up to 8 feet, with three rods of each length. Greater 
lengths are best made of watertight tin tubes, weighted with shot; indeed, this 
material should be adopted wherever gaugings are taken in close succession ; 
for wooden floats, if used so frequently as to get water-logged, are liable to sink. 

The Punjab instructions are that 5 rods should be run in each vertical, 
and the mean be taken as the velocity in that vertical. The verticals are 
equally spaced across the canal, 10 feet apart in large, and 5, 4, or 2 feet apart 
in smaller channels ; and there are usually 10 verticals in the total width. 

The relative errors of good gaugings in the Punjab have already been 
given. There is, however, very little doubt that all rod float gaugings over¬ 
estimate the discharge, and that the whole evidence shows very clearly that all 
Punjab gaugings are, on the average, some 3 per cent, in excess of the truth. 
In good observations, such as were alone considered when obtaining the above 

figure, —is rarely greater than 0^05 ; so that the application of Francis’ 

correction would leave about one-half the difference unexplained. While the 
individual observations are probably subject to at least this amount of error, 

I consider that the mean result is quite sufficiently accurate to permit the 
statement to be made that a correction formula : 

Q = Qr {1 -o' 2 (Vd -o*i)}' 

where D, represents the mean value of ^ ' J\ for all the floats observed, is 

probably more accurate than Francis’ when applied to gaugings in earthen 
channels, provided that D, does not greatly exceed o’10. The formula has 
been systematically checked for discharges up to about 0 = 150 cusecs. 
Above this value the checkings are less reliable, and the principal evidence in 
its favour is the fact that if the discharge of a canal is observed with say 
D =0*20, and simultaneously with say D=o*o5, the two values of the discharge 
are found to agree very closely when corrected by this method. 

It is believed that the value of the coefficient which Francis gives as o‘ii6, 
and I give as 0*2, increases with the roughness of the bed. The figure 0*2, 
corresponds approximately to Bazin’s 7=1*54, or Kiitter’s 72 = 0*020. 

Summing up, the rod float system of gauging is a very practical method for 
systematic work, and untrained men can rapidly be taught to do good work. 




SURFACE FLOATS 


61 

In my opinion, the smaller size and weight of a current meter constitutes its 
only decided advantage in gauging regular canals. For natural streams and 
rivers, however, the current meter should be adopted. 

Surface Floats.—The use of surface velocities in estimating the discharge 
of a river can only be considered as a makeshift. The method is justifiable 
under the following conditions : 

(d) In floods, when a boat cannot be accurately manceuvered on the river, 
and where the soundings are consequently known to be subject to errors which 
render any more accurate method of obtaining the velocities unnecessary. 

(b) In rough reconnaissance work, when time, material, and labour for the 
more accurate systems are not available. 

The surface velocity is probably less affected by irregularities of the water 
motion than any other velocity of the stream. On the other hand, it is greatly 
influenced by wind and bends in the course of the stream. 

In order to avoid wind effects I have found it best to use globular floats, rather 
than flat pieces of circular board, such as are usually recommended. Where a 
supply of oranges is available, they form ideal surface floats, and have the great 
advantage that they can be thrown to the desired position with fair accuracy. 

The best method of treating the observations is due to Harlacher, and 
appears to accord very closely with the real facts. 

Harlacher (. P.I.C.E ., vol. 91, p. 399) states as follows : 

No very constant ratio exists either between V m , the mean velocity over 
the whole cross-section, and the maximum surface velocity, or v ms , the mean 
of the surface velocities ; but if v s , be the surface velocity at any point, the 
total discharge of the stream is represented by : 

Q =p'2v s x corresponding partial area 

Thus, pv s , may be considered as a quasi mean velocity over the vertical 
below it, although it is not equal to v m the mean velocity in that vertical as 
obtained by direct observation. 

In 28 gaugings in the Danube and Bohemian rivers, with widths ranging 
from 160 to 1400 feet, maximum velocities varying from 2 to 10 feet per 
second, and depths between 2*5 and 25 feet, the value of/, was always between 
079 and 0*91, and lay between 0-83 and o*88 in 23 cases. 

Harlacher also states that /, is greatest for sandy beds, and that the 
minimum value occurred with beds of gravel of fist size. 

He suggests that fi, may generally be taken as 0*85. 

In Switzerland, for 200 cases, the mean value is 0-835, an< ^ it is evident that 
this smaller figure is due to mountain streams, possessing gravelly or stony beds. 

For the Rhine, in Holland, the value rises to 0*87, owing to the finer quality 
of the sand. 

For the Punjab rivers, where the sand is extremely fine, the ratio is usually 
taken as 0-93 ; but I consider that this is somewhat high, since these gaugings 
are taken with a view to estimating flood discharges, and a slight overestima¬ 
tion is recognised as by no means undesirable. 

Thus, if the surface velocities are observed at points distant l feet from 
each other, all across the river, and if d m , be the mean depth corresponding to 

the width — on each side of the point where v s , is the surface velocity, then : 

2 J 

D i scharge = p^ld m v s 


6 2 


CONTROL OF WATER 


The rule given above may be supplemented by Grunsky’s results for 
25 Californian streams (Tram. Am. Soc. of C.E ., vol. 66, p. 123). Grunsky 

assumes that —, is approximately the same for all verticals in a river, and 
v s 

consequently we can put: 


Vyn _ ^Vm _ a 
V s 27's 


as 


in Harlacher’s rule. 


In streams with sandy bottoms, Grunsky finds that /, depends only upon 
the ratio : 


Width of stream 
Mean depth 

and gives the following table : 


w 

d 

P 

W 

d 

P 

5 

IOI 

3 ° 

o’89 

10 

°'97 

40 

o'Sj 

15 

°’94 

5 ° 

0-85 

20 

0*92 

100 

» 

0*82 


An examination of the individual results shows that 14 cluster very closely 

W 

round/=o‘9o, and these 14 include values of , from 18 to 32. The evidence 

afforded is therefore not in conflict with Harlacher’s rules, and classification by 
the character of the bed appears to be more likely to produce accurate results. 

*v - 

Hoyt and Grover (River Discharge ) give a large number of values of 

V s 

The maximum value is 0*98, and the minimum 078, but the average of 138 
curves is o‘85, and the figures cluster closely round this value. For small 
streams with rough beds the maximum value is 0*89, and the minimum 078, 
and the average of 219 curves is o’84. 

In practice these authors only employ the method in gauging floods, and 
state: 

The deeper the stream, the larger is the coefficient. 

For average (American) streams, in moderate freshet, 0-90 will generally 
give fairly accurate results. In floods, 0*90 to 0*95 should be adopted (see 
P- 55 )- 

Special Methods of Gauging. —The following methods are approximate. 
The only justification for giving any details of such methods lies in the fact 
that a bad gauging is better than none at all. In actual work, good observers 
should obtain their own values of the ratios now enumerated from the results 
of two or three careful preliminary gaugings conducted by accurate methods. 
Discharges which are obtained in this manner may be expected to agree 
inter se within about 5 to 7 per cent, of error. Thus, the following tables are 
in reality suggestions for preliminary observations. 

If the ratios are taken from the table, and are blindly applied, the compar- 





















APPROXIMATE METHODS 63 

ative errors will not of course be increased, but the absolute errors may be 
doubled. 

It is usual to give certain tables showing the probable ratio of the mean 
velocity in a vertical v m , to the surface velocity v s , or the maximum velocity 
^max, or the velocity near the bottom v^q. 

So far as can be ascertained, these ratios are extremely variable, and are 
considerably influenced by irregularities in the motion of the water. I have 
been unable to trace any case in which ratios obtained by one observer were 
found to agree accurately with those obtained by another observer, even under 
circumstances which were apparently quite similar. 

Central Vertical Method. —Bazin’s experiments, as calculated by Bellasis, 
(.Hydraulics , p. 165) give : 


RATIO. 

Mean width 


r 5 





Mean depth 

Mean velocity 

1 

o*86 

2 

o*88 

3 

0*89 

4 

0*90 

5 

0*91 

0-87 

Mean velocity in central vertical 

Mean width 

6 

7 

10 

20 

30 

5 ° 

Mean depth 


Mean velocity 

0’92 

°'93 

0-94 

°‘95 

o'96 

0*97 

Mean velocity in central vertical 

Mean width 

90 






Mean depth 






Mean velocity 

0*98 






Mean velocity in central vertical 


• • • 





These are applicable to rectangular and trapezoidal sections, and are 

. . mean width . . . , 

probably correct to 1 or 2 per cent, when the mean dept h 1S eSS than IO ’ and 

to o*5 per cent, when this value is exceeded, except when the side slopes are 
very flat, provided always that the channel upstream of the point of observation 
has no marked irregularities for a length equal to at least 20 times the width. 
If there are great irregularities, say 5 times the width above the point of 
observation, errors of 5, or even 10, per cent, may occur in either direction. 
Maximum Velocity Method—¥ ox a single vertical, it is usual to state that 

— has values varying from 0-98 for the deepest portion of large rivers, down 

^ma x 

to 0-85 for shallow and gravelly streams. On investigating the original 
authorities for these statements I am inclined to believe that no reliance can 
be placed on these figures. In any case, I am totally unable to conceive what 
practical object can be attained by a knowledge of their values. I have 
already stated what I believe to be the most useful function connecting v s and 
v m the mean velocity over the vertical. 

Surface Velocity Method. —Bellasis {lit supra , p. 169) gives a table of values 






























64 CONTROL OF WATER 

of , for verticals not too close to the banks, classified according to the depth, 

Vs 

77 

and Kiitter’s n. The general law is fairly well known, —, increases as the 

v s 

depth increases, and as n decreases. 

The following portion of his table is probably as accurate as any estimation 
ofor y, without systematic measurements, will be : 


d in feet 

Knitter’s. 

n = 0 '020 

« = o'oi75 

zz = o*oi 5 

7Z = 0 ' 0 I 3 

zz = o'oio 

°’9 

0-83 

o'86 

o'88 

0-89. 

CC9I 

i’i 

0^84 

0*87 

0*89 

0*90 

0*91 

1-25 

0-85 

0*87 

o '89 

0*91 

o'9I 

i'5° 

0*87 

o'88 

0*90 

0*91 

0*92 

Bazin’s y . 

i *54 

°‘ s 33 

... 

C290 

0*109 


For values of n, greater than n = 0*020, better information is now available 
from the results of the current meter gaugings undertaken of late years in the 
United States. 



Ktitter’s. 




Cl 




11 = 0-030 

n = 0*025 

I 

078 

0*82 

2 

0*80 

0*86 

3 

0*83 

o*88 

5 

0-85 

0*89 

10 

o'86 

0*90 

T 5 

0*87 

0*91 

20 

o-88 

0*92 

Bazin’s y . 

3-i7 

2 ‘35 


Bellasis’ figures for n = 0-025, show a decrease for depths greater than 
10 feet. The more modern figures do not confirm this, and Bellasis probably 
relied too much on old twin float results. A test of this table on 100 curves 
taken at random allows me to state that these figures are probably accurate 
to 3 per cent, when there are no marked disturbances upstream. The ratios 
are, however, almost useless, as Harlacher’s fi, is better adapted for practical 
purposes. 

Central Surface Velocity .—There is a certain amount of evidence to show 

























































PITOT TUBES 65 

that the ratio between v Cft , the central surface velocity, and V m , the mean 
velocity, is approximately constant. 

In a regular channel with no marked irregularities, 

V m = o‘8i to 0*89 v cs , 
or, as a mean, V m = cr84 t cs : 

The ratio is a useful one, and if determined for a well selected site by 
special experiments, it will be found to be but slightly affected by small 
alterations in the water level. 

Bottom Velocities. —The ratio has been stated to range from o'68 to 

070. As a matter of fact, what has probably been observed is not v 1<0 , the 
velocity at the bottom, but T 0 . g , or v 0 . gB , according to the depth of the river, 
since it is hardly safe to allow a current meter to be less than 6 inches from 
the bottom of the river. 

The following values are obtained from Bellasis’ suggestions : 


Ktitters n. 

0-030 to 0-0275 

0’020 

0-015 

O'OIO 

Depth .. 

5 to 18 feet 

i to i *5 foot 

1 to 1*25 foot 

I foot 

zVo 





v m 

°’5° to °*55 

°*5° to 0*55 

o‘6o 

• 

0-65 


My own experiments on silt-carrying canals with n — C019, ory= 1*5 approxim- 

ejj 

ately, give =0*50 to 0-62; and as a mean, 0*58 for depths ranging from 

Tm 

o'8 to 2*4 feet. I believe that the method used to observe the velocities is 
likely to give results which are less than the truth. 

None of the figures given have any real accuracy, being undoubtedly subject 
to 10 per cent., and possibly even 20 per cent., of error. 

Pitot Tubes. —Pitot tubes, or more accurately Darcy’s modification of 
Pitot’s original apparatus, are instruments consisting essentially of two tubes 
with orifices so situated that in the one tube (the impact tube) the orifice can 
be made to face the current and receive its full impact; while the orifice in the 
other tube (the pressure tube) is parallel to the direction of the current. Thus, 
theoretically, in the first tube the water stands at a height equal to the static 
pressure, plus the dynamic pressure; while in the second tube the static 
pressure alone is indicated. 

It will be seen that the water level in the second tube (if exposed to atmos¬ 
pheric pressure) would be level with the surface of the stream, and would, 
therefore, be rather hard to observe. Hence, in Darcy’s form of the instru¬ 
ment, as a rule, both tubes are united at their upper ends, and air can be 
removed (usually by sucking) so as to raise the water levels by the same 
amount. 

Theoretically, if h, be the difference in level of the water columns, then 
t/2 — 2 gk, gives the velocity of the current. In actual practice, it is extremely 
difficult to prevent the pressure orifice from being exposed to some action by 
the current, usually in the nature of suction, producing a depression of the 

5 

























66 


CONTROL OF WATER 


corresponding water column. Hence, as a rule, v = C V2 gh, where C, is a 

coefficient. ... 

It may at once be stated that all, or nearly all, our difficulties in using 

Pitot tubes arise from the pressure tube. White ( Journ .. of Assoc, of Eng. 
Societies, August 1901) has proved that the water level in the gauge con- 



' w 
<v 
tb 
3 
cj 

o 

"XU 

C 

<u 

S-. 

Q 

C 

d 

in 

<U 

22 

3 

H 

4-> 

o 

(S 


1n 

s 

3 

Eb 

d 


O 

£ 

X 

U 

H 

Ed 

CO 


nected with the impact tube (when exposed to atmospheric pressure) 
always stands at a height h x above the surface of the water in the channel, 
given by v 2 = 2 gh v whatever be the form of the orifice. White’s orifices 
included such diverse forms as knife-edged orifices in finely tapered pipes, 
conical trumpet mouths, and small holes in wide flat surfaces. Consequently, 





































































PRESSURE TUBES 


67 

it may be said that it would be very difficult to design an impact tube orifice 

r> 2 

which did not indicate an excess of pressure equal to — relative to the free 
water surface. 

On the other hand, it appears to be a difficult matter to construct a pressure 
tube which does not show either a slight rise, or a small depression, caused by 
the velocity of the water passing its orifice. If this rise be represented by 
2/2 

/i^ = k it is plain that the difference of level read in the two columns, when 

lifted above the water level for convenience in observation by exhausting 
air, is : 

h — h x — /z 2 = (1 — k) —. 

2 g 

I 

So that v — C V zgh, where C = ^ ^ ; and k is usually negative, so that 

C is less than 1. (See Sketch No. 11, Figs. 1 and 2.) 

The information at present available on the laws affecting the value of C, 



is not of much practical value. It was believed that the form of the impact 
orifice had the greatest effect on C, and it was not until White (ut supra) 
carefully investigated the matter, that the paramount importance of the circum¬ 
stances of the pressure orifice became known. 

The most favourable position for the pressure orifice appears to be in the 
side of a tapering pointed rod, as indicated in Sketch No. 12, which shows a 
combination of pressure and impact orifices in one piece, which has certain 
advantages as regards compactness. 

Here White, in flowing water, with a — 2 >i inches, b = \ inch, and c = |th 
inch, obtained C — roo7i in one instrument, and C — 0*993 * n a “duplicate 
copy” ; which would suggest that the true value for both was C = rooo. 

The first tube was afterwards provided with a linseed oil differential gauge 
(theoretical magnification 12*8), and was tested at 26 known velocities, in 
flowing water, against a Price current meter which had been previously rated. 
The results were : 

For the Pitot tube, 

2/ == 0*993 v' 2 gh, in place of 1*007. 

The maximum value was C = 1*028, and the minimum C — 0*910, which is 
almost certainly an error in reading. 



































































68 


CONTROL OF WATER 


In the case of the current meter, 


the true velocity = 0-983 indicated velocity, 


the maximum being roi8, and the minimum (probably erroneous) 0-893. 

We may, therefore, consider that a properly designed Pitot tube is capable 
of giving results which are as accordant inter se, as those of a current 
meter. 

So also, Gregory {Trans. Am. Soc. of Meek. Eng., vol. 25, p. 184), in 
flowing water, obtained with a = 1inches, b — f inch, c = Jth inch, C = 1-003, 
and C = 0-995 in a “duplicate.” 

The experiments of Lawrence and Braunworth {Trans. Am. Soc. of C.ELs, 
vol. 57, p. 273), who obtained C = 1-005 with a blunt ended tube, where 
a = 0*03 inch, b =0-17 inch, and c — o*i inch, indicate that the taper form 
of the tube is of little importance, provided that the orifice is in the side of 
the tube, and is not too close to other tubes. 

In the case of a smooth pipe under pressure, it would appear that a smooth 
hole |th of an inch in diameter (with all burrs carefully removed) bored in the 
side of the pipe, gives C = rooo, when used for a pressure orifice ; but if the 
surface of the pipe is in the least encrusted, C, may vary between 0-95 and ro6. 
C, is also influenced, even in smooth walled pipes, by curves or other ir¬ 
regularities in the pipe above the orifice, and in some cases this influence may 
extend for several hundred diameters of the pipe, down stream of the curve. 

Practical Details .—All water motion is irregular, and it is only because 
our apparatus possesses inertia that we obtain even the amount of apparent 
constancy actually observed. 

A Pitot tube has exceedingly little inertia (that of the water columns and 
their frictional resistance only). Thus, in default of some artificial inertia being 
added, we should have a continual fluctuation of the water surface, which would 
entirely preclude accurate readings. The usual method is to enlarge the tubes, 
just above the orifice, into a drum-shaped vessel, as per Sketch No. 11. 

For values of v, exceeding 4 feet per second, h , is fairly large, 3 inches or 
over, and can therefore be observed with some exactitude ; but where it is 
desired to accurately observe small velocities, a differential gauge must be 
used. Here, if water and a liquid of a density be employed, h, is increased 

in the ratio —-—; but in actual work, tests must be undertaken in order to see 
1 ~~P 1 

whether capillary attraction, or viscosity, alter this ratio. 

The general formula for a differential gauge containing liquids with densities 
equal to p 1 and p is : 


Observed h=h for a water gauge x and if air is included, as in Sketch 


P~P 1 


No. 11 (Fig. IV.), the factor is 


■a 


where a, is the density of air. 


P~P 1 

As an example, take kerosine, p x — o*8o approximately. In the first case, the 

factor is =5- In the second case, "y—= 4'994 say. 

Actually, the best method is to observe the ratio when the height on the 
water gauge is sufficiently large to be read with accuracy, as shown in Fig. iv. 
Sketch No. 11. 

In Williams’ experiments {Trans. Am. Soc. of C.E., vol. 47, p. 1), the 




VALUE OF C 


69 

observed ratio was about 4 per cent, greater than the calculated ; and the 
small alterations in p x due to the change in temperature did not appear to 
affect this excess. In White’s ( ut supra) linseed oil gauge, p x = 0*922, and the 
increase was probably 2*8 per cent. 

A Pitot tube, as described above, probably forms the most accurate method 
of observing velocities. 

Reference may be made to papers by Stanton ( P.I.C.E. , vol. 156, p. 86), and 
by Smith ( Proc. of Victorian I?ist. of Engineers, November 1909) for details of 
such instruments. 

I am, however, inclined to believe that this very possibility of intense refine¬ 
ment renders a Pitot tube unsuitable for purely engineering purposes, where, 
as is almost invariably the case, the water is in turbulent motion. An engineer 
generally wishes to obliterate the effects of this turbulence, and desires a mean 
result corresponding to the undisturbed portion of the motion. He also usually 
wants to observe the average velocity of the water, and not an average of the 
squares of the momentary velocities as given by a Pitot tube. As indicated by 
the second formula on page 49, the current meter also appears to average the 
squares of its own momentary velocities ; but owing to its greater inertia, the 
results do not materially diverge from the average of the momentary velocities 
of the water, since the vanes of the current meter do not follow the momentary 
variations of the water velocity so closely as the water columns of a Pitot tube 
do, even when the tube is enlarged, as already suggested. 

If the various cases in which the Pitot tube is practically employed are 
considered, it will be found that they are usually restricted to the measurement 
of velocities in pipes, and that the best results are obtained at, or close to, 
nozzles or other orifices ; and further, that the motion in these cases is almost 
invariably less turbulent than in open channels, especially if these have rough 
boundaries, such as occur in earthen channels, or river beds. 

Thus, it will readily be inferred that the calibration of a Pitot tube presents 
difficulties analogous to those found in the calibration of current meters, but in 
a more marked degree. 

The experiments of Darcy and Bazin ( Recherches Hydrauliques ), or of 
Murphy ( Trans . Am. Soc. of C.E., vol. 47, p. 197), are the most complete. 

Putting v — C V 2 gh in the following cases we have : 

(1) 92 ratings in moving water, v, being obtained by floats. 

Mean value of C = roo6. Maximum value, ro39. Minimum value, 0*981. 

(ii) 87 ratings in moving water, tube used to determine the discharge, and 
checked by a weir. 

Mean value of C = 0*993. Maximum value, 1*029. Minimum value, 0*965. 

(iii) 32 ratings, in still water. 

Mean value of C = i'034. Maximum value, 1*053. Minimum value, 1*015. 

With another tube they obtained the following results : 

I. Impact orifice directed against the current, pressure orifice parallel to current. 

C = 0*848 by floats. 

C = 0*797 in still water. 

II. Both orifices directed against the current, but the pressure orifice 
plugged, and a small hole 0*04 inch in diameter pierced laterally. 

C = 0*875 by floats. 

C = 0*864 in water. 


70 


CONTROL OF WATER 


III. Impact orifice directed against the current, pressure orifice facing 
downstream. c = 0 - 99 8 by floats. 

C = 0*991 in still water. 

Williams, Hubbell, and Fenkell {Trans. Am. Soc. of C.E. , vol. 47, p. 199) 
find as follows : 

(i) Pitot tube No. 3. 

Rated in still water. 85 observations. 

Mean value of C = 0*914. Maximum value of C = 0*975. Minimum value 
of C = 0*821. 

(ii) Rated in a 2-inch brass tube (the impact tube held in centre of pipe), 
and the volume obtained by weighing the discharge, so that the absolute in¬ 
dications are subject to some uncertainty. The pressure orifice was a hole in 
the side of the tube. 

13 Ratings. Mean value of C = 0*729. Maximum value of C = 0*740. 
Minimum value of C = 0*718. 

(iii) Do., but pressure orifice a circumferential slit in the side of the tube. 

13 Ratings. Mean value of C = 0*779. Maximum value = 0*789. Minimum, 

value = 0*764. 

II. Pitot tube No. 5. Gives under circumstances similar to the above : 

(i) 133 observations. Mean of 0=0*835. Maximum, 0*916. Minimum, 
0*677. 

Or, with another pressure tube : 

112 observations. Mean of C = 0*851. Maximum, 0*942. Minimum, 0*705. 

(ii) 29 observations. Mean of C = 0*694. Maximum, 0*727. Minimum, 
0*647. 

III. Pitot tube No. 6. As above. 

(i) no observations. Mean of 0 = 0*966. Maximum, 1*091. Minimum, 
0*895. 

(ii) 13 observations. Mean of C = 0*683. Maximum, 0*695. Minimum, 
0*659. 

(iii) 13 observations. Mean of C = 0*784. Maximum, 0*799. Minimum, 
0*749. 

The final coefficients employed were : 


Tube No. 

In Still 
Water. 

In Pipes. 

Diameter of Pipe 
in Inches. 

3 

0*926 

0*89 

2, 5, and 12 

5 

0*859 

0*75 

3° 

6 

0*950 

0*846 

16 and 30 


The skill and care displayed by the experimenters was most remarkable, 
but a study of the above figures seems to afford ample proof that their tubes 
were unreliable when applied to absolute measurements of the velocity at 
a point. 

The experiments are otherwise of great interest. I have studied them 


















“ PITOMETERS ” 71 

very carefully by mean square methods, and am inclined to believe that the 
effect of the irregularities is very nearly eliminated in their discharge measure¬ 
ments, and that their discharge values are rarely subject to 1*5 per cent, of 
error. Thus, the application of even such tubes as the above, to obtain 
discharges, appears permissible. 

The whole available experiments (without exception) indicate that a still 
water rating of the normal Darcy tube will give a higher value of C than 
that obtained in flowing water. There are also indications which show that 
the difference is greater, the more C (as found in flowing water) diverges 
from unity ; but there are exceptions to this rule. Also in each case, the 
values of C, vary somewhat irregularly, through rather wide limits. 

It will be observed that rating in flowing water is productive of far more 
concordant results, and many of the divergencies there observed are to be 
ascribed to imperfections in the method of rating. This is especially the 
case when the method used by Williams and others is adopted, which consists 
in observing the central velocity by a Pitot tube, and calculating its ratio 
to the volumetrically observed mean velocity by equations which are them¬ 
selves subject to a certain amount of probable error (roughly 0*85 that of C). 
We may thus assume that the C, given by ratings in flowing water, is far 
more constant than that given by still water ratings. 

Comparing these results with those of White (see p. 67), we are led to 
infer that the variations in C, from run to run, are not entirely due to errors 
of observation, but have a real physical existence dependent on the irregularity 
of the motion of the water, and are the more marked the greater the difference 
between the mean coefficient and unity. 

When accuracy is desired, it is therefore essential to calibrate Pitot tubes 
in flowing water, and to design them so as to obtain C^rooo, which is best 
attained by following the lines of Sketch No. 12. 

The general impression left on my mind is that each Pitot tube (or rather 
the pressure orifice of each tube), even when supposed to be an accurate 
duplicate of one already calibrated, must be individually calibrated. There 
is no doubt that this is the case when the accuracy of duplication is equal to 
that of ordinary handwork. 

In order to avoid these uncertainties, Gregory ( Trans . Am. Soc. of Meek. 
Eng., September 1908) and Cole, have designed Pitot tubes where the pressure 
tube is an exact reduplication of the impact tube, except that its orifice is 
turned downstream. The experimenters assume that the indications of 
duplicate instruments of this construction, will agree ; and if this is the case, 
the device has made the Pitot tube a standard instrument which can be 
manufactured in quantities, and distributed for use. Nevertheless, definite 
proof is desirable ; since, at present, general practical employment forms the 
only basis for the above statement. 

Gregory obtains for his type . . v = 1'133V igh 

Cole obtains for his type . . . v — IT9V2 gh 

apparently by calibration in flowing water in pipes (see Sketch No. 12). 

Thus, I consider that the usual field of utility of a Pitot tube will be found 
to lie in gaugings of pipes and other extremely smooth channels of small 
dimensions. 



72 CONTROL OF WATER 

The preliminary studies require time. We must (so I believe) calibrate the 
tube in the actual pipe which it is intended to use, and fix the instiument at 
a point in the cross-section of the channel where its indications aie found to 
bear a definite ratio to the mean velocity of the water flowing in the channel. 
Then, as the tube offers an extremely small resistance to the motion of the 
water, it can be permanently left in the pipe, and can be used as a lecording 
instrument. Cole, by employing photography to record the oscillations of 
the water columns, has constructed a water meter which lecords the total 
quantity passing through the pipe each hour, or each day. 

The method is open to many theoretical objections. In the first place, 
Williams (ut supra) and Bilton (Pros, of Hictorian I?ist. of Engineers , 1909) 
have shown that the distribution of velocities over the cross-section of a pipe 
greatly depends on the mean velocity, and Bazin {Trans. Am. Soc. op C.E ., 
vol. 47, p. 258) has shown that it depends on the roughness of the pipe. 
Thus, the Cole pitometer will probably record a velocity which is only equal 
to the mean velocity for one particular value, and this value will vary from 
year to year as the pipe becomes more encrusted. On the other hand, with 
the exception of the more costly, and less easily fixed Venturi meter, no 
other simple instrument exists which will permit the momentary flow to be 
as easily ascertained as time is read from a watch ; and personally, I should 
prefer to know the quantity of water used within 10 per cent, without trouble, 
at any moment, rather than to ascertain it to within 1 per cent, once a week, 
with difficulty. 

The original apparatus used by Pitot consisted of one tube only, i.e. that 
which has here been termed the impact tube. ' As already stated, this apparatus 
may be regarded as needing no calibration, provided that the zero of can be 
accurately ascertained. 

In the case of open channels, the free water level can be very closely 
determined by means of Bazin pits (see p. 101), or ordinary gauge wells 
(see p. 103). When studying silt problems I have found the simple impact 
tube most useful in obtaining velocities near to the bottom of a canal. These 
velocities being low, the two fluid gauge must be employed. So far as my 
experience goes, the method is the best which we possess for ascertaining 
bottom velocities in silt-laden water, as it has none of the defects of current 
meters or of sub-surface floats ; although, where the bottom can be seen, 
these latter (preferably in the form of red currants) are very simple, but 
less reliable. 

So also, an impact tube attached to a mercury column, or the ordinary 
Bourdon pressure gauge, is very useful for the study of jets, such as are 
employed in impulse wheels. Here, a design is required possessing sufficient 
strength and stiffness to resist the pressure of the flowing water (which may 
amount to values equal to 100 lbs. per square inch), and of such a form that 
spattering and splashing from the jet does not occur. Eckhart’s design 
{Proc. of Inst, of Mech. Engineers , 1910) seems very excellent. A piece of 
sheet steel f inch thick, and 2\ inches wide, is drilled through its 2b inch 
width with a inch hole, and the back of this hole is connected by a fair 
curve with an £ inch steel tube, soldered to the back of the plate. The 
front of the plate, and the tip of the front end of the hole, are sharpened off 
to a knife edge ; and the whole plate can be slid in and out of the jet by a 
screw and lock nuts working in a fixed grooved clamp. 


CHEMICAL GAUGING 


73 


Gauging by Chemical Methods. —The principle is very simple. Sup¬ 
pose that a weight of iv lbs. of a chemical be added each second to a stream 
discharging Q cusecs, and that after thorough mixture a sample taken from 
the stream is found to contain i lb. of the chemical per n lbs. of water, then 
evidently : 

w _i nw 

62‘5Q n ° r,< ^~62*5’ 


The practical details require somewhat careful consideration, and investiga¬ 
tions of the necessary conditions lead me to believe that, when these are 
properly fulfilled, the method is a very excellent one. 

The two crucial points are : Firstly, that the chemical is added at a definite 
and constant rate. Secondly, that thorough mixture takes place before the 
sample is drawn off for analysis. 

In order to ascertain the necessary conditions for ensuring these results, I 
carried out 84 tests on streams varying from 15 to 96 cusecs, flowing in earthen 
channels 5 to 20 feet in width, and with mean velocities ranging from 1*5 to 
5 feet per second. 

The obvious method of adding the chemical (which in 78 of my tests was 
common salt, and in the other 6, calcium chloride), is to dissolve it in water, 
and deliver the solution through a small orifice under a constant head. While 
a saturated solution is liable to deposit crystals in the measuring orifice, and 
so interfere with the regularity of the flow, it is plain that it is advisable to use 
a concentrated solution in order to handle as small a volume as possible. 

Such a solution has a specific gravity greater than unity, and consequently 
the volume discharged cannot be calculated by ordinary rules, but must be 
observed by weighing the quantity discharged in a given period. 

Owing to evaporation and impurities existing in all commercial chemicals, 
it is impossible to make up, day after day, a solution of a sufficiently constant 
specific gravity to produce a constant discharge, so that it is necessary to 
observe the discharge of the orifice with each fresh batch of solution. 

In order to ascertain the conditions for a satisfactory mixture of the solution, 
and the water of the stream, samples were taken at points at various distances 
below the point where the solution flowed into the stream, and at different 
intervals during the period when the solution was in flow. 

The solution was assumed to be thoroughly mixed with the stream when the 
proportions of the added chemical in the various samples thus obtained did not 
differ by more than 1 per cent. It is believed that under the circumstances of 
the analyses a variation of ^ per cent, could be detected. Thus, it is possible 
that the following rules would require modification if they were employed by a 
more skilful analyst. 

It would be impossible to quote details of over 1000 analyses, but the 
general results are as follows : 

Let V mj represent the mean velocity of the stream, and b, its breadth. Then, 

for streams with depths between —, and —, complete mixture (as above 

^ 3 

defined) does not occur until a distance of at least 6 b, has been traversed, 
and the discharge of the solution has continued for a period equal to at least 


24 



seconds. 


Also, if, under these conditions, samples are taken more than 




74 


CONTROL OF WATER 


— seconds after the discharge of chemical has ceased, a diminution in the con- 
V m 

tent of chemical occurs, owing to the stoppage of the addition of the chemical. 

These results suggest that the ratio between the maximum and minimum 
velocities existing in the cross-sections of the streams experimented on, is 
always less than 2 to 1 ; which agrees very fairly with our general knowledge 
of the subject. 

Let us now consider the practical effect of these conditions. 

Assume a stream 20 feet wide, and 3 feet deep, carrying 90 cusecs, 

i.e. V m =i*5 foot per second, or = 320. 

v m 

Thus, we must add solution for 320 seconds, and sample about 120 feet 
below the point where the solution enters the stream. 

Using the ordinary volumetric methods for the determination of chlorine, 

I found that it was possible to determine the fraction — with an accuracy of 

1 per cent, so long as 71 did not exceed 30,000 ; and that the task was less 
difficult when n — 20,000, or less. Thus, for the determination of a 90 cusec 
flow, with an accuracy of 1 per cent., it was necessary to add salt (NaCl) at the 
rate of at least 0*19 lb. per second, and preferably at 0*28 lb. per second. 
Hence, one gauging required an expenditure of at least 61 lb., and preferably 
90 lbs. of salt ; and the solution containing approximately j lb. of salt per 
pound of solution (saturated solutions possessing 0*312 lb. per pound of 
solution), the least possible volume of solution was approximately 4, or 6 cube 
feet, and was added at the rate of 0*013 to °'° 2 cusec. 

In practice, since the available orifices discharged approximately 0*005, 
o*oi, 0*02, and 0*04 cusecs, the minimum quantity of salt consumed in this 
gauging was about 90 lbs., contained in 6 cube feet of solution ; and the actual 
results were no lbs. and 7*2 cube feet, since the experiment continued for 
nearly 400 seconds. 

This particular stream was the most difficult example dealt with, owing to 
its low velocity ; but as a favourable case I found with : 

A stream 3 feet deep, and 10 feet broad, with a mean velocity of 3 feet per 
second, i.e. 

Q = 90 cusecs as before, but 24 ~ = 80, 

V m 

only one quarter of the above quantities were required. 

The method is capable of great accuracy. Thus, in determining a stream 
of approximately 7 cusecs, which was passed over a weir (not for measurement, 
but as being the best method of keeping the discharge constant), the results of 
eight observations gave : 

Discharge = 7*473 ± 0*15 cusec, 
i.e. a probable error of 0*2 per cent. 

If this be the true accuracy of a chemical gauging, it is plain that com¬ 
petition by any other method is hopeless. 

The real criterion for the adoption of this system is : Does thorough 
mixture occur? Thus, it is admirably adapted for such purposes as the 
determination of the coefficients of discharge of weirs or orifices, and of the 
quantity of water utilised by all types of hydraulic machinery. It is less suit- 


CHEMICAL GAUGING 


75 

able for the gauging of rivers ; large and placid streams requiring considerable 
quantities of chemical, and the preparation of much above 8, or 9 cube feet of 
solution, of uniform composition, is a difficult matter. 

If a bulk of solution much exceeding 4 or 5 cube feet is necessary, very 
careful and systematic mixture of the solution is needed. 

As an example, a volume of 11 cube feet of salt solution, was discharged at 
a rate of about o*oi cusec, and samples were taken every 100 seconds. The 
analyses were as follows : 


Time. 

Per cent. Content 
in Salt. 

Time. 

Per cent. Content 
in Salt. 

0 

2 2*8 

600 

22*4 

IOO 

22*7 

700 

2 2*6 

200 

2 2'6 

800 

22*8 

300 

2 2 ’7 

900 

22*8 

400 

2 2*9 

1000 

22*9 

5 °° 

2 2*6 




The maximum content is 22*9 per cent., and the minimum 22*4 per cent., or 
a variation of 2 per cent, in the strength of the solution occurs. The stirring 
and mixing was as systematic as was possible with unlimited labour, but no 
mechanical appliances were employed. The volumetric method used was 
certainly capable of detecting variations in the strength of the solution of 
o'5 per cent., and is believed to be accurate to 0*2 per cent. Thus, it may be 
inferred that at least 1*5 per cent, variation in strength occurred in certain 
portions of the solution, and these differences cannot be avoided unless special 
mixing tanks are provided. 

The above information is entirely founded on experiments conducted by the 
addition of chlorides to the stream. The chlorine was estimated volumetrically 
by silver nitrate, with potassium chromate as indicator. Reference is made to 
Sutton’s Volumetric Analysis for details. 

The method has many practical advantages, and was well adapted to the 
water experimented on, which was naturally almost free from chlorides. If 
chemical difficulties alone are considered, greater accuracy can be obtained by 
adding acid (preferably sulphuric acid), or an alkali (preferably caustic soda). 
The best substance depends on the salts originally present in the water. 

The following table is derived from one given by Stromeyer ( P.I.C.E ., 
vol. 160, p. 351). 

Column 3, 4, 5, and 6, indicate the figures which I believe should be obtain¬ 
able by volumetric methods, by an engineer who is not a skilled chemist. 
Column 5 is calculated on the supposition that dilutions only two-thirds as great 
as those employed by Stromeyer are advisable, and the volume of solution in 
Column 6, is calculated on the basis that a solution is employed which is only 
five-sixths saturated. 

Such concentrated solutions of common salt, and calcium chloride, carbonate 
and bicarbonate of soda, etc., are easily handled ; but caustic soda and 
sulphuric acid should be used in a more diluted form, as the concentrated 
solution is very viscous. 






















CONTROL OF WATER 



a, 

a 

<u 

i~! 

o 

X) 

C 

aS 

JL> 

3 

rt 

3 




to* 


r—-* 


3 


toO 


rsi 

# 

ai 

(U 

V 
.-1 

C 


<L> 


ju <u 

-q 5 3 

cS 2 ai 

• *"HI . t-H 

3 ■ 4_ ’ 3 

p4 P4 


i 

a 

S-S 

-O o 

4 -> 

A? ^ 


_ o 
.2 cj 

"<5 


in «n 


>% 

3 

,£> 

4 -> 

3 

.O 

3 

3 

.g 

3 

Pi 


Maximum 
Value of n 
that permits 

I p.c. accur¬ 
acy to be 
attained by 
gravimetric 
Methods. 

o o o o 

o o o o 

o o o o : : : 

io CT 6 ' 

M rf O 

M M LO 

Approximate 
Volume of 
partially satur¬ 
ated Solution 
used per 
Second per 
Cusec of 
Stream Dis¬ 
charge. 

ID |0 !° P 145 

P to to —v ° U 

hP h|o Hto n-. Q-. HO H, 

t to to- w ^ to ” 

P |H |H |H 

Lbs. of 
Chemical per 
Second per 
Cusec of 
Stream Dis¬ 
charge that 
should be 
used in 
Practice. 

Tf O CO r-. un (N 

oi ci .-i O O 1-1 — 

o o o o o o o 

o o o o o o o 

o o o b b o b 

Ratio : Weight 
of Chemical to 
Weight of Water 
under these 
Circumstances. 

. 

o o o o o o o 

o o o o o o o 

O o to O O O 

cS to cT w to vO r— 

co ^ to to VO r>. 

>-i H 

a a a c a c s 

• r—4 • r—4 • r— 1 • rH • • *—• • 

M M M M M i-H 

Dilution of this 
saturated Solu¬ 
tion that will 
just give an 
accuracy of 
i p.c. by Volu¬ 
metric Methods. 

I in 12,160 

i in 21,490 

i in 24,360 

1 in 132,300 

1 in 213,500 

1 in 29,500 

i . ■ /■ s 

1 in 6,250 

Weight of 
Anhydrous 
Chemical in 

I cubic Foot 
of saturated 
Solution. 

r 

w y to O yf -00 hi 

-^OnOnCNiovo 0 - to 

1 — 1 HI Cl 0 H Cl 




rt 

_o 

s 

<L> 

X 3 

u 


















































CHEMICAL GAUGING 


77 


Column 7, is calculated for gravimetric methods, on the assumption that a 
i litre sample of the mixture is taken, and that the precipitate obtained 
should then weigh o*oi gramme, a saturated solution being used. 

My own experience with gravimetric work has been unfortunate, but I 
attribute this entirely to lack of skill, and consequently am unable to state 
whether these figures are as reliable as the others. 

It will be noted that Mr. Stromeyer, being a skilled analyst, is able to get 
good results with considerably more dilute solutions than my limited ex¬ 
perience permitted. It will be seen, however, that even with his values we 
must be prepared to deliver fairly large volumes of solution, unless the costly 
and tedious gravimetric methods are employed. 

The above considerations permit us to state that the chemical method is : 

(a) Best adapted for systematic gaugings of a stream in such work as 
turbine testing, where a suitable installation for chemical gaugings would 
allow us to dispense with the cost of installing a weir, and the loss of head 
entailed. 

(b) The necessary apparatus entails greater first cost, but the expense of 
each gauging is far less than that of a current meter gauging, and requires a 
shorter time. 

( c ) The probable error, in the case of quantities under ioo cusecs, is about 
one half that of a current meter gauging, and is approximately equal to that of 
a good weir gauging. 


Having expressed the opinion that the method is quite inapplicable to 
pioneer, or reconnaissance work, I feel it due to Mr. Stromeyer to state that he 
gives instructions for what he terms a “ gulp method ” ; which consists in 
pouring solution containing a known weight of chemical as quickly as possible 
into a stream, and taking a continuous sample of the resulting mixture. 

My tests of this system (when its results were checked by those of weir and 
rod float determinations) were decidedly adverse, as I found that errors of io, 
to 15 per cent, occurred. I must, nevertheless, acknowledge that the process 
obviously needs very careful and well thought out preparations for securing 
continuous samples of the mixture, and that my arrangements were by no 
means satisfactory. 

It appears that such a sampling apparatus, when practical, lacks portability, 
and is therefore unlikely to be employed in reconnaissance work. 

The method has one vfery practical application. It can be used to rapidly 
and cheaply determine the coefficients of discharge of weirs, or other falls of 
water. Here the conditions for producing a thorough mixture are very efficient, 
and an addition of the chemical for periods much exceeding one minute is 
unlikely to be required. 

Let it be assumed that we wish to determine a 1000 cusec flow, and are 
using common salt. 

A solution containing 16 lbs. per cube foot is easily made up, and such a 
solution can be detected with an accuracy of 1 per cent, when diluted to 1 


in 12160 x 


16 


1 in 10.000. 


1 9*5 

Thus a flow of o'l cusec will suffice, or we can use about 6 cube feet of 

solution and 96 lbs. of salt per minute. 

For gravimetric methods, let us suppose that an accuracy of o 5 per cent, 
is required, and that the balance available will indicate o‘i mgrm. We there- 



78 


CONTROL OF WATER 


fore wish to have 20 mgrms. of precipitate, and find that with a 16 lbs. per cube 
foot solution, 1*64 cube mm. will give 1 mgrm. of precipitate ; or, that our sample 
must contain the equivalent of 32*8 c.mm. of concentrated solution. Now, 
assume that we take a litre sample, equal to 1000 c.c,, or 1,000,000 c.mm. Thus 

a dilution of == 30,000, is permissible, or say approximately three parts 

per 100,000. Or, we could use 2 cube feet per minute, and 32 lbs. of salt; 
and if we chose (as a skilled chemist probably would) to work with 5 litres, 
and a balance indicating T ^th of a mgrm., we could work with 0*04 cube foot 
per minute, and about 0-64 lb. of salt. 

Any of these dilutions, however, are approximately identical with the 
quantities of salt normally occurring in British waters, and in such cases it is 
plain that sulphuric acid will probably give more accurate results. In any 

actual case, a preliminary study of the 
natural chemical contents of the water 
is required, and the advice of a skilled 
chemist is useful. 

Practical Details. — The only 
real difficulty lies in the steady discharge 
of the solution. Sketch No. 13 shows the 
arrangement which I finally adopted 
The vessel was 6 in. x 6 in. x 2 feet high, 
and discharged through a small Borda 
„ mouthpiece B, screwed into the plate 
04 AA, riveted to its side. 

The solution was fed to the vessel 
by a pipe C, which was provided with 
a tap (not shown) for approximately 
regulating the flow. Any excess in the 
discharge at B, was allowed to escape 
by the overflow weir W, and was drawn 
off by the second tap. 

The calculations are fairly plain. 
The head over the orifice measured 
Sketch No. 13.—Apparatus for Chemical from B, to W, is 1*5 foot. The maxi- 

Gauging. mum discharge which it is intended to 

pass is 0*04 cusec. Suppose that C, 
supplied 0-05 cusec, then o*oi cusec must escape over the lip W, which is 18 
inches long. The rise in the water surface above W, is then given by : 

r 5 x 3’33 o-o 1, /z 15 = 0*002. Therefore, h — 0*015 foot, 

and the discharge through B, is consequently : 



0*04 x 


X / 1 ' 5 ' 5 0 

v IT 


04x1*005 cusec. 


So that, even with a very rough regulation of the tap on C, the discharge 
through B, will not vary % per cent. 

Care being taken to accurately regulate the tap, the actual discharge 
easily kept constant to o*i per cent. 


is 































VENTURI METER 


79 


I found that a set of orifices discharging approximately o'oo5, o'oi, o‘o2, 
and 0*04 cusec were quite sufficient for practical use. 

So far as my experience goes, discharges up to 100 cusecs can always be 
gauged with an accuracy of 1 per. cent., provided that 10 cube feet of solution 
can be made up, and can be thoroughly mixed, and that orifices delivering 
o‘oo5, o*oi, 0*02, and o’oq cusec (approximately) are available. For larger 
discharges the table will permit the necessary quantities to be estimated. 

The chief difficulties (other than chemical ones) will be found to arise as 
follows : 

(i) In preparing a large volume of dosing solution of uniform strength. 

(ii) In determining when complete mixture has occurred. 

The chemical difficulties are probably easily surmounted by a practical 
chemist. To an engineer unprovided with an accurate balance for making up 
the test solutions the following points appear to be the most important : 

(i) The determination of the end point of the reaction. 

This is very marked if an acid or alkali be employed, but is somewhat 
blunt when chlorides are estimated. 

(ii) In hot climates the strengths of the solutions employed are affected by 
evaporation. This can be allowed for (since the quantities required are 
relative and not absolute) by blank experiments, but these are tedious. There 
is, however, little doubt that any large scale gauging operations of sufficient 
importance to occupy two engineers, could be better effected by an engineer 
assisted by a chemist. Judging by my own experiments, the cost in labour 
and material will be less than half that required for current meter gaugings of 
the same magnitude. The only possible exception is that of a large and very 
slow flowing river ; and such cases are easily detected by a preliminary 
experiment with colouring matter, as described under the heading Pipes. 

Venturi Meters. —The Venturi meter was first applied to water 
measurement by Clemens Herschell. It consists of a double cone forming a 
constriction in a pipe, as shown in Sketch No. 14. 

Let the area of the unconstricted pipe at S, be represented by A s , and let 
A* represent the area of the throat, or smallest portion of the constriction. 

Put p = —. Let v s , and v t , be the corresponding velocities, and p s , and p t , be 

A< 

the pressures in feet of water at these points. 

Then, assuming that the flow is regular : 

If Q be the quantity of water passing per second, we have : 

Q = z/ S A S = ^A/, or vt^pv s 

Neglecting friction, and other losses in the cone ST, we have : 


, ,v/ v t * 


V.„ 


or, ~(p 2 -i)=A-pt 

z a 


Thus, Q = A ,v, — A, W 


Similarly, if we assume that the frictional losses between S, and T, are 
equal to h\ feet of water : 

We have, Q-A e 



p 1 “ 1 






8 o 


CONTROL OF WATER 


Now, Zq, is small. Thus, in practice a corrective factor is allowed for the 
neglected shock and skin friction. So we get : 

q=ca 'JMEEM 

V p 2 — i 

In actual working it is found that C, is approximately equal to unity. It 
will also be plain that since the skin friction of water moving in smooth pipes 
does not vary exactly as the square of the velocity, C varies with v 8 . Actually, 
however, these variations are very small ; and for all practical purposes C, is 
constant. 

Herschell {Trans. Am. Soc. of C.E ., vol. 17, p. 228) gives a very careful 
series of experiments on two Venturi meters, each with p = 9. But in one case 
A.,, was approximately a circle of 9 feet in diameter, while in the other A s , was 
approximately a circle of 1 foot in diameter. 


r< 



The curves foi C, show marked variations when 77, is less than 10 feet per 
second. The values for the 9-foot pipe rise in a quasi-parabolic curve to 
C = 1 08, when i>t — 2 feet per second ; and, in the case of the i-foot pipe, fall 
in a similar curve to C = 075, when v t = i-foot per second. 

Foi values of 74, greater than 10 feet per second, however, C, is as 
follows : 


1 

Vt 

HerschelPs Values, p = 9. 

* 

Coker’s Values for 
a 1 *6-inch Pipe, 

P= 18*4- 

9-foot Pipe. 

I-foot Pipe. 

IC 

0*980 

0*980 

1*368 

20 

0*970 

0*990 

poo 3 

3° 

0*960 

0*992 

0*978 

40 

... 

°‘995 

0*967 

5° 

• • • 

0*999 

0*956 
































































THEORY OF VENTURI METER 


8r 


Coker’s values are taken from a smoothed curve of his results, as given in 
Proc. of Can. Soc. of C.E., October, 1902. 

The Venturi meter is probably a far more accurate water measurer than a 
weir, so that only the last two columns (which are obtained from direct 
volumetric measurements) need be considered as of use in determining the 
law of the variations of C. 

Since the meter is so accurate, the following investigation will be found of 
practical use. 

Assuming that v — <Z F I rs, represents the law for all the losses in the 
Venturi meter, then the head lost in a frustrum of a cone of which the initial 
and terminal diameters are d s , and d t , and the vertical angle is 2y, is given by 
the equation : 




-v? 


C F 2 tan y 




where C F may be taken as having a value very close to that which occurs 
in a pipe of an area A*, when the velocity is v t . 

Thus, the frictional head lost in the upstream cone ST, is very approxim¬ 
ately equal to : 

h v? l n 

1 C F “ tan y x t p 2 / 

and the similar loss in the down-stream cone TU, is : 


ho. — 




ri - 4 } 


C F 2 tan y 2 l p 

and provided that the area at S, is equal to the area at U. 

Thus, if a third gauge be established at the point U, and the difference 
between p s , the pressure in the gauge at S, and the pressure indicated by the 
gauge at U, be k, we have : 

k cot y x 


k = h x + /z 2 and h x = 


cot y x + cot y 2 


where yi, and y 2 , are the semi-vertical angles of the two cones. This last equation 

Y. , v n 

holds if the law of frictional resistance is of the form, h f = ; provided that 


in, and n, are constant. 

XT . 24 * 

Now, cot y x = -7-7 

' d s — d t 

Thus, h x = k — t-d —— 
ist *r Hu 


cot y 2 = 


2 L 


tu 


ds dt 


Hence, h x , can be calculated. 

In practice, the areas at S, and U, are not always exactly equal; and this 
should be allowed for by decreasing the observed difference in the pressures by 


the quantity 


v f — Vs 2 
2 g 


, regard being paid to the sign of this quantity.- 


It is, however, doubtful whether the investigation is entirely reliable in this 


case. 


K 


o H v H t 

An experimental proof of the relation, C 2 = ~~ p — p t ' ^ on a ^ ar & e scale is 

greatly to be desired. 

6 













82 


CONTROL OF WATER 


Working with a very badly proportioned and roughly made constriction (it 
would be unfair to call it a Venturi meter), I found as follows : 


Vt, feet per 
Second. 

Calculated Value 
of C. 

C, by volumetric 
checking. 

117 

0-983 

0*987 

I 2-8 

o*99i 

0-988 

14*2 

0*984 

0*986 

2 1*4 

o*973 

o*977 


The agreement is satisfactory ; but the methods of observation were not 
sufficiently accurate to enable any real reliance to be placed on the results, as 
the volumetric measurements are known to be subject to an error of 07 per 
cent. It is, however, plain that the method of correction adopted enabled an 
otherwise unreliable instrument to produce results which were quite as accurate 
as a volumetric measurement in the field. 

It is believed that calculations founded on this corrected form of the 
Venturi equation permit greater accuracy in water measurement than any other 
method, and any inaccuracies are probably due to the difficulties of observing 
k, quite as much as to defects in the theory. It is, however, certain that the 
calibrated commercial Venturi meter which can now be obtained from many 
firms is so accurate that only volumetric methods, or the very best weir 
observations, can be employed to check it. 

The following investigation of the possibilities of changes in C, is therefore 
only useful when extreme accuracy is required. 

The losses represented by h lt are due to skin friction, and changes in the 
direction of the velocities as the water passes through the cone. These last 
Alexander (P.I.C.E., vol. 159, p. 341) has shown to be probably expressed by 
terms of the same form in v , as the frictional losses. Thus, 

h x — K7/ s ” (where v s , is the velocity in the pipe). 

Now, p s — pt, is approximately proportional to v s 2 . 

Hence, approximately C 2 =—^-7—^ 

Now, so long as v s , is greater than Osborne Reynold’s higher critical value, 
n, varies between 175 and 2*1. (See p. 20.) 

Thus, we have : 

(i) v s , is greater than v d (or, as practically discovered by Herschell when 
Vi, is greater than a certain value), 


So, for'smooth, new pipes where n, is less than 2, we may expect that C, is 
less than 1 ; and that C, increases as v s , or Q, increases. 

For encrusted pipes, n = 2, and C, should be constant. For old, encrusted 
pipes, where 11 exceeds 2, C may be expected to decrease as v s , increases. 

(ii) If, however, v s , is so small that the velocity falls below the critical value 
at some point in the meter (which Coker’s experiments have shown may 


l 










VENTURI—PRACTICAL DETAILS 83 


probably occur in cones, for values which considerably exceed those at which 
it occurs in cylindrical pipes) we have : 


q 2 _ (I + «)?' 2 — <v n 
(1 + ft)v 2 


where a and /3 are coefficients of the character discussed on page 15, and 
express the fact that the square of the mean velocity no longer accurately 
represents the mean energy of the motion of the water. Any estimation of the 
values of a and /3 is impossible ; but it will be plain that the peculiar values of 
C, found by Herschell, when Vt, is small, do not conflict with theoretical 
results. 

The practical effects of the above investigation may be summed up as 
follows : 


(i) For each Venturi meter a minimum value of v t , or Q, exists, and the 
meter coefficient C, varies very rapidly when Q, is less than this value. Under 
these circumstances, C, is dependent upon the temperature of the water, and 
upon the character of its motion before reaching the meter ; so that the meter 
may be regarded as useless for measuring quantities less than this minimum 
value. The minimum value of Q, may be assumed to be determined by the 

fact that the friction law for a velocity^-, differs from that for a velocity ^ ; 

A t 

Q 

A s 


and this probably occurs when = v s , is approaching Osborne Reynold’s 


critical velocity, so that the minimum value of v s , possibly varies as where 

a s 

d s , is the diameter of the pipe. 

This matter has been recognised by Herschell, and his rules are given later. 
They may be regarded as specifying v s , as greater than 1 foot per second, and 
probably apply to pipes 12 inches in diameter, or larger. Coker’s results show 
that v s , should be still greater in the case of smaller pipes. 

(ii) For values of Q, exceeding this minimum, C, is very nearly constant, 
and may be expected to increase slightly as Q, increases, for new pipes; but 
this increase will diminish, and may even possibly become a decrease as the 
meter grows encrusted, and ages like a pipe. 

I am not aware that this effect has yet been observed, although Herschell’s 
results show that it is possible. 



Herschell has laid down standard proportions for the Venturi meter (see 
Sketch No. 15). When the approximate theory is followed, these should be 
adhered to, in order to obtain the advantage of his careful calibrations. The 
necessity is not so acute where the corrected theory is employed, and I have 
been unable to ascertain whether Herschell’s proportions are founded on 



















84 CONTROL OF WATER 

experiments. Herschell states that for values of v t , exceeding io feet per second, 
C, may be taken as 0*99 without very much error; and for values down to 
Vt — 2 feet per second, it is probable that C, does not greatly depart from 
values between 0^99 and o'96. 

The gauge requires some consideration. The pipe may be under so great 
a pressure that the water columns would be inconveniently long ; 01, on the 
other hand, the pressure may be such that air would be sucked into it at T. 



Sketch No. 16. —Metcalfe’s Gauge for Venturi Meters. 


These troubles are obviated by the double gauge shown in Sketch No. 16 
(due to Metcalfe, see Engineering News, 28th February, 1901). 

We have plainly: 

ft a—ft s h$ ftb—ftt — hi 

Therefore, ft s —ft t = {ft a ~fti>) + {h s —ht), 
which are all easily read on a scale of convenient length. 

Measurement of Water by a Travelling Screen.—T he principle 
of this method is simple. A very light screen of varnished canvas with a 
stiff framing of angle iron is hung from a wheeled carriage, and is allowed to 






















































TRAVELLING SCREEN 


35 


move with the water along a short length of regular channel of rectangular 
section. The velocity of the screen is observed electrically; and, after certain 
corrections for leakages past its edges, this velocity is taken as the mean 
velocity of the water. 

The method is described in the Zeitschrift des Deutscher Ingenieure Verein , 
of the 20th April, 1907. In the actual installation used for turbine tests, by 
Voith at Heidenheim, the channel is 2*992 metres wide, and the screen 2*972 
metres wide ; so that there is a clearance of 0*4 inch at each side. The 
depth of the stream is observed on either side of the screen, and the mean is 
taken for calculating the area of the stream. 

The pressure producing leakage through the clearances is estimated from 
the rolling resistance of the screen, and is stated to be less than o*oooi metre 
(0*004 inch) of water ; and the coefficient of discharge through the clearance 
is taken as 0*65, both at the sides and at the bottom of the channel. 

It is maintained that the method is more accurate than a weir gauging. 

It is quite evident that the apparatus is complicated, and that the pre¬ 
liminary calibration is arduous. The actual gauging, however, is very simple ; 
and, owing to the velocity being electrically recorded, the results are obtained 
directly in a sense that mere written data of a gauge reading cannot be. 
The only uncertainty is in respect to leakage, which, in Voith’s application of 
the method, is so small a fraction of the total discharge, as to be of little 
moment. 

It would therefore appear that for permanent work on water which is 
absolutely free from drift and silt, the method is probably one of the best yet 
employed ; since, once installed, it does not require the presence of a trained 
observer, nor is any head lost, as in the case of a weir. Its adoption is well 
worth consideration in such cases as large town water supplies, or power 
schemes where the water is clear, and passes through an open conduit, as the 
records can be worked up at a distance, and at leisure. 

Discharge Curves. —The obvious method of determining the daily dis¬ 
charge of a river is to use the individual observations of discharge obtained 
by the various processes discussed above, in order to determine a relation 
between the quantity discharged, and H, the height of the river surface, as read 
on a fixed gauge at the point of observation. 

We can thus determine a relation : 

Q=/(H) 


The following are actual examples of such formulae r 


The Loire at Roanne 
The Seine at Mantes 
The Isere at Grenoble 
The Drac at Grenoble 
The Adda at Como 


Q = ioo(H+o* 25) 1 - 5 

Q= 95 ( h +°‘ 7 o) 1>5 
Q = i2i(H+o*86) 1 - 5 
Q = 28 o(H-o* 7 o ) 1 - 5 
Q = iooH 1 - 5 — 3*2 oH 2 - 5 


where Q, is expressed in cubic metres per second, and H, in metres. 

The forms arrived at above appear to be somewhat influenced by 
theoretical considerations. The French rivers are expressed according to 
Boussinesq’s theoretical formula : 

Q = M(H + ^) 1 - 5 





86 


CONTROL OF WATER 




The Adda is expressed in Lombardini’s formula : 

Q = NH 1 - 5 ±PH 2,5 

Evidently, the most general form is : 

Q=a + m+cH 2 + dH 3 + etc. 

The simplest method of determining such a formula is to plot the observa- 
tions graphically, and to determine the form of the function /(H), by trial 

and error, and then the constants 
can be ascertained by the method 
of mean squares. 

The following mathematical 
investigation is founded on the 
assumption that, on the average, s, 
the slope of the water surface, is 
very nearly constant. The process 
permits a prediction of the general 
trend of the discharge curve to 
be made, together with possible 
irregularities in its shape, with a 
fair degree of accuracy, by a study 
of the form of the cross-section of 
the river-bed. 

The advantages are plain. 
Although we must attend the 
pleasure of the river in order to 
obtain a discharge observation at 
any particular gauge, we neverthe¬ 
less can study the cross-section of 
its channel at leisure. 

The ordinary theory gives : 

v=C V rs, and, Q = wA = vpr 

Where A, is the area of the cross- 
section ; 

r , is its hydraulic mean 
radius ; 

/, the wetted perimeter ; 
and v, the mean velocity. 


CdSC Z. 



Casc5 ,.. 



Sketch No. 17.— Types of Cross-sections 
of Streams. 


Now, plot A, and r, graphically, as functions of H, the gauge reading. 
Let /, be the width of the river at the gauge H, we consequently have : 

dA = ldhl 


Four cases usually occur (Sketch No. 17) : 

(i) /, is constant, i.e. the banks of the river are approximately vertical. 

I—a, say. Then A =ag, where g=H + c, and a, is roughly the mean 
value of /, and c , is easily determined arithmetically. 

(ii) The banks of the river become flatter as the gauge height increases, 
(see Sketch, Case 2). 


l=aj/, where n, is less than 


say, and A = 


a 

n+i 


■g n+ 1 












DISCHARGE CURVES 


87 


(iii) The river-bed is approximately triangular in section. 

l=ag, and — 

(iv) The river-bed has a section resembling that of a saucer, the banks 
becoming steeper the higher the river rises. 


/=££■"*, where //*, is greater than 1. 


A = 


a 


rtn+i 




In the last three cases, and at first sight the determination of c, 

may appear to be difficult ; but, in actual practice, once the curve of A, and H, 
is plotted, the matter becomes far clearer than any mathematical investigation 
can make it. 

Now, in all these cases /, is very approximately proportional to /, so that 
-6 = el. 


g 


A A 

And r= —, may be written as r——.— ,—-. N 
p' 3 el (m + i)e 


We thus get as a first approximation to the discharge curve : 

Q = CA VP5 = CV 7 —■g” + \/ , -f —= 

m+i V (m+i)e 


where C = K ^ m ^~ 

a 


and all the quantities comprised in K, can be obtained by surveys of the cross- 
section of the river-bed. 

The four cases above considered lead to the following: 


(i) Q = K 1 VJ / 5 

(ii) Q = K 2 V}^- 5 +* 
(hi) Q = K 3 V^ 2 - 6 
(iv) q = k 4 vj^- 5 +- 


In practice the above theory is best applied by plotting log A, and log r , 
in terms of log g ; and thus obtaining 

> A = a\g m+1 and r = r x g 2x 

directly. 

Thence we find that, Q = Ki*/Jg m+I+x i etc., 
and, if as in Manning’s formula (see p. 401), it is assumed that C = C^- 17 , we get 
as the final form of the relation between the gauge height and the discharge : 

Q = Ks/' s g m+x+VZ7 

Sketch No. 18 shows a case where m = 1*91, 7 .x — 1*12, and, as will be seen, 
the observed values give Q = K V j g 2 ' 67 in place of Q = KVj g 2 ' r,i as the above 
theory would indicate. 

The value of was very nearly constant, and averaged ^5. A smoothed 
discharge curve and a graphic determination of the values of y. for this smoothed 
curve are given in Sketch No. 19. The value obtained for 7, is 2-45, and the 
results agree almost suspiciously well. Some compensating error in the deter¬ 
mination of j, may be suspected. 








CONTROL OF WATER 


88 


3-3 


52 


5-1 


5-0 


29 


£■8 


Quantities obtained 
by Survey 


R 

r 

J5 

05 9 

695 

14 

826 

6-44 

S3 

7/9 

59l 

12 

617 

5-57 

U 

522 

4-96 

10 

454 • 

4-45 

9 

552 

5-82 

S 

285 

345 

7 

215 

2-82 

6 

ISO 

24-7 

5 

983 

2-0f 

L_ 


1 

» 

©/ 

j °° 

i .. ■ ( 

to 

% 


* ' 

^ °/ 

^ 7 

/ \ 
<*y? o/ow 


\ 

% 

^ 7 n: 

7 & 
/? 

/ 

# 

V 

I n 

/ 

I 

t 

k J 

' 

O j 

Jje 

^•4. 

_ 




Sketch No. i8,— Logarithmic Plot of Areas and Discharges of a Stream 

at various Gauge Heights. 



























































DISCHARGE CURVES 


89 


It should be remembered that where some attempt at a discharge curve 
must be given, and only one gauging is available, the value of m, can be 
obtained by survey, and KV^, can be deduced from one observation only, which 
may be checked to some slight degree by observing s, and seeing whether the 
value of C, thence calculated, is a likely one. 





1 


I 


1 


1 


s 



■- ! 




C\ 

C> 


8 


£ 




00 

1-1 

o 

£ 

o 

4 -* 

1 ) 

>/» 


V 

in 

3 

L) 

O 

V-l 

c- 

in 


3 

M 

1 

o 


05 

C 


<u 


"O 

C 

3 

<u 

> 

3 

u 

aj 

to 

Vh 

Cj 

rC 

o 

in 


a> 

to 

O 




6 

£ 

w 

u 

Ch 

Cd 

W 

W 


The practical value of the work, however, is far greater than such rough 

approximations indicate. 

Firstly, by survey we obtain c , in the formula : 

g — H+c 

Now, plot the discharge observations against g, in logarithmic form. 
































































90 


CONTROL OF WATER 


The above work shows that the points (log Q l5 log g{), (log Q 2 , log^ 2 )> etc - 
may be expected to lie very fairly close to a straight line, so long as the general 
aspect of the cross-section of the river-bed does not materially change inside 
the limits of^*, under consideration. 

Secondly, should the aspect of the cross-section change suddenly, as is 
indicated in Sketch No. 20, we may suspect that the logarithmic plots of Q and 



A will consist of two straight lines, probably connected by a curve. It will also 
be plain that discharge observations Ties.? g = g p are urgently needed. 

Above and below g = g p , a few observations may suffice (if in good agree¬ 
ment) to determine the curve over a wide range of H or g. 

In my own practice I have found that the results of actual observation a°-ree 
surprisingly well with the above theories. I have such confidence in the vvork 













































VARIATION OF s 


9 1 


as to use it in order to obtain by extrapolation the discharge at gauges which 
are higher than those for which discharges have been observed ; and in twelve 
out of fourteen later checkings I found that my confidence had proved to be 
justified. 

The process, however, must not be considered as universally applicable. 
The root assumptions are that: 

(i) C, is either constant, or varies as some power of g, i.e. C = C y g y say. 

(ii) j, is constant. 

The first assumption is probably correct, so long as the hydraulic character 
of the bed does not materially alter. A study of the vegetation, and of the 
quality of the soil or silt deposits, will permit exceptions to be predicted. 
Alterations (usually in the direction of increased roughness) may be expected, 
when the river rises in high flood. Nevertheless, it is noteworthy that 
Bazin’s y is generally far more steady under such circumstances than 
Kiitter’s n ; and a calculation of C, according to Bazin’s rule, with the value of 
y obtained in ordinary stages of the river, is sufficient allowance for this factor. 
Cases where the flood bed is encumbered by trees, fences, etc., must of course 
be excluded, but under such circumstances no really accurate observations can 
be taken. 

The constancy of s, during large variations of H, or g, is a bigger assumption, 
and cannot be regarded as justifiable. 

If we consider individual discharges, during a rise of the river, s, is in¬ 
creased ; and during a falling stage, j, decreases. If, however, we regard the 
average of the discharges at the same gauge when the river is rising and falling, 
the assumption leads to but a slight degree of error ; and for the practical 
purpose of obtaining the total quantity discharged, the assumption is justified. 

Where damage by momentary flooding is ascribed to backing up of the 
water surface produced by works in a river bed, calculations founded on the 
assumption that s, does not widely depart from its usual value must be regarded 
with suspicion. An engineer will hardly be well advised to fight such a case 
on the assumption that s, is constant during the flood. 

For this reason, a subsidiary gauge situated two or three miles above the 
observation gauge is valuable, as also are readings from such a gauge during 
floods ; for in many rivers the variation in s, will explain all divergencies from 
the normal discharge curve. 

hifluence of a Tributary .—In certain cases, as for instance on the Blue 
Nile at Khartoum, this explanation is quite insufficient to account for the 
difference. Craig (see Lyons’ Physiography of the Nile Basin, p. 265), 
discusses the problem for the Blue and White Niles at Khartoum, in the light 
of Tommasini’s theoretical investigations. 

The general effect of a flooded tributary entering a river just below a gauge 
station (when the river is rising) is to shift the discharge curve as shown ; 
where AD, is the normal curve, and ABCD, is the shifting due to the flooded 
tributary, where A, is the point where effect is first felt, and B, the point where 
the tributary begins to ebb (see Sketch No. 21). 

When the river is falling, the upward rise of the curve in the portion DC, 
is not possible, and the loop is now as indicated in Sketch No. 21, Fig. 2. 
Where the tributary does not rise more rapidly than the main river, the portion 
DC, may be perpendicular to the gauge axis, thus producing a stage where 
gauge and discharge are unconnected. 


9 2 


CONTROL OF WATER 


This species of irregularity may be expected in all cases where a gauge is 
established, close to, and above the junction of two rivers. 

The circumstances of a properly selected gauging station are usually such 
that all variations in discharge caused by rising and falling stages, can be 
amply allowed for by drawing two discharge curves. One curve represents the 
falling, and the other the rising stage. The difference does not generally 
exceed 5, or 7 per cent.; while in a really satisfactory site, 2, or 3 per cent, is 
more usual. 




K Main River Fa Hin o 


Sketch No. 21. —Effect of a Tributary on the Gauge-discharge Curve of a Station 

upstream of the Junction. 


Rivers with Shifting Beds. —The foregoing work refers entirely to 
rivers with a fairly stable bed. Where the river carries much detritus, the 
aspect of the cross-section may largely depend on the stage of the river, or on 
the motion of sand or gravel bars travelling down the stream. 

The question of these “ deeps ” and “ shallows ” has been the subject of 
much discussion, and two theories are usually put forward. 

According to German ideas, such waves in the bed travel down the river 
at a fairly constant rate, preserving their form unaltered. 

For example : 

In the Rhine between Basle and Coblentz, the velocity is 735 feet 
(225 metres) per year. 

In the Elbe, 820 feet (250 metres) per year. 

In the Vistula, 1310 feet (400 meters) per year. 

In the Waal, 820 feet to 1640 feet (250 metres to 500 metres) per year. 

In the Loire, 1200 feet (365 metres) per year. 

Most Indian engineers would be disposed to agree with this statement. 

Lokhtine, in Russia (Mechanisme du Lit Fluviale), as also the majority of 
French engineers, and (so far as I can gather) the American engineers working 
on the Mississippi, consider that deeps and shallows are fixed with respect 
to the horizontal meandering of the river, and only alter their position to 
any marked degree when the river shifts its bed. The divergences may be 
reconciled by the statement that in a natural river, which is not restricted by 
training works, the deeps and shallows are mainly fixed by its horizontal plan. 
If the river is forcibly straightened and is restricted to a determined course, 
deeps and shallows move according to the German theory ; and apparently 
the usual German method of regulation by spur dykes accentuates this move- 








SHIFTING BEDS 


93 

ment somewhat more than regulation by dykes parallel to the general flow of 
the river. 

The explanation is not complete, as the Indian rivers are entirely un¬ 
regulated ; but it is quite possible that further study will show that fixed deeps 
and shallows also exist in these rivers, and several cases of a fixed deep are 
already known. 

The question is of little importance as regards its effect on discharge curves. 
It will be found in certain rivers that the bed alters in form at the gauging site ; 
and consequently, in place of obtaining one approximately definite relation 
between Q, and H, we find (after long studies) that a sheaf of two or more 
discharge curves exists, as in Sketch No. 22. 

The question has been investigated by Tavernier (.Etudes des Grandes 
Forces Hydrauliques des Alpes , vol. 1, p. 160). It appears that after three or 
four years’ study it is usually possible to reduce the sheaf to three or four curves, 
and that the change from one curve to another occurs not gradually, but per 
saltum , one curve being accurate for three or four months at a time, and then 
another curve becoming applicable the next day. 

It would also appear that this sheaf of three or four curves recurs year 
after year. 

Such studies require a longer time than can be afforded by anybody except 
a Government Department. The practical method is to institute systematic 
surveys of the cross-section, and to divide the sections thus obtained into three 
or four classes, and then to treat the discharge observations of each class as 
though they referred to separate rivers, using the methods already developed. 

In such work it would be as well to take into account Tavernier’s statement 
that as the waves of sand or gravel above referred to pass the gauging station, 
the effective slope may differ considerably from the mean slope of the river bed, 
or even from the mean slope of the water surface over say a length of a mile. 
In Tavernier’s actual example, varies from o’oo86 to o'ooiq, the mean value 
being o’oo5o. 

The problem is therefore very complicated, and it appears that only 
systematic gauging can really secure the required degree of accuracy. 

In such cases, studies by Harlacher’s method of the relation between the 
surface velocities and the mean velocities may prove of great value, as an 
ordinary gauge reader can be rapidly trained to observe surface velocities. 

The rod float method will of course secure better results. In the Punjab 
Irrigation Branch such cases are treated by systematic rod float work, and the 
gauge readings are not trusted for more than three or four days at a time. 
This evidently necessitates the permanent employment of a man capable of 
taking accurate rod float observations, and is hardly justifiable except in 
countries where the requisite intelligence can be obtained at a fairly cheap rate. 

While my own applications of the method of logarithmic plottings of the 
mean velocity and the hydraulic mean radius have been confined to channels 
in which the silt was nearly all carried forward by the water, so that the cross- 
section at the gauging site did not vary markedly, there is little doubt that a 
similar method should be applied when studying the discharges of a channel 
of which the cross-section varies rapidly. 

So far as any statement which has not been checked by observation is 
worth making, it would appear that each curve of the sheaf referred to 
above should be represented by a straight line on the logarithmic diagram 


/ 


94 


CONTROL OF WATER 



1 


» 

\ 

V© 

f\* 


I 

< 

^Vg\ 

% 

« 


'\F-\cCi\ 
w \ \> \ 

& 



1 

\ ^ 


1 

\* 

v\ 



X 

5 '2Jpt 

[uiiWipt 

^ « 

<3_ 


) 


Sketch No. 22. —Logarithmic Plot of the Discharge of the Isere, showing Influence of Changes in the Bed of a River. 








































GA UGING OF STREAMS AND RIVERS 


95 


(see Sketch No. 22). Confirmation of Tavernier’s statement that the change 
from one curve to the other occurs per saltum would then be easily obtained, 
and is greatly to be desired. 

In this connection it must be noted that the method adopted by the 
United States Geological Survey for obtaining the gauge-discharge relation 
at a station where the bed is shifting, assumes that the changes occur gradually. 
It is hard to believe that the simplification in calculation which is possible if 
Tavernier’s statement is generally true would have been overlooked by the 
United States experts. 


CHAPTER IV 


GAUGING BY WEIRS 


Weir Formulae.—Definitions. 

Measurement of the Head.—Effect of errors—Gauge pits, or stilling wells—Effect on 
coefficient. 

Weir Discharge Formulae.—Correction for velocity of approach—Francis formula 
—Practical formulae—Definitions—Contraction. 

Practical Rules.—Francis’ weir formula—Weir formulae as applied to measurement of 
discharge—Accuracy. 

Formulae of First Class. —Francis’ Formula —Description — Conditions. 

Bazin Formula. —Description—Conditions—Approximate formula—Shorter formula 
—Corrections when nappe expands. 

General Formulae.—With end contractions—Without end contractions. 

General Agreement of Weir Discharge Formula. —Corrections for velocity of 
approach—Distance at which head is measured—Experimental results—Correction 
for end contractions. 

Sharp-edged Notches of other than Rectangular Form.—Triangular—Trape¬ 
zoidal—Cippoletti. 

Weir Gauging of Water containing Silt.—Triangular and Cippoletti. 

Suppression of Contraction.—Experimental weir formulae—Freeze’s formula— 
Logarithmic plots. 

Inclined Weirs. 

Oblique Weirs. 

Weir with Rounded Edges. 

Drowned Weirs.— Francis’ Formulae. 

Fteley and Stearns’ Experiments. 

Herschell’s Formula. —Triangular notch. 

Bazins Formula for Notches without Side Contractions. —Nappe forms— 
Discrimination of Cases. 

Weirs with other than Sharp-edged Notches. 

Flat-topped Weirs. 

Triangular Weirs. —Do. with curved downstream prolongation. 

Wa ter-falls. 

Coefficients of Discharge for Large Weirs. 

Sharp-edged Weirs. 

Flat-topped Weirs.—With down-stream slopes—Drowned ditto.—Drowned weirs. 

SYMBOLS. 

A, is the area in square feet of the cross-section of the channel of appoach at the point 

where D, is measured. 

B, is the breadth of the channel of approach in feet. 
a and b (see p. 102). 

C, is the coefficient of discharge of the weir when the formula Q = CLH 1 - 5 is used. 

C 1 , is used in the formula Q = C 1 LD 1 * 5 , when distinction is required, and similarly 

Q = KD 1 - 5 or KD”, and Q = f- MLH x^H are used for distinction if necessary. 

D, is the observed head in feet. 


96 


GAUGING BY WEIRS 


97 


d , d x (see p. 121), 
D 2 (see p. 130). 


v 


h = —, where v, is the velocity of approach in feet per second. 


2 <r 


H, is the corrected head = D + ah, etc. (see p. 104). 

Hj, and H 2 (see p. 122). 

k, is a coefficient used for various ratios (see p. 130). 

K (see pp. 105 and 119). j 

K, (see p. 105). 

L, is the length of the sill of the weir notch in feet. 

Lj, is the width in feet of a triangular notch at a height D, above the vertex. 

L b , Lf (see p. 113). 

/ (see p. 102). 
m (see p. 102). 

N, is used in the formula Q = KH N . n (see p. 105). 
p, is the height of the notch sill above the bottom of the approach channel. 
p x , and P 0 (see pp. 121 and 124). 

Q, is the discharge over the weir in cusecs. 

Qb, Qf (see p. 113). Q s (see p. 126). 

s, is the slope of the face of a triangular weir (see p. 130). 

t = D + p (see p. 118). 

w, is the width in feet of the top of a broad-crested weir (see p. 128). 
v, is the velocity of approach in feet per second. 

z, is the slope - horizontal to 1 vertical of the sides of triangular notches (p. 114). 

a, is a coefficient in the equation H = D + ah. 
e (see p. 119). 77 (see p. 118). 

X (see p. 102). 

SUMMARY OF FORMULA. 


Velocity of approach. 


Q , 

v = -g /* = — (see p. 99). 
A 


2^ 


. , . , SQ 3 5 D 

Errors in measurement ot the head. ft* 

Q 2 D 

Note.—All formulae are subject to error if D is less than 0*30 to 0 40 foot. 
Francis’ Formula (see p. 105). 

Q - 3*33 (L-«H x o-iJH 1 - 5 , end contractions, 

Q = 3'33LH 1 ' 5 , no end contractions. 

with H 1 * 5 = (D + h ) 1 ' 5 - 7 / 1,5 , or H = D + ^1 ~ z\/ 

or > Q = 3'33 j 1 + °' 2 5 ( ^p ) }lD 1,5 , no end contractions. 

Bazin’s Formula for weirs with no end contractions (see p. 109). 

D 


Q = (3*248 + 9 ^??) jr + 0-55( 
or, Q = {3-41 + i' 69 ( 


<p + D 
2 




p + D 


)“}ldh 


General Formulae for weirs with end contractions, D, greater than 0-40 foot (see p. 1 J2 ) 
Q = 3‘i 10 L 1,02 FI 1,465 . L, less than 4 feet 1 ^ ' 


Q = 3-122 L 1 * 016 H 1 - 476 . L, between 4 and 10 feet VH = 
Q = 3*148 L 1,013 H 1,485 . L, greater than 10 feet J 

Triangular Notches (see p. 114).— 


D + 1 -4 h. 


z — ^. 

Q = 0707D 2 - 5 . 

2=1. 

Q = 1 -3iD 2 * 5 . 

2 = 2. 

Q = 2- 55 D 2 - 5 . 

2 = 4 . 

Q = S- 3 QD 2 * 5 . 


Cippoletti. — 

Q = 3-367LH 1 - 5 . H U =(D + h)™-h l '\ 
Q = 3-30ILH 1 * 5 . H = D + 1-4//. 

7 






CONTROL OF WATER 


98 

Constricted Cippoletti (see p. 117)- — 

Q = 3’82D 1,57 . L = 1 foot. 

Q = 5’42D 1,57 . L = 1*5 foot. 

Q — 7'38D 1,57 . L = 2 feet. 

Submerged Weirs .— 

Q = 3'33 L(H 1 -H a ) 1,5 + 4 , 6 oLH 2 \/H 1 - H 2 (see p. 122). 

Q = 3-33 KLH 1,5 . See page 123 for table of K. 

Broad-crested weir. Q = Qj (07 + O'185—) (see p. 128). 


Weirs.—A weir is essentially an irregularity in the stream bed, over which 
the water falls in a sheet of a certain depth. It is found experimentally that 
the observation of the absolute value of this depth permits the quantity of 
water passing over the weir to be calculated by formulas of a more or less 
simple character, provided that the weir is properly constructed. 

The usual terminology is somewhat redundant, and I therefore suggest the 
following : 

The term “Weir” refers to the whole constructional apparatus used to 
produce the definite sheet. In a weir there is a more or less well defined and 
measurable orifice through which the water flows, which determines the form 
of the issuing stream. This orifice I propose to define by the restricted term 
“ Notch,” which was formerly used as an equivalent for a weir, especially in 
America. 

The circumstances and form of the issuing stream have an appreciable 
effect on the discharge, and the term “Nappe” (used by Bazin—in English, 
“ Sheet”) will be employed to define the issuing stream. 

The term “ Channel of Approach ” defines the body of water immediately 
upstream of the weir in which is situated the gauge on which the thickness of 
the nappe produced by the weir is measured. The velocity of approach is the 
mean velocity of the water in the channel of approach at the point where the 
measurement of the head is made. 

The “ Head ” is the measured height of the water surface in the channel of 
approach above a fixed point in the weir, usually the lowest portion of the 
notch. When this is corrected for the velocity of approach by the formulae 
which will be given later, the term “ Corrected Head ” is used. 

As a matter of experiment, neither the head nor the corrected head 
accurately represent the nett thickness of the nappe. The measurement of 
this last quantity is attended by great experimental difficulties, and even Bazin’s 
most exhaustive researches have not satisfactorily determined the relation 
between the nappe thickness and the head, or the corrected head. It is there¬ 
fore better to regard the head as an observed quantity, and its corrected value 
as a quantity which the results of observation show to be more closely con¬ 
nected with the discharge over the weir than the observed head. 

The height of the sill or lower boundary of the notch above the 
bottom of the approach channel is important in some of the discharge 
formulae. 

Using feet, feet per second, and cubic feet per second as units, the follow¬ 
ing symbols are employed (see Sketch No. 23) : 

The head is denoted by D, 






99 


GAUGING BY WEIRS 


The velocity of approach is denoted by ?/, 

and h , is used to denote the quantity 
The discharge over the weir is denoted by Q. 


v 2 


2 g 



In practice, it will be seen 
approximation. “ We|have : 


that v y must usually be 



determined by successive 


where A is the area of the cross-section of the approach channel at the point 


— Half Plans of Conditions of Nolcti l Name . 

Sketch No. 23.—Generalised Sketch of a Weir. 












































IOO 


CONTROL OF WATER 


where D is measured. We therefore calculate an approximate value of 0 , 
from the observed value of D, say, Q x = CLD 1 * 5 , and thus obtain 

Vi — and h x — ,. 

A 2g 

We can now calculate H = D + a/zj, and : 

Q 2 = CLH 1 - 5 

and, if necessary, new values of v x , and h x , say v 2 , and /z 2 , can be obtained. 
This process is necessary, for as will hereafter appear, Q, depends more closely 
on a quantity H = D-f a/z, where a is a coefficient, than on D, the observed 
head. (See p. 104.) 

H, is therefore used to denote the “head corrected for velocity of approach.” 

In rectangular or trapezoidal notches, 

L is used to denote the length of the sill of the notch, and 

the height of the sill above the bottom of the approach channel. 

The general formula for weir discharge is of the type : 

Q = CLH 1 - 5 
or : 

Q = C'LD 1 - 5 

according as the corrected or observed head is used. C, or C', is termed the 
coefficient of discharge of the weir, and if distinction must be made, the terms 
“ coefficient for the corrected head,” or “ coefficient for the observed head ” are 
employed. The other terms employed in weir calculations will be defined as 
found requisite. 

Measurement of the Head.—The measurement of the head entails the deter¬ 
mination of the level of the water surface with as much precision as the 
available apparatus permits. The accuracy of the measurement and the 
circumstances under which it is effected are fundamental in all weir observa¬ 
tions. The effect of a small error in the observed head may be investigated 
as follows : 

The typical weir discharge formula is : 

Q = CLD 1 - 5 


where C, is a constant for small variations of D, and L, a length which can be 
measured with far more accuracy than D. 

Thus, we have : 

8 Q = i‘5CL V DSD 


or : 


8Q 

Q 


i*5 


SD 

D 


Now, the probable error in the observation of D, is independent of its 
magnitude. Hence, the larger D, is, the more accurately the discharge can 
be observed. 

As an actual example :—If D, be read on a fixed gauge, it is impossible 
to determine the water level with certainty to more than 0-005 foot, so that 
if an accuracy of 1 per cent, in Q, is desired, D, must be at least 0-75 foot, 
and this accuracy is only attainable with practice. 

If a hook gauge is used, a skilled observer will read to cooi foot, (I have 
never been able to attain 0-0005 foot as Francis states is possible). Conse- 




OBSER VA TION OF THE HEAD i o i 

quently, D, must be at least 0*15 foot in order to secure an-accuracy of 
1 per cent. 

The wheel gauge used by Bazin, and now employed for investigating the 
sieches in lakes, is probably somewhat more accurate. (See Sketch No. 24.) 

It has, however, been shown (see p. 23), that owing to certain peculiar¬ 
ities in the motion of water, it is useless to work with values of D, less than 
o'15 foot ; and values of D, exceeding 0*40 foot are preferable. 

Thus, in a properly designed weir, it appears that an accuracy of 1 per cent, 
(so far as this particular source of error is concerned), can usually be secured 
with a hook gauge, even with comparatively unskilled observers. 



In this connection, the theory of gauge pits as developed by Murray 
(The Fresh Water Lochs of Scotland, vol. 1, p. 51) deserves consideration. 
The oscillations in the water level caused by wind and waves, or by irregular¬ 
ities in stream motion, may be represented by : 

8D ® A sin nt 

where n T -= 27r, gives T, the period of oscillation. 




























102 


CONTROL OF WATER 


Now, let : 


a, be the diameter of the gauge well, 

b, be the diameter of the pipe connecting the gauge well with the approach 

channel, 

/, be the length of the pipe ; all expressed in inches. 


Put x = 7 ( accuratel y X = where all dimensions are expressed in 

centimetres). Then the oscillations in the gauge pit are expressed by 

n 

SG = A cos 71 t sin n(t — r), where tan ?it =—. 

X 


Thus, the oscillations in the gauge pit are diminished in the ratio i : cos «r, 
and “ lag,” or are delayed by a certain interval of time when compared with 
the oscillations in the channel of approach ; the absolute value of this interval 
being m seconds. 

The lag in time does not materially affect the observation of the head, but 
the diminution in amplitude of the oscillations affords a ready means of prevent¬ 
ing slight disturbances by wind or waves from affecting the gauge readings. 

Thus, consider a well with a — 6 inches, / = 72 inches, and b = \ inch, 
j inch, and inch. Murray gives : 


DAMPING RATIO = cos nr 

T. |-inch Tube. £-inch Tube. T \-inchTube. 

870 seconds 0*9992 0*8320 0*4213 

60 „ 0*8630 0*1028 0*0320 

So that short period wind or wave disturbances are almost entirely 
eliminated in the last two cases, and unless abnormally large, would not 
materially affect the readings of a gauge in the well. 

The effect of such methods of observation on the discharge formulas has 
never been investigated. It is plain that if the discharge of the weir at each 
moment is actually determined by a relation such as Q = K(D + SD) 1,5 where 
D, is the mean head, and D + SD the momentary head, the effect of any 
damping of the oscillations is to cause the average head, (as read in the 
gauge well), to be less than the average head which is effective in producing 
the discharge. Thus, the more the oscillations are damped, the greater the 
experimental coefficient K, will become. 

Under the above assumption, it would appear that if the amplitude of the 
waves is AD, the actual discharge may possibly be as large as : 



KD 1 - 5 


{ 


1 3 2 

r + o ~ 
O 7T 



and if these waves are entirely damped out, the gauge well reading will be 
D, so that the experimental coefficient is increased in the ratio : 



1 


or, taking AD = 0*04 foot, and D = 0*5 foot, the ratio becomes, 1*0016. But 
for AD = 0*08, D = 0*25 (which I have seen in bad cases), the value is 
1*0256. 





GAUGE WELLS 


103 


The figures available on this subject are somewhat discordant. 


In Bazin’s observations . 
In Francis’ 


In Fteley and Stearns’ observa¬ 
tions 


X = 294. 

X — 21 for weirs with side contrac¬ 
tions. 

X = o*4 for weirs without side con¬ 
tractions. 


X = o*i. 


The stardard well gauge of the Punjab Irrigation Branch has x — °’3 to 
o*6 approx. (See Sketch No. 25.) 

My own trials lead me to consider that x — B is well adapted to^secure 
accurate work with a fixed or hook gauge. The value used by Bazin is 
abnormal, and must not be regarded as expressing the whole damping, since 




Plan 



Tenth ofa Foot Cau ge. 


Sketch No. 25. —Punjab Gauge Well, with typical Gauge Graduations. 


his wheel gauge introduces an undetermined, (but very considerable) amount 
of damping. Comparison with observations made by other methods is there¬ 
fore difficult, and this must be considered as the one obvious defect in 
Bazin’s observations. In practice, the oscillations of the water level in a 
gauge pit constructed in accordance with Bazin’s rules will be found to be 
too great to permit really accurate work when the level is observed by a 
hook or fixed gauge. When Bazin’s wheel gauge is used, the observations 
are very easily made; and I believe that the results are not only more 
accurate, but that they more closely represent the head which is effective in 
producing the discharge, than do those which are obtained by any other 
method. 

Weir Discharge Formulae.—The usual formula for the discharge of water 
over a weir is that obtained from the ordinary approximate theory : 


Q = fMLH V2£-H 





























































io 4 CONTROL OF WATER 

where H, is the corrected head over the weir, and L, is the length of the notch, 
supposed to be rectangular in section. 

Now, the quantity actually measured, is not H, but D, the difference in 
level between the sill of the weir, and the surface of water when moving with 
a velocity v , towards the weir, where v 2 = 2 gh, say, and the first correction that 
must be made is for the “velocity of approach.” (See Sketch No. 23.) 

Francis, following an approximate theory, gets : 

H 1 - 5 = (D+A) 1,5 -k 1 ’ 5 

which is obviously a very cumbrous form. 

Other experimenters (especially Fteley and Stearns, and Bazin), have 
abandoned the theory, and used the empirical relation : 

H = D +ci/i 

where a is a coefficient. 

This is evidently less satisfactory theoretically, and the fact that each 
experimenter uses a different value for a seems to show that Francis’ theory 
has some foundation. The practical advantages in simplicity of calculation 
are, however, very evident, and have sufficed to cause the general adoption of 
the second form. 

Let us now consider the value of M. This depends on the shape of the 
cross-section of the notch, and on its position relative to the sides of the 
approach channel. 

We define a sharp-edged weir as one in which the edges bounding the 
notch are so thin that the nappe, or stream issuing from the orifice, springs 
completely clear of them. 

We also state that a weir possesses complete contraction when every wetted 
portion of the walls of the approach channel is at least 2L, or 2D, distant from the 
boundaries of the notch, whichever of these quantities happens to be the lesser. 

Contraction is completely suppressed at any point when the notch boundary 
at that point and the walls of the approach channel coincide. Any condition 
intermediate between complete contraction and completely suppressed con¬ 
traction is termed incomplete, or partially suppressed contraction, and if accuracy 
is desired, the condition can only be expressed by measurements of the distance 
between the boundaries of the notch and of the approach channel. 

The following varieties of sharp-edged weirs are used for accurate 
measurements : 

(i) Complete contraction all round the notch. (Sketch No. 23, upper 

portion.) 

(ii) Contraction complete at the sill of the notch, and completely sup¬ 

pressed at the sides ; such a weir is usually referred to as being 
without end contractions. (Sketch No. 23, lower portion.) 

Certain formulae are given on page 118 which permit approximate corrections 
to be made for the effect of incomplete contraction. The formulas are, however, 
unreliable, and accurate results are obtained only by using one or other of the 
above types of weir. 

The general effect of partial suppression of contraction is well known. The 
discharge is always increased, and the percentage of increase becomes greater 
the more the contraction is suppressed. Thus, the larger the head the greater 


GENERAL RULES 


io 5 

is the increase in discharge. The final effect therefore is that while the dis¬ 
charge of a rectangular weir with complete contraction is expressed by : 

Q = KH N 

where N, varies from 1*45 to 1*50, or perhaps even 1*52, the discharge of a 
similar weir with partially suppressed contraction is expressed by : 

Q = K X H N 

where N, varies from 1*5, to 1 *6, and K 1} is somewhat larger than K, the increase 
in K 1} and N, being roughly speaking proportional to the amount the contraction 
is suppressed. This method of regarding the matter proves very useful when 
it is desired to obtain a weir formula from actual observations, as although no 
definite rules for K 1} and N, can be given, the calculations are far easier than 
those required when a formula : 

Q = CH 1 - 5 

is used, and C, is variable. (See p. 118 and Sketches Nos. 18-20.) 

Practical Rules.—Francis gives the following equations for these standard 
cases : 

Q = 3’33 (L — «H xo*i)H 1,5 .case (i) 

Q = 3‘33LH 1,5 .case (ii) 

where n, is the number of side contractions, i.e. 

n — 2, in the ordinary weir with end contractions, 
n— 4, in a weir with a sharp-edged pier in its midst, 

and if there is a velocity of approach, — 

H1.* = (D + h) 1 -*—h 1 - 5 = D + (1 — | sj ^ ) h approx. 

Now, as already stated, the correction for velocity of approach is cumbrous ; 
but otherwise the formulae are simple, and easily remembered. Further, 

10 

3*33 = — 

j 

so that in the case of rough calculations and approximate results, where the 
correction for the velocity of approach need not be considered, these formulae 
may be adopted. 

Weir Formula, as applied to Aleasurement of Discharge .—It is believed that 
a weir gauging (failing an actual volumetric measurement) is the most accurate 
method of measuring a discharge. When applied for such purposes, it is 
necessary to consider the effect of local peculiarities on the discharge of a weir. 
It can at once be said that a weir is a very accurate measuring instrument, but 
like all other measuring instruments it must be carefully standardised in order 
to get the best results from its use ; and the standard should be copied in 
details which at first sight appear to have no real effect upon the discharge. 

The two reliable series of standard experiments (when considered fiom thi 
point of view) are those of Francis and Bazin, and of these Bazin s aie by far 
the most comprehensive in range. 

If we erect a weir, and carefully and systematically copy the details either of 
Bazin’s or Francis’ original apparatus, it will be found that the dischaiges agiee 
with those found by the appropriate formulae, within \ per cent. It will also 
be found that the errors are nearly all attributable to one cause, namely, the 


io6 


CONTROL OF WATER 


difficulty of accurately observing the level of a water surface to more than 
0*005 foot, especially when large volumes of water are dealt with. 

If, however, we erect what may be called a generalised weir, i.e. a weir 
constructed in accordance with the specification of Francis or Bazin, but the 
details of which (say, for instance, the method of observing the water level, 
or the material lining the approach channel between the weir and the point 
where the water level is observed) are varied according to local convenience, 
it will be found that the formulae given by both Francis and Bazin may lead to 
results differing from the true discharges by 2, or possibly even 3 per cent. 

We cannot therefore state that the formulae are wrong, but merely that 
we have used an unstandardised apparatus for measurement. 

Besides the experiments of Francis and Bazin, others exist, notably those 
of Fteley and Stearns, also of Lesbros, and Boileau, etc. A study of their 
results, assisted by Hamilton Smith’s computations, permits me to state that 
for these generalised weirs a formula can be found which is applicable to weirs 
with complete side contraction, and which is more easy to calculate than the 
one adopted by Francis, and which can be employed over a wider range of 
conditions. 

We thus have two series of formulae : 

1. Formulae applicable to standard weirs : 

{a) Francis’ formula for completely contracted weirs. 
b ) Bazin’s formula for weirs with suppressed end contractions. 

2. Formulae applicable to generalised weirs : 

(а) For weirs with complete contraction. 

( б ) For weirs with side contractions suppressed. 

The first class produce results which are correct to about i per cent, when 
the observers are sufficiently skilful to work the weir as it deserves. 

The second class give a mean result, and may be as much as 3 per cent, 
in error. It will, however, be found that when applied to weirs which are not 
carefully constructed, so as to agree with the standard type, they usually yield 
results which are less subject to error than those given by the formulae of the 
first class. 

I. Formulae of the First Class (Francis’ Formula). —The weir must be 
constructed as shown in Sketch No. 26 which is copied from Plates 11 and 12 
of the Lowell Hydraulic Experiments. The head D, is measured by hook 
gauges in boxes, 6 feet upstream of the weir, the water being admitted to these 
boxes by holes 1 inch in diameter. On scaling the original drawing we find 
that : p = 4 ‘ 6 o feet. 

The formula is : 

Q = 3*33 (L — n x H xo'i)H u 
with : H 1,5 = (D +/?) 1 - 6 — h 1,b 

and H, was varied in the experiments between o*6o foot and r6o foot; but the 
formula is probably applicable between H =0-50 foot, and 4’oo feet (see 
Horton, p. 39), provided that fi, is greater than 3H. 

The side walls of the approach channel were of granite masonry, and the 
bed of timber, although possibly timber all over will suffice for copies. 

The side walls of the approach channel should be at least 2D, distant from 
the ends of the notch. The nappe should be allowed to expand freely at its 


FRANCIS' FORMULAE 


107 


sides aftei leaving the notch. It is believed that if this side expansion is 
prevented the discharge is increased by about ^ per cent. Francis states that 
if P ~ 2 D, and if the sides of thefapproach channel are distant D, from the 


75 

r - . 

1 





n t 
*) 


*0 

<0 


N. 


Centre of 



Channel 



Sketch No. 26. —Standard Dimensions of Francis’ Weir. 

ends of the notch, the discharge is increased by 1 per cent., but these state¬ 
ments are only approximate. 

The term —o’mH, which represents the correction for the end contractions, 
is not very accurately determined ; except when L, is greater than 3D, and D, 
lies between 0*50, and r6o foot. It is probable that the coefficient on, should 




























































io8 


CONTROL OF WATER 




'SThumdSf 

Screw 





Side li/er/ 





21 


k - 4 - — >< £ ! 


E> 


«l 

>1 


Section 


Sketch No. 27.—Hook Gauge. 

















































































BAZIN'S FORMULA 


109 

be increased if H, is less than 0*50 feet, and should be decreased if H, is 
greater than r6o feet; but the facts stated on page 114 show that the question 
is not of great practical importance. 

A weir of similar construction, without end contractions, can also be used as 
a standard weir, and the formula : 

Q = 3 ’ 33 LH 1<s 

is accurate for all values of H, between 0*50, and r6o feet; and is believed to 
be applicable up to H = 5 feet, although it possibly overestimates the discharge 
by 1*5 to 2 per cent, near H = 2*5 feet. 

The Bazin weir, however, is better adapted to this case. 

Bazin Formula. —Bazin’s standard weir ( Ecoulement en deversoir , Pt. I. 
p. 9) was erected in a rectangular cement-lined, and smoothly rendered 
approach channel 6*56 feet wide, by 5*25 feet deep, and 49*2 feet long (2 metres 
xr6 metre x 15 metres). The water surface level was observed in lateral 
pits, 1‘64 foot square (o’5 metre) communicating with the approach channel at 
a distance of 16*4 feet (5 metres) above the weir, by a circular pipe 0*33 foot 
(o*io metre) in diameter, and about roo foot long (scales as 0*31 metre). 
(Sketch No. 28.) 

The water level was observed by a float and indicating quadrant, as per 
Sketch No. 24, and an alteration of 0*0002 foot in the water level could certainly 
be observed, although it is not so certain that equal accuracy in the absolute 
value of D, was obtained. 

The weir itself was built up of beams, and the sharp-crested sill of the notch 
was made of o*28-inch iron plate, as indicated in Sketch No. 28. 

There were no side contractions, and the nappe was not permitted to 
expand laterally after leaving the weir, but special care was taken to prevent 
a vacuum being formed below the nappe in consequence. 

The sill of the notch was 372 feet (1*135 metre) above the bottom of the 
approach channel, and its length was either 6*56 or 3*28 feet (2 metres and 
1 metre). 

Experiments were also made on a notch 1*64 foot long, with a sill 3*3 feet 
(1*005 metre) above the bottom of the approach channel, and for the shorter 
notch one side of the channel of approach was of planed planks. Notches 
approximately 6*56 feet long (2 metres), and with their sills 2*46 feet, 1*64 foot, 
1*15 foot, 0*79 foot, (0753 metre, 0*502 metre, 0*349 metre, 0*240 metre), 
above the bottom of the channel were also less systematically experimented on. 

The results were as follows : 

(i) For D, greater than 0*62 foot (0*19 metre) the length of the weir has 
no appreciable effect on the coefficients of discharge, and it is doubtful whether 
the differences observed below D =0*62 foot are not entirely those of observation. 

(ii) The effect of variations in p, the height of the notch sill above the 
bottom of the approach channel is reduced to a table, which gives the discharge 
with errors not exceeding 1 per cent., and usually less than 0*3 per cent, except 
in the case of the notch with a very low sill, p = 0*79 foot where errors of 2*5 
per cent, occur ; but the formula given below occasionally introduces errors of 
2, to 3 per cent. when is small, say less than 1*5 F). 

This approximate formula is : 

Q = (3-248+ {>+o -55 (^Vd) 2 } LD>-« 



no 


CONTROL OF WATER 


The errors never exceed i per cent, over the range 
D = i’45 foot, provided that/, exceeds i foot. 

The shorter formula : 


Q= { 3 ' 4 H-r 69 f^ D )} LU 1 ' 5 


I) = o’3o foot to 



may be used for values of D, between 0*33 foot and roo foot if errors of 2, or 
3 per cent, are permissible. (See Horton, Weir Experiments, p. 32.) 

The Bazin weir must be regarded as an instrument of great delicacy, and is 
therefore easily put out of order if carelessly used. As an example : If the 
















































































GENERAL FORMULAE 


in 


nappe is allowed to expand laterally, after leaving the notch, the discharge in¬ 
creases about o’5 to I per cent. So also, owing to this prevention of lateral 
expansion, the nappe (under favourable circumstances) may assume various 
forms. The typical form, and the only one that can be employed in accurate 
gauging, is the Free Nappe (Nappe Libre), Sketch No. 28. If, however, the 
under side of the nappe is not properly mrated, or rather, if the circumstances 
are such as not to produce perfect aeration, the nappe becomes Depressed 
(Deprimee), see Sketch No. 28, and the discharge may be 8, to 10 per cent, 
greater than that given by the formula. If the air is completely exhausted from 
under the nappe, the air-free (Noyee h dessous) form may appear, and another 
10 per cent, increase in discharge may occur. (See p. 126.) 

Under favourable circumstances, and especially if the wall of the weir is in¬ 
clined upstream, we may obtain the striated (adherente) nappe, see Sketch 
No. 29. This form permits of a discharge which is 20 to 30 per cent, greater 
than the normal. The matter is carefully discussed by Bazin (ut supra), but 
the practical result of his work is that such forms should not be permitted in 
accurate work. (See p. 126.) 



Sketch No. 29.— Striated Nappe and Types of Nappe occurring with 

broad-crested Weirs. 


With great diffidence I venture to suggest that were the nappe allowed to 
expand after leaving the notch, it is probable that the length of the weir would 
in no way affect the coefficients of discharge (although these would no longer 
agree with Bazin’s determinations), and it is quite certain that the peculiar 
forms above enumerated would not occur. 

If for any reason, the nappe is allowed to expand laterally after leaving the 
notch, the Francis form of weir and gauge pits should be adopted, and the 
formula : 

Q = 3 * 33 LH L5 

with Francis’ correction H 1,5 = (D+Zz) 1 - 5 — used. 

II. General Formulae.— (a) Weirs with complete contraction. The general 
results of all existing experiments have been very carefully discussed by 
Hamilton Smith. I am inclined to believe that the agreement between the 
various series is not quite as close as would at first sight appear, since 
Hamilton Smith seems to select the correction for the velocity of approach with 
but little regard for the method of observation employed by the original 
experimenter. 

I should not, however, feel justified in proposing a formula differing from 























I 12 


CONTROL OF WATER 


that deduced by Hamilton Smith, were it not that I find that the mean result 
of the observations can be very well represented by formulae which permit us 
to obtain the discharge by a multiplication of two figures taken from tables, in 
place of three required with the coefficients given by Hamilton Smith. 

The proposed formulae are, with H = D + rq/z. 

(i) For heads less than 0*40 foot. 

Q = 3*101 L 102 H 1 * 46 , so long as L, is less than 2*6 feet. 

Q = 3'i46 L 1 005 H 1 - 46 , where L, is greater than 2*6 foot. 

(ii) For heads greater than o’4o foot. 

Q = 3*iio L 102 H 1 - 465 , so long as L, is less than 4 feet. 

0 = 3122 L 1016 H 1 * 475 for L, between 4 and 10 feet. 

Q = 3*148 L 1013 H 1 - 485 for L, greater than 10 feet. 

These formulae hold up to L = 30 feet, and possibly for greater values of 
L ; and for H, as high as 17 foot, and possibly further. (See p. 132.) 

{b) Weirs with side contractions suppressed. 

Bazin’s formula should be used, and the head should, if possible, be 
measured 16*4 feet above the weir. 

The following are the chief corrections which should be made : 


(i) If the nappe be allowed to expand after leaving the weir, increase the 
discharge as obtained by Bazin’s formula, by | to ^ per cent., or use the 
Francis’ formula, and measure the head 6 feet above the weir. 

(ii) If the stream is unusually deep, say more than 4D, in depth, and the 
head is measured closer to the weir than 16*4 feet, it may be better to employ 
Francis’ formula, with Hunking and Hart’s correction. 

Q = 3*33 (1+0-25 

where is less than 0*36 ; while be greater than 0*36, the original 

Francis formula for the correction for velocity of approach must be used, 
though in such cases the Bazin formula is certainly more accurate. 

General Agreement of Weir Discharge Formulae.— hi first sight 
it would appear that the various weir formulas are so discordant as to produce 
a certain distrust in weirs as a method of measuring water. 

For example, taking a weir without end contraction, we have : 


Francis 

Hamilton Smith . 
Fteley and Stearns 

Bazin . 


Q = 3-33 LH 1 * 5 
Q = 3 ‘ 3 r t0 3 ’ 5 i LH 1 - 6 
Q = 3*31 LH^+o'ooyL. 




+°*55 



LD 1 * 5 


and it would therefore appear that differences as great as 6 per cent, might 
occur. 

As a matter of practice, if all considerations except the numerical result are 
disregarded, differences of 2, or 3 per cent, can be obtained ; and I am by no 
means satisfied that such juggling is entirely unpractised in commercial testing. 
When, however, the matter is treated in a scientific manner, it must first be re- 





AGREEMENT OF WEIR FORMULAE 113 


marked that the H, in the above formulae is by no means the same quantity. 

7/2 

Putting — = h. 

2 g 


Francis defines 

. H L5 = 


and very nearly . 

. H = 

£>+/;( 1-! ^ 

Hamilton Smith puts 

. H = 

D +h 1*33 

Fteley and Stearns . 

. H = 

D-f-/z i*5 

Bazin ..... 

. H = 

D T h 1 ’68 



Thus, we see that with the exception of Hamilton Smith’s general formula, 
the smaller the coefficient C, in the equation Q = CLH 1 - 5 , the larger will be the 
value of H, as calculated for the same values of D, and v, the quantities 
actually observed. The water surface of the stream above the weir is not 
absolutely horizontal, but drops down in a flat curve towards the weir. Thus, 
the observed value of D, depends to some degree upon the exact point at which 
the observations are taken, and the greater the distance of the gauge from the 
weir, the larger will be the values which are obtained. 

The balancing goes even further. Bazin observed D, at a distance of 
16 feet from the weir, and obtained the smallest coefficient in the whole series. 
The other observers generally used 6 feet as their standard ; although, in some 
cases, where other distances (usually less than 6 feet) were used, corrections 
for surface curvature appear to have been applied. Owing to the curvature of 
the water surface as it approaches the weir, it is certain that the D, as observed 
by Bazin, is appreciably larger (my calculations indicate 07, to 07 per cent, 
larger ; but I would lay no stress on an obviously flimsy piece of evidence) 
than that which would have been observed by the methods of Francis, or 
Fteley and Stearns. 

I had an opportunity of testing the question, and conducted 18 experi¬ 
ments as follows : 

An unknown volume of water was passed over a weir constructed according 
to Bazin’s specification, except that the sides of the channel were of wood, in 
place of cement plaster. The value of D, was observed according to Bazin’s 
methods, say D B , at i6’4 feet above the Bazin weir. The water then passed 
over a standard Francis weir, and D, was observed in a box according to 
Francis’ methods, at 6 feet above the standard Francis weir, say D P . The 
lengths of the sills of the two weirs were as follows : 


L b =4'o8 feet, L F = 4*04 feet. 

D b , and D f , were then corrected by the proper formula?, and H B , and H F , 
were used to calculate the quantity discharged according to Bazin’s and 
Francis’ formulae. 

The ratio ~ B ~~Qf varied between + 1*4 per cent, and — r6 per cent., with a 

Q b 

mean error of — o*2 per cent. I was not at the time so skilled an observer as I 
later became (this being almost my first attempt at large scale weir observations). 
I am now inclined to believe that a skilled worker would have obtained less 
concordant results by selecting quantities of water which were better suited to 
disclose the lack of agreement in the formulas, (e.g. in all my observations the 
values of D, lay between 07 and ri foot, and this range is probably the one 
over which the formulae agree best). 

8 



CONTROL OF WATER 


114 


Nevertheless, the agreement is well within the probable accuracy of my 
observations, and I believe that the various weir formulas, when properly 
applied, lead to results which agree with each other quite as closely as would 
those obtained by two independent observers working up their separate obser¬ 
vations, and using the same formula. 

If the reverse method is adopted, and Bazin’s formula and methods of 
observation are applied to calculate the discharge over a Francis weir, where 
p = 4*6 feet, the reasoning already employed indicates that the agreement will 
• probably be less accurate, but experiments do not exist. 

For weirs with side contractions, the apparent agreement in the formulas is 
somewhat better. The formulas must be considered as less accurate, and the 
correction : 

Effective length = Measured length — »Hx o*i 

(see p. 105) must be regarded as subject to some uncertainty. 

The only definite experiments, other than the original ones by Francis, were 
undertaken by Bazin (as yet unpublished). 

It would appear that under certain circumstances (usually at low heads) 
the factor o’i, may attain the value o’14. The fact that the French official 
instructions do not give any other rule than that of Francis, is fair proof that 
the present formulas do not depart very widely from the truth, under any 
circumstances. 

Sharp-edged Notches of other than Rectangular Form.—The only notches 
which have been sufficiently experimented on to be used in accurate measure¬ 
ment are the Triangular Notch, and a special form of Trapezoidal Notch known 
as the Cippoletti Notch. 

(a) Tria?igular Notches .—The usual theory leads to the following formulas : 

Q = AML 1 V'^D 1 -5 

and L 1} the width of the notch at the water level varies as D. 


Let L 1 =zD say, so that Q = i^MV2^b 2,5 

We find experimentally that M, varies with z , but is quite unaffected by D, 
probably owing to the fact that the cross-section of the issuing stream remains 
similar to itself for all values of D. 

The following special cases may be given : 


z=\. 


z — 1. 
z — 2. 


Or L 1 = —. 

1 2 

Or L 1 = D. 

Or Li = 2D. 


Q = o-7o 7D 2 - 5 up to D = 1 -6 foot. 

Q = i* 3 iD 2 - 5 up to D = i *5 foot. 

Q = 2*545D 2 - 6 up to D = no foot, 

with the floor of the approach channel at 
least D, below the vertex of the notch. 

Q = 2’56D 2 - 8 up to D = rio foot, 

with the floor at the level of the notch. 

Q = 5 ’3 oD 2 - 5 up to D = ro6 foot, 

with the floor well below the vertex. 

Q = 5*22D 2 - 5 

with the floor at the level of the vertex. 

The above formulas are due to Thomson (Brit. Asscn. Report , 1861, p. 155, 
not the usual reference of 1858) and Leslie. The upper limits of D, are 


z = 4. OrL 1 = 4D. 


TRIANGULAR NOTCHES 


”5 


the greatest values observed in my own experiments which ranged from 
D=o’6o foot upwards, by intervals of o’oi foot. A special examination was 
made of each o’io foot interval, in order to detect variations in M, with 
negative results. 

I obtained my results by a series of systematic volumetric checkings into 
a tank of 2900 cube feet capacity, the head being read directly on a carefully 
adjusted brass scale. The probable error was o'4 per cent. Consequently, it 
may be assumed that these notches afford a ready means of gauging water up 
to a discharge of about 5 cusecs, with an accuracy of 0*4 per cent., and the 
coefficients given above probably hold good for heads greatly exceeding those 


stated. 


I do not give any formula for the correction for velocity of approach ; since, 
with a properly proportioned approach channel, v, cannot exceed o‘5 foot 
per second, unless contraction is incomplete ; and for v=o’$ foot per second, 
h = o'oo2 foot, which is inappreciable in direct readings on scales. 



Fi$I. Crist of Notch Rounded %M. Cippotetti Notch 

Sketch No. 30.—Notch with Rounded Edge, Triangular and 

Cippoletti Notches. 


I have, however, purposely tried the effect of high velocities of approach, 
and incomplete contraction, and can state that the full results of both effects 

combined can be allowed for by putting H = D + — in the formulae. 

(b) Trapezoidal Notches .—The theoretical formula is as follows : 


Q= f ^ c 2 z \/ 2 gH 2 - 5 


where c 1} and c 2 , are coefficients of discharge, and *,■ is the slope of one side of 
the weir to the vertical, L, being the length of the sill of the weir. 

if we consider Francis 5 formula, we see that the effect of side contiac 
tions is to decrease the discharge by an amount equal to 





























116 CONTROL OF WATER 

Equating this to the amount passed by the two triangular end pieces, i.e. 

T5 zc 2 ^ 2£'H 2 - 5 , we get, z — \. (Sketch No. 30.) 

Cippoletti experimented on a weir of these proportions, which otherwise 
satisfied Francis’ specification, and came to the conclusion that its discharge 
could be represented by : 

Q = 3*367 LH 1,5 

with the Francis velocity of approach correction (Cana/e Villoresi , Modulo per 
le Dispensa della Acque). 

Flinn and Dyers’ experiments gave the formula : 

Q = 3'3oiLH ls 

with H = D +1*4/2, which is more easily applied {Trans. Am. Soc. of C.E ., 
vol. 32, p. 9). 

Weir Gauging of Water containing Silt.—In order to obtain any real 
accuracy in gauging, it is necessary to render the velocity of approach small, 
and this encourages the deposit of silt. If the action is not carefully observed, 
it will be found that these deposits rapidly accumulate, and may very appreciably 
alter the coefficient of discharge of the weir, by suppressing contraction. 

The matter was most forcibly brought before me in connection with the 
accurate measurement of water containing silt in proportions up to 3^ of its 
volume. The following methods are the fruit of systematic volumetric check¬ 
ings, and are subject to a probable error of 0*7 per cent. 

The ordinary Francis weir (with end contractions), or the Cippoletti type, 
are quite useless, as the conditions for complete contraction cannot be preserved. 
The Bazin, or Francis weir, without end contractions, is less rapidly affected ; 
but is not really reliable unless the depth below the weir crest is systematically 
preserved at about 2H, at least. 

The methods finally adopted were two in number, viz. : 

{a) The Triatigular Notch. —This was found to be unaffected in its discharge 
by any deposit of silt that could be induced to remain in front of it, even by 
such methods as laying down straw mats immediately above the notch. This 
statement holds for the L 1 = D, L 1 = 2D, and Lx = 4D notches, under heads 
ranging from o*6o foot upwards. 

The results given by Thomson (see p. 114) indicate that a straw mat or 
“ floor” will have some effect in the case of heads lower than o'6o foot, but 
the effect was not observed in my experiments. 

This method is the best if the quantity of water, and the available head 
permits its adoption. 

( b ) For quantities of water greater than those which could be conveniently 
measured over triangular notches I employed a weir of Cippoletti form, but 
with partially suppressed contractions. Sketch No. 31 shows the elevation and 
cross-section, and it may be noted that the somewhat peculiar stopping of the 
brickwork on either side of the notch was necessary in order to prevent the 
wooden board in which the weir notch was cut, from warping. 

The position of the brick sill in relation to the sill of the notch was fixed 
so as to cause the natural flow of the water to sweep away any silt deposited 
on it. 

Subject to the above condition, it was found that deposits of silt outside the 


WATER CONTAINING SILT n 7 

brickwork had no effect on the discharge, and the following formulas were 
adopted : 

For a Cippoletti weir with a sill 12 inches long, we find from 23 observations 
that : 

(i) When D, is less than o’^o foot, 

log Q = i*6i log 10D —1’030. 

(ii) When D, is greater than 0*50 foot, 

log Q = i *57 log 10D— o ’988. 

The formulas hold over the range D=o’i5 foot to D=o’9o foot and the 
observed discharges agree with the calculated figures in every case if an error 
of o'oo5 foot or less in D, is assumed to occur. 



For a Cippoletti weir with a sill 18 inches long, we find from 17 observations 
that : 

For all values of D, between o - 25 and 075 foot, 

l°g Q = i '57 log 10D —o - 836 

and all differences can be explained by assuming an error of o - oo5 foot in the 
observed value of D. 

For a Cippoletti weir with a 2 foot sill, we find from 14 observations that : 

For all values of D, between 0*30 and 070 foot, 

log Q = i ’57 log 10D— 0702 

These formulas may be expressed in the forms : 

(i) 1 foot weir .... Q = 3*82D 1,57 

(ii) 1*5 „ .... Q = 5‘42D 1,57 

(iii) 2 „ .... Q=7‘38D 1,S7 

If errors of 2 per cent, are permissible, the general formula Q = 378L° ,95 D 1,57 
may be used for Cippoletti weirs with contractions as shown for values of L, 
between 1 and 2 feet 

Suppression of Contraction.—The question of the effect of partial sup¬ 
pression of contraction over portions of the notch boundary is obscure. The 
discharge will be increased in all cases. Hamilton Smith ( Hydraulics , p. 120) 
states as follows : 

Let X, be the least dimension of the notch, whether L, or H. 

Let R = L + 2H, be the wetted perimeter of the notch. 









































118 


CONTROL OF WATER 


Let Y, be the distance of any boundary of the notch from the corresponding 
side of the approach channel. 

Let S, be the length of the portion of the notch boundary over which this 
distance Y, occurs. 

Then, the discharge of the notch with partially suppressed contraction is 
ZS 

i -f — that of a similar notch with complete contraction all round its boundaries 
JK 

(the general formula being used) and 


Y 

X 


Z 


3.. . o'ooo 

2 .C ’005 

I.0’025 

ijr.0'o6o 

o.o’i6o 

The above formula can be considered only as a rough guide, and it would 
be futile to expect to secure the accuracy of either the accurate Francis or 
Bazin formulas. 

Some of my own experiments on a rectangular notch lead me to believe 
Y . 

that when — is i, the actual flow is usually larger than the corrected value as 

A 

above obtained, and Freeze’s formula (see below) seemed to accord better. 
Prasil {Schweizerische Bauzeitung, 1905) finds the reverse to be the case, and at 
present no general formula for a suppressed notch can be regarded as accurate 
to even 5 per cent, over large ranges of H, or L. 

Experimental Weir Formula .—The usual method of allowing for the 
effect of partial suppression of contraction, and other deviations from the 
standard weir form, is to state the equation in the following manner : 

Q = CLD 1 - 5 


and to give an expression for C, in terms of D. 

As an example, Freeze’s formula may be taken ; which, if B, be the breadth 
of the assumedly rectangular approach channel, and T, is its depth, so that: 

T = D+/ 


where /, is the height of the weir crest above the bottom of the channel, is 
represented by : 


Where : 


Q — S'SS^W - 5 including velocity of approach. 

„_J n . r „ rr . °‘°558 _ 0-246 1 

'‘-L 0 5755 +0+^59 L+3-94J’' / 

and „=i +jo-25 (^)'+o-o2 5 + . a ° . g 37 - 5 -!(?-) 

\ Vqv +0 ’ 020 


1 lie agreement with the observations discussed is good, but the practical 
application of the formula is somewhat wearisome. 

On the other hand, a wooden flume with a terminal weir is practically a 
standard hydraulic apparatus, and considerations of available space usually 
prevent the weir from being made of the standard Francis or Bazin type. 











INCLINED WEIRS 


n 9 

It therefore beeomes necessary to inquire whether some more convenient 
discharge equation cannot be obtained. 

The method of logarithmic plotting, enables me to say that all accessible 
experiments agree very accurately with formulae of the type: 

Q = KD N 

provided that D, is over 0*40 foot. The same form holds when D, is less than 
this value, but the values of K, and N, are changed. 

At present I cannot give rules for the values of K, and N ; but would 
observe that the more the contraction is suppressed, the greater is the 
value of N. 

Inclined Weirs. —When the whole barrier forming the weir is inclined in a 
vertical plane, and the notch is sharp-edged, Bazin (Ecoulement en deversoir , ii. 
p. 43) gives the following ratios for : 

Discharge of inclined weir 
Discharge of standard weir 

the D, and p y being the same for both weirs : 


Inclination. 

Ratio. 

Approximate Value 

Horizontal. 

Vertical. 

of C in Q = (JLD 1,5 . 

i Upstream 

I 

°'93 

3'°97 

3 ” 

2 

0-94 

3* T 3 

3 5 } 

I 

0-96 

(Boileau finds 

3* 1 97 

Verti 

cal. 

0-973) 

1 -oo 

3*33 

3 Downstream 

1 

1 *04 

3'463 

3 55 

2 

1*07 

3 * 5 6 3 

1 » 

1 

no 

3*663 

1 „ 

2 

I -12 

3 * 73 ° 

1 „ 

4 

1*09 

3-630 


The maximum value of the discharge occurs when the inclination is about 
7 horizontal to 4 vertical. 

Oblique Weirs.— The case of a weir oblique to the approach channel has 
been studied by Aichel ( Ztschr . Deutsche Ingenieure Verein, October 31, 1908). 

The notch had no side contractions, and the sill was 10 inches (0-24 metre) 
above the bottom of the approach channel, the heads ranging from 6 inches 
upwards. Except for its obliquity the weir was of the standard sharp-edged 
Bazin type. 

Taking L, as the length of the sill of the notch, 

p, as its height above the bottom of the channel, 

e, as the angle the weir makes with the sides of the channel, 

D, as the head, 




























I 20 


CONTROL OF WATER 


Let Q b be the discharge over a weir of notch length L, and height p , under 
a head D, as computed by Bazin’s formula (p. 109). Then Aichel finds : 



where p is given in the following table. 


V 

For Channel 0^25 Metre 
(say 10 Inches wide). 

For Channel 0*50 Metre 
(say 20 Inches wide). 

15 degrees 

305 

362 

3 ° „ 

53 2 

700 

45 

893 

1250 

60 „ 

1923 

2275 

75 

6579 

6579 

'.r !' 


The observations are accurate, but it can hardly be supposed that they 
disclose the whole law, especially the effect of variations of p. 


3-6 


3-2 


28 


24 





1 



^ Coe 

' 4 . 

* 

•5 / 

0 / 


3-6 


Vo 


52 

^26 

I 


Value of % Feet. 


24 


Nat 

/ 

be free 


1 ^ 

1 ^ 

1 5$ 

1 ^ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

( 

4 

h 

/ 

0 / 

- 7 — 

/ - 

e 

Crest 0 - 

Crest / 

3 

479rv/de 

MDw/de 

4 

Value of H*[( D+h) %-/}%]$ 

5M 


53/ 


- Crest OiSChride 

- Do Do. but rounded 

to 05b radius dt upstream corner. 




Sketch No. 32. —Coefficients of Discharge for Broad-crested Weirs. 

We can, however, be fairly certain that where p, is not too small in com¬ 
parison with D, and especially where the weir has side contractions, the effect 
of a slight obliquity is not very marked. 

Certain escape weirs in America have been constructed with the sill 
crenellated in plan, so as to give a sill length which is three or four times the 
















































ROUND-EDGED WEIRS 


121 


width of the escape channel. These are stated to discharge the same quantity 
as a straight weir of equal length. 

Aichel’s values show that if be large in comparison with D, this is 
probably approximately correct, and in cases where the nature of the ground 
is such as to permit a very deep escape channel to be excavated more readily 
than one which is somewhat wider, but shallower, such construction appears 
to be desirable. 

I should, however, prefer to deduct some io per cent, from the sill length in 
calculating the discharge, and should like to have /, at least equal to 3D. 
This is not impossible, as assuming that D is equal to 5 feet and that the sill 
length is three times the width of the channel, it is evident that each foot width 
of the escape or approach channel must carry at least 100 cusecs (allowing 
10 per cent, deduction), and this would require about 10 feet depth, so that the 
bottom of the channel must be some 15 feet below the sill of the weir in order 
to avoid drowning the weir. 

Weir with Rounded Edges. —In some cases the edges of the notch are 
not perfectly sharp, although sufficiently sharp to cause the nappe to spring 
clear of the sill of the notch (Sketch No. 30, Fig. 1). (Compare p. 141.) 

Fteley and Stearns {Trans. Am. Soc. of C.E ., vol. 12, p. 97) working with a 
weir the notch sill of which was 0*035 foot wide, and with an upstream edge 
rounded to radii of j inch, h inch, and 1 inch, found that the usual formulae applied 
provided that 07 radius was added to H. D, must exceed 0*17 foot, 0*26 foot, 
or 0*45 foot, in order that the nappe may spring free from the sill. When the 
sill was 4 inches wide the correction is : 

H = Observed H -f- 0*41 radius 

When the sill is sufficiently wide, or the radius is sufficiently large to cause 
the nappe to adhere to the sill of the notch, the formulas for sharp - edged 
weirs are inapplicable (see p. 128). 

These corrections will be found very useful when weirs in which the notches 
are constructed from wooden planks are used for measuring small quantities 
of water. 

I have applied the correction 070 radius to cases where the radii were 1 inch, 
and 1^ inch, and find that it leads to results which agree very closely with 
volumetric checkings, provided that the nappe springs free. Since I could not 
observe D, more closely than 0*005 foot, I am unable to state that the ratio 
0*70 is correct, as o’65 or 0*75 would have answered equally well. 

Drowned Weirs (Sharp-edged). —The following notation will be em¬ 
ployed (Sketch No. 33). 

d, is the difference in level between the upstream water surface and the 
sill of the notch. 

d u is the same quantity for the downstream water surface. 

7^, is the difference in level between the sill of the notch and the bottom of 
the upstream channel. 

is the difference in level between the sill of the notch, and the bottom 
of the downstream channel. 

Thus, the depth of water in the upstream channel is represented by d+f, 
and in the downstream channel by d 1 +f 1 . 

D, the head over the weir is : 

d— dy 


122 


CONTROL OF WATER 


The problem is complicated, and has by no means been completely 
investigated. In the first place, the corrections for velocity of approach are 
obscure, and in theory at any rate, it is plain that : 


*/ 2 


H = D + a- 


2 ? 


2JT 


where v x , is the velocity of “ escape,” i.e. the mean velocity in the lower 
channel. 

The existing experiments refer solely to weirs without end contractions. 
Francis {Trans, of Am. Soc. ofC.E., vol. 13, p. 303), following the approx¬ 
imate theory that the discharge is the sum of that of an ordinary weir under a 
head equal to D, and of an orifice with a length L, and a height d lt under a 
head D, finds that: 

Q = 3 , 33L(H 1 -H 2 ) 1 - 6 + 4 -6 oLH 2 V W-H* 


where H 1} is the value of d, measured to a still water surface ; and H 2 , is the 
value of measured at a point where the oscillations did not affect the 
result. 



So far as can be gathered from the figures given in Francis’ paper, the 
weir was a standard Francis weir in all respects, but the velocities of approach 
and escape were so small that H 1 = d, and H s =d 1 . 

The formula is the result of 24 experiments on a 22*2 feet notch with : 

Q, ranging from 72 to 224 cusecs. 
d, ranging from 0*99 to 271 feet. 
d ly ranging from 0*02 to rn foot. 

The least value of d^ is determined by the condition that air had dis¬ 
appeared from under the nappe, which usually occurred at rt'^o’oS foot, to 
0*10 foot, but was delayed until d x = 0*17 foot, when d= 1*96 foot. 

Francis assumes that the coefficient of the first term in the expression 
for Q, is always 3*33, an d under this assumption the minimum value of the 
coefficient which is represented by 4-60, was 4-55, and the maximum 4*64. 

The formula agrees within 1 per cent, with the experiments of Fteley and 
Stearns on a notch 6 feet wide, with f=p 1 = yi 7 feet, and d, varying from 
o’4 foot to o'8 foot, and d ly from 0*01 foot to 079 foot in 14 of the 22 cases. 
In two of the exceptions, di is less than 0*10, and the nappe was probably 






























DR O WNED WEIRS 1 2 3 

aerated, ancl in two other cases d—d lx was less than 0*05 foot, so that accurate 
results could not be expected. {Ibid. vol. 12, p. 103.) 

In no case, except the last two, does the difference exceed 2 per cent. 

Until further experiments are made, we may therefore adopt Francis’ 
formula as a general basis, subject to the conditions that the nappe is not 
aerated on the under side, and that there is a wide pool below the weir, so that 

the nappe not only expands laterally, but falls into a body of water almost at 
rest. 

The most important case in practice is that in which is small. Clemens 

d 

Herschel {Tians. A.in. Soc. of C.E. , vol. i4> p. 180), has collected the experi¬ 
ments of Francis, and Fteley and Stearns, and gives a formula that can be 
reduced to : 

Q — 3’33 KLH 1 - 6 

where H =d. 

The values of K, are as follows : 


1 

IC 

d x 

d 

K 

0*00 

I *000 

0*12 

1*003 

0*01 

i *006 

o'i 3 

1 *ooo 

0*02 

1 *009 

0*14 

0*997 

°'°3 

1 *009 

0*15 

0*994 

0*04 

I *OIO 

0*16 

0*991 

0*05 

I ”OI I 

o*i 7 

0*988 

0*06 

I 'OIO 

0*18 

0*984 

O’OJ 

1*009 

0*19 

0*981 

0*08 

I '009 

0*20 

0*978 

0*09 

1 *008 

0*21 

o ‘973 

0*10 

1*007 

0*22 

0*970 

0*1 1 

1*005 


! . 


These values are stated to be accurate to 1 per cent., while the remainder 
of Herschel’s table is subject to errors exceeding 1 per cent. I have been 
accustomed to apply these ratios to Francis’ weirs (with and without end 
contractions), and to Cippoletti weirs under circumstances where the checking 
and comparison of the observations with other methods was so systematic 
that non-systematic errors of 1 per. cent, were certainly detected, and 
systematic errors of 0*5 per cent, would probably have been detected. No 
such errors were detected. I therefore believe that accurate comparative 
gaugings may be made with partially drowned weirs by applying this table. 


d 

When Herschel’s table for values of greater than 0*22 was similarly applied, 


non-systematic errors of 2 and 3 per cent, were discovered, and I therefore 
abandoned its use. The errors are known to have been caused by waves in 
the escape channel. 





















124 


CONTROL OF WATER 


I also systematically checked a drowned (L 1 = 2D), triangular notch against 
a similar undrowned notch. 

I was unable to discover any difference between the gauge readings, so 
long as was less than 0*25 ; consequently, I believe that this amount of 


drowning does not alter the discharge by 0*5 per cent. 


For values of 


di 

d 


, greater 


than 0*30 certain differences could be detected, but these were very irregular. 
The difficulties were apparently caused by waves in the escape channel, but 
certain capillary phenomena also occurred. It is believed that accurate field 


gaugings can be undertaken only when 


dy 

d’ 


is less than o'2o, or 0*25. 


Better results can be obtained when the escape channel is of the same 
breadth as the notch, and the approach channel, provided that the form of the 
nappe is carefully observed. 

The following abstract of Bazin’s work is given, as the question of 
accurately measuring large quantities of water with the smallest possible loss 
of head is of great importance in modern turbine tests. The difficulties are 
obvious. The gauging weir must be specially constructed so as to conform to 
Bazin’s standard ; and the observers must be skilful, for not only must the 
form of the nappe be carefully noted, but the difficulties attending the deter¬ 
mination of the quantities d, and d lf are great, and a small error in d ly will 
materially influence the results obtained. The method has, however, been 
systematically employed by French engineers with satisfactory results. 

Sketch No. 33 represents a drowned weir and nappe of the Francis, or 
Fteley and Stearns type, although in the last the sides of the nappe were 
apparently confined for about 6 inches beyond the notch sill. 

Bazin ( ut supra ) employed an escape channel of the same dimensions as 
the approach channel, so that the level of the water in this channel had a 
marked effect on the form of the nappe. 

The typical form is the waved nappe ( nappe ondulee ), as shown in 
Sketch No. 34, Fig. I. 

My own experiments lead me to believe that this form of nappe is identical 
with that obtained by the earlier experimenters. 

There is also the “drowned” nappe or air-free form {nappe ?ioyee par 
dessous), see Sketch No. 34, Figs. II. and III., and the adherent form {nappe 
adherente ) see page in and Sketch No. 34, Fig. IV., and the nappe with a 
standing wave { 7 iappe a ressaut eloignee), Sketch No. 34, Fig. V. 

The experiments cover a very large range of values of d, d^ and p , although 
Pi, is always equal to p. 

The only rational method of discriminating between the various cases is to 
calculate the quantity P 0 , which is actually the pressure existing under the nappe 
close to the notch sill as observed by a special piezometer (see Sketch No. 33). 

The cases run as follows : 



between —0*00 and —0^36, 


i.e. the weir is, geometrically speaking, not drowned, though the under side of 
the nappe is not aerated ; hence owing to the relatively narrow escape channel 
adopted by Bazin, the tail water influences the discharge (this effect appears to 


Waved Na ppes 


























126 


CONTROL OF WATER 


be entirely due to the relatively narrow escape channel used by Bazin, and no 
trace of it can be found in the experiments of Francis, or Fteley and Stearns). 


Then, | = —o- 26 +o 7 s(^+o-os)^ 


There are two sub cases according as : 


Po ' J ft 

~ is less than, or greater than — 1*33+0*16^ 

(a) When less, the nappe is adherent, or striated, and the circumstances 
are unsuitable for accurate gauging. This is not of much importance, as the 

weir is not usually drowned. The formula Q = Q S ^1*124 — 0*115 may be 

used, but is not very trustworthy unless P 0 is observed directly. 

P 

(b) If (which may be negative) is numerically greater than the above 

expression, the nappe may assume either the typical drowned weir form, or 
the wavy form. 

This sub case is subject to the same laws as the geometrically drowned 

weir, in which ~~ is positive, and is suitable for accurate work. 

Pi 

(ii) The second case therefore includes both geometrically drowned weirs 
d 

in which is positive, and the sub class 

d * 

(i) (b), in which is negative, but 

— o*26 + o 75(—+0*05)-^ is greater than —1*33+0*16^ 


P 0 • 


The value of —is now given by the equation : 

^=-(o- 2 6 + o-54|) + {o-02 + i- 24 | + o-54(|) 2 g 

and, except for certain cases which will be considered later, the nappe is 
either typical or wavy. 

Put Q s , as the discharge of a non-drowned weir, with the same d and /, as 
the drowned weir, i.e. 

Q .. ( J - 2S , + «gt.){, + „ S! (^y} Li ,. 

and Q, is the discharge of the weir considered : 

P 

[a) is negative. 

Q = Q»{.-o-235K-+7 It)} 

p 

(b) is positive, but less than 0*6. 

Q-Q s {i—0-235^(1+^)} 

p 

is positive, and greater than o*6. 


Q=Q‘{. + o-o 4 |}v / ‘-£ 


{c) 




DROWNED BAZIN WEIRS 


127 


As an approximation which may be used when the weir is not of the typical 
Bazin form, the following formula : 




d—d x 

J 


covers all cases included under ($) and (c), with an error not exceeding 1 per 

J 

cent, to 2 per cent., except in the cases where —, and h are very small, and 

, . P A 

these are obviously unfitted for accurate work. 

The above formulae hold until the nappe form changes to a nappe with a 
standing wave, when 

, J, is less than o’6o —o*59 

In such cases, although the weir may be drowned, (i.e. d u is positive) the 
nappe .itself is not drowned (see Sketch No. 34) and the formula : 

Q = Q a {i-o,- 0 - 245 |°)} 

or approximately : 

Q = Q s (o‘878+o*i28^) 

and the formula 

Q = {377+0*06}l^ L5 

may be used as a general expression. 

The above formulae are complicated, and the graphic diagram given above 
(No. 34) renders the matter more easily comprehensible. 

I 

Here, the abscissae are the values of and the ordinates are the 


values of 


P o 


The observations should be plotted as points on such a diagram, and 

(i) Any observation which is represented by a point falling below the 
line AB, 

y = -1*33+OT da¬ 
is a case of an adhering nappe. 

(ii) Proceeding round the diagram, observations which fall between AB 

and AC : y _ o-6o—0*58^: 

are cases of drowned, or wavy nappes, and the formulas hold. 

As a general principle, the drowned forms of nappe occur near the 
lines AB and AC, and wavy nappes are found at a distance, but no rule can be 
given, as the forms depend to a large extent on the preceding circumstances 
of the discharge over the weir. 

(iii) Points to the left of the line AC, are cases of a nappe with a standing 
wave. 

The diagram, however, suffices to discriminate between the cases suitable for 
accurate work, and the unsuitable cases which are usually not geometrically 
drowned. Although the precise form of the nappe cannot be predicted, there 
is never any real doubt as to which formula should be selected for calculating 
the discharge. 


128 


CONTROL OF WATER 


Weirs with other than Sharp-edged Notches. —It is quite impossible 
to give any rules for the discharge of such weirs. (See Diagrams Nos. 2 and 3.) 

Our accurate knowledge of the subject is mainly due to Bazin (lit supra), 
but a large amount of work has been done of late years in the United States. 
The whole information has been collated and re-calculated in a most able 
manner by Horton ( Weir Experiments, Coefficients and Formula ), and this 
book must be regarded as absolutely indispensable for all engineers who have 
any occasion to consider weirs other than those of standard form. 

The coefficients of discharge as determined by various experimenters show 
large differences. These are probably due to the causes discussed under 
Sharp-edged Weirs ; but such matters as the place where the head was 
observed, and the method of observation being rarely recorded with sufficient 
completeness, it is impossible to elucidate fully the obscurities. The following 
examples must therefore be considered merely as a selection from several 
hundred recorded observations ; and my choice is unfortunately somewhat 
influenced by accidents such as having had occasion to use or check the 
results personally, or finding that either Mr. Horton or myself were able to 
express the facts in a short formula. 

It appears that the form of the weir has a very great effect upon the 
coefficient of discharge when the head is small, and below a certain limit the 
coefficient of discharge varies very rapidly with the head. Sketch No. 35, 
Fig. I., shows an actual example, but it must not be taken as typical; the 
limit where variation ceases being usually well marked as in Fig. II. Sketch 
No. 32. This limit may be said (very roughly) to occur when the head 
exceeds twice the longest horizontal dimension of the weir crest. Above 
this limit the coefficient C, is usually constant, or it may be found that: 

C = a-\-b H 

The variations below this limit are not as a rule reducible to any mathe¬ 
matical formula, although this is probably merely due to lack of adequate 
and detailed information, and there is a certain amount of evidence to show 
that a formula of the type : 

C = £H R 

is very generally true. 

Flat-topped Weirs— Put w, equal to the width of the flat top (sketch 
No. 32, Fig. I.). 

(i) If D, is less than 1*5 w, the nappe adheres to the notch 

crest, and 

Q = Q. (07+0-185?) 

holds for a weir of the Bazin type, and with a very fair approximation for all 
weirs; Q s , being the discharge of a sharp edged weir of the same length 
and height under the same head. 

(ii) If D, is greater than 1*5 w 

the nappe springs free from the upstream edge of the flat top (see Sketch No. 29), 
and the weir is sharp edged for all effective purposes (see Diagram 2, Sketch No. 32)! 

The various formulae often given for flat-topped weirs such as : 

Q = 2*64 LH 1 - 5 \ , __ 

and, Q = 3-09 LH>-« / where H = D+/ * 

can be applied within certain limits, but these are badly defined. 


FLAT-TOPPED WEIRS 


129 


Horton ( Weir Experiments ^ p. 121) considers that: 

Q = 2-64LH 1 - 5 

is applicable when w, exceeds 3 feet, and —, lies between and 0^25, and 1*5. 
The weir top must be horizontal, and my own experiments lead me to believe 



Sketch No. 35.—Diagram of Triangular and Overflow Type of Weir. 
9 























CONTROL OF WATER 


130 

that if the water surface on top of the crest is at all wavy, the value 2*64 is 
exceeded, and 273 may be taken as more probable. 

The value 

Q = 309LH 1 - 5 

as theoretically obtained (see Ency. Brit. “ Hydraulics,” p. 472) may be con¬ 
sidered as a maximum, which is approached in cases where the upstream edge 
of the crest is rounded, and the top is very smooth and slopes downward in the 
direction of stream flow. 

If we put D for the head observed (say 6 feet or 10 feet above the upstream 
face of the top of the weir), and D 2 = for the depth of the stream above 

the centre of the flat top, or wherever the stream surface first becomes 
approximately horizontal (Sketch No. 32, Fig. 3), there is a certain theoretical 
basis for the assertion that : 

Q = Z'oiksf i—k LH 1 - 5 

where H, is the corrected value of D. In practice, it is probable that 
o*95 to o' 98Q, better represents the true discharge, and the fraction will be 
found to decrease as the top becomes rougher. The formula is probably most 
accurate if the upstream corner of the weir is rounded off. The observations 
are, however, easily taken, and the results thus deduced are likely to be more 
accurate than those which are obtained by assuming the value of C. 

The experiments of Bazin and of the United States Deep Waterways 
Board (see Horton, pp. 66 and 88) enable the following values to be given 
for C, in the formula : 

O = CLH 1 - 5 

where H = 


Value of C, from 

Width of Weir Top in 
Feet. 

Bazin’s Experiments. 

H = o'5 to 1*3 foot. 

U. S. D. W. Experiments. 

H = i*5 to 5 feet. 

I' 3 I 5 

2 * 35 +°' 5 H 


2 ‘62 

2‘53 + o-iH 

2-40 + o-i8H 

676 

2*47 + o‘iH 

2 '35 + °*° 3 H 

Upstream corner 

• • • 


rounded 



2*62 

2*90 + o*iH 

2-65 + 0T7H 

Upstream corner 

Expression is not 

2-81 

rounded 

linear, but C = 2*90 


676 

approximately 

• • • 

• • • 


See also Figs. I. and II., Sketch No. 32. 


Triangular Weirs. —For weirs with a vertical upstream face, and the 
downstream face sloping at 1 vertical to j horizontal (Sketch No. 35, Fig. 1) 
we have from Bazin’s experiments : 



(Horton, at supra, p. 125.) 


























WATER-FALLS 


The head should exceed 0*3 foot when s, is less than 2, and 075 foot for 
larger values of s, and Bazin’s experiments cease with H = 1*5 foot. 

So also, the U.S. Deep Waterways Experiments give for a flat-topped 
crest o‘ 67 foot wide, with a vertical downstream face, and the upstream 
face sloping in 1 in s, the following values for heads exceeding 175 foot. 


S — I 

0 = 370 

S = 2 

C = 374 

s ~3 

C = 3’58 

s = 4 

C = 3'49 

s = 5 

C = 3'39 


For weirs of the type shown (Sketch No. 35, Fig. 2), if the crest radius is 
large enough to cause the nappe to adhere to the face of the dam : 

C = {3 , 62 —0*16 (s— i)}H 0 - 05 

Water-falls. —The measurement of the discharge of a fall such as occurs 
at the end of a gutter or launder, and in a more irregular fashion in natural 
water-falls, is of importance. Unfortunately, experiments are very few and far 
between. 

If the discharge is regarded as occurring over a very wide crested weir the 
experiments of the U.S. Geological Survey (see Horton, ut supra, p. 104) give : 

Q = CLH 1 - 5 

where, H 1>5 = (D+Zj) 1 - 5 —Zd* 5 

and D, is measured 10 feet to 16 feet above the crest of the weir. 

C = 2*58 to 271 for H = o'8 foot to 4*5 feet 

Bellasis (. Hydraulics , p. 99) finds that: 

Q = 474 LD 1,5 

where D, is measured close to the fall, i.e. on top of the crest. 

Bazin finds that : 

Q = 2*50 to 2*64 LH 1 - 5 where the crest is sharp-edged upstream, 

and Q = 2*65 to 2*91 LH 1,5 with a rounded upstream edge to the crest, 

with H = D -\-h 

and D, measured 16 feet above the crest. 

My own experiments, which are comparable to the theory of Bellasis (being 
taken in a launder 2 feet x 1 foot deep, of planed boards) give : 

Q = 4*43 LD 1 - 5 

with D, measured 1 foot from the end of the launder, i.e. as was the case with 
Bellasis, and 

Q = 3’i2 LD 1 - 5 

where D is measured 20 feet above the fall. 

The difficulty is that if D, is measured far enough above the fall to eliminate 
the effect of variations in the velocity over the cross-section of the approach 
channel, the roughness of the sides of the channel affects the observations, 
and vice versa. 

On re-computing my observations, it appeared that for the launder used, 
D, should preferably be measured 10 feet (approx.) above the fall. 

Coefficients of Discharge for Large Weirs. — It frequently happens in 


132 


CONTROL OF WATER 


practical calculations that either L, or D, are far greater than in any accurate 
experiments. Bazin’s experiments were intended to apply to cases where L 
was very great; and his results agree generally with the formula given by 
Francis when L is large, and D exceeds o‘ 6 o or 070 foot. This is sufficient 
to render it probable that no very great error will be introduced by the applica¬ 
tion of either formula to the calculation of such discharges. 

Sharp-edged Weirs.—The maximum length of weir over which the dis¬ 
charge has been accurately measured is 29-87 feet. The side contractions 
were partially suppressed, and Carpenter ( Trans . of Ain. Soc. of Mech. Eng ., 
vol. 19, p. 255) finds the following values of C 1} in the equation : 


Q = C 2 (L — o'2 D) {(D+ 7 /) 1 - 5 -^ 1 - 5 } 


H, in Feet. 

... ■. " r 

Cx 

H, in Feet. 

c, 

1 *9 to 0*9 

3*53 

o'6 to 0-5 

. . < > 

3 ' 5 8 

o"9 ,, o*8 

3*54 

rf- 

• 

0 

b 

3 * 6 1 

o-8 „ 0-7 

3*55 

o *4 5 , 0-3 

3-66 

°'7 )> o-6 

3 * 5 6 

’ , j; . . . " ■' 

f 

, ■ j 


These values agree very fairly well with those which are obtained by 
applying Freeze’s formula to a short weir similarly suppressed. The length of 
the weir sill would therefore appear to have but little effect upon the general 
laws of weir discharge. 

For high heads, we find eight observations on a Bazin type of weir con¬ 
ducted at Cornell University, and checked over a standard Bazin weir, which 
give : 

0 = 3-278 L {(H + /?) 1 - 5 -/^ 1 - 5 } 

with H, from 2'oo to 4-88 feet, and a probable error of 0-050, say 1-5 per cent, 
in the coefficient (see Horton, Weir Discharges). 

The three cases for heads over 3 feet give C = 3*321. 

Thus, for sharp-edged weirs with complete contraction, Francis’ formula 
holds up to H = 4-7 feet at least. 

Flat-topped Weirs.—Certain experiments on the Bari Doab, on a weir 
80 feet long, as per Sketch No. 208, when compared with rod float observations, 
gave the following result: 

Q = 3‘49LD 1,5 

; / v V w, U; c\ • -i- - .. t * . . • ji. i-.-» iJll'J/ wI.J : i - . i . - v iL -i | H ; j. jf 

D, varying between 2*5 and 4-2 feet. 

Similar experiments on other weirs of the same section gave the following 
results : 

L = 29 feet C = 3-52 

L = 37 „ C = 3-54 

L - 46 „ C - 3-58 

L = 50 „ C = 3*59 

with v = 2 to 3 feet per second. D, ranging in each case from 3 to 3-5 feet. 

Bazin’s experiments on similar weirs, but with a slope of 1:5, in place of 
1 in 10, checked by a standard weir, give : 













LARGE WEIRS 


i 33 


C = 3*48 to 3*45 in the equation 
Q = CL +—J , with 

D '= o*6 to 1*30 feet. 

At Cornell, with standard weir checking 

C = 3*43 to 3*58 

f° r D = 2*62 feet to 4'2o feet. 

Thus, for such weirs, the value C = 3*50, may be considered as well 
established. 

Chatterton ( Hydraulic Experiments in the Kistna Delta) worked on flat- 
topped weirs 2 feet wide, with p = 2 to 3 feet, and L = 18 to 30 feet, and found 
by current meter observations that: 

C = 2*99 to 3 21, in the equation Q — CLU 1 - 5 , with D = 3 to 4-5 feet. 

The higher values are probably affected by suppressed contraction, and 
for a weir with complete contraction the value C == 3'09 may be adopted. 

Chatterton also experimented on the Kistna Anicut (see Sketch No. 177), 
in which L = 3,500 feet approximately. He found as follows : 

(i) With the tail water below the crest : 

Q = 3-13 LD VD + 0-035Z/ 2 
with D = 4*64 feet. 

(ii) With the tail water above the crest : 

Q = 3 -o 9L {(D+^ 5 -^ u } + C 2 L^VD+A 

where D, is the difference of level between head and tail waters, and is the 
depth of the tail water over the crest. 

We thus get the following table : 


D, Feet. 

d lf Feet. 

v, Feet-seconds. 

c 2 . 

C 2 from the Formula 
4*90 + 0*32^4. 

272 

870 

5 ‘ 21 

7'65 

7*68 

3*43 

633 

4'63 

7 *i 9 

6*93 

3 'i 5 

6*i8 

4‘28 

6-86 

6-88 

367 

4-48 

3*73 

6*05 

6*09 


Lewis, at Rasul, on a flat-topped drowned weir (see Sketch No. 164), 3 feet 
wide, with/ = 3 feet, D=o‘7 foot, <fi = 5'5 feet, found a discharge equivalent to 
that obtained by putting C 2 = 6*57, in the above formula. The expression 
4'9o-f-o'32 d u gives 6'66. 

In the case of flat-topped drowned weirs, of all kinds, it is therefore probable 
that the above formula with C 2 = 4‘9o-f 0*32^, is not very far removed from the 
correct value ; and that C 2 = 8*o2 if d ly exceeds 10 feet (see p. 289). 

The available evidence seems to indicate that in the case of sharp-edged 
weirs, the general formulas of Bazin or Francis may be applied for large values 
of L, or D, without any serious error. 

For flat-topped weirs, the theoretical formula : 

Q = 3 ’ 09 LD 1,5 





















134 


CONTROL OF WATER 


is probably sufficiently accurate ; and, if drowned, this formula holds for the 
unsubmerged portion of the discharge, and the formula for C 2 , already given 
is not likely to introduce serious error. 

For flat-topped weirs, with an apron sloping downstream, the formula : 

Q = 3 ‘ 5 ° LD 1 - 5 

appears to be well established. 

Horton {Weir Experiments, Coefficients , and Formulce) suggests that the 
Francis formula is probably applicable to nearly all weirs when D, is large. 
The experiments tabulated in Horton’s book may be advantageously consulted 
when determining the discharge of ogee, or broad weirs, under high heads. 

Further information will be found in a graphic form under Diagram No. 2 
(p. 1018). The statements concerning the accuracy of the diagram and the 
accompanying sketches must be carefully borne in mind. While I have found 
the accuracy of 3 per cent., which is there stated to be possible, amply sufficient 
in my own practice, I believe that in many cases the tables given by Horton, 
if used with judgment, permit better results to be obtained. 


CHAPTER V 


DISCHARGE OF ORIFICES 

Discharge of Orifices.— Definitions. 

Causes of the Variation of C. —Velocity of approach. 

Circular Orifices. —General rules—Sharp-edged orifice—Hamilton Smith’s table— 
Critical head—Modern experiments by Bilton, Judd, and Strickland—Accuracy. 
Temperature —Horizontal orifices—Velocity of approach—Rankine’s and Goodman’s 
formulas. 

Submerged Discharge. 

Partially Suppressed Contraction.—Bidone’s formula. 

Bell-mouthed Orifices. 

Conical Converging Tubes. —With rounded edges. 

Cylindrical Mouthpieces projecting Outwards. —Unwin’s theoretical formula— 
Practical rule—Pulsatory flow. 

Cylindrical Mouthpieces projecting Inwards. —Borda’s and Bidone’s mouthpieces. 
Fountain Flow from Vertical Pipes. —Weir and jet discharge. 

Discharge of Water through Orifices of other than Circular Form.— 
Approximate rules for square or rectangular orifices—Application for purposes of 
measurement. 

SQUARE Orifices. —Hamilton Smith’s table—Rectangular orifices—Fanning’s table— 
General rule—'Strickland’s values—Large sizes. 

Suppressed Contractions. 

Orifices with prolonged Boundaries. 

Submerged Orifices. 

Orifices of other than Circular or Rectangular Form. 

Large Orifices. 

Sluices and Gates. —Bornemann’s experiments—-Benton’s experiments—Chatterton’s 
experiments. 

Non-circular Orifices under Large Heads. 

SYMBOLS. 

a, is the area of the orifice, in square feet. 

C, is the coefficient of discharge of the orifice. 
c c , is the coefficient of contraction of the orifice. 

Cv, is the coefficient of velocity of the orifice. 

C 1} or C i f is the coefficient of discharge of a partially suppressed orifice, or of an orifice 
subject to velocity of approach. 

C p (see p. 149). 

d , is the vertical height of the orifice, or the diameter of a circular orifice. 

d, is also the diameter of a pipe connected with the orifice when this is equal to the 

diameter of the orifice. 

D, is the diameter of the fountain pipes, in feet (see p. 152). 

e , is the thickness of the walls of the metal tube forming a Borda mouthpiece (see p. 151). 
h , is the head, in feet, measured to the centre of the orifice. H, is used for h , in those 

equations in which d, is measured in inches. 

k x , and h 2 , are the depths of the top of a submerged rectangular orifice, below head and 
tail water levels. 

hdy is the effective head — h x - h 2 , for a submerged orifice. 

H 1} and H 2 , are the depths below head water level, of the top and bottom of a large 
unsubmerged rectangular orifice. 


135 


CONTROL OF WATER 


1 3 6 


k, is the vertical height of a rectangular orifice. 

/, is the length of the tube forming the mouthpiece of an orifice. 

m, is the length of the portion of the perimeter of the orifice over which contraction is 

wholly or partially suppressed. 

. . Diameter of channel of approach 

n, is the ratio -^- 

Diameter of orifice 

A is the perimeter of the orifice. 

Q, is the discharge of the orifice in cusecs. 

u, is the velocity of approach, in feet per second. 

v, is the velocity, in feet per second, at the smallest area of the jet issuing from the 

orifice. 

w, is the horizontal width of a rectangular orifice, in feet. 

SUMMARY OF EQUATIONS AND FORMUL/E 


Velocity of efflux : [ v = ^ ^ 2 S h feet P er second. 

{c v = o'97 to 0-99. 


A 

t 


Discharge : Q = Ca /J 2 gh cusecs. 

Correction for velocity of approach, or suppression of contraction. Q = C t a \ f 2gh cusecs. 
Circular Orifices : 

Sharp-edged : Q = 4-9 a\J 7 i (see Table, p. 142). 

Bell-mouth : Q = ySaiJh (see Table, p. 147). 

Tubular, projecting outwards : Q = 6 ’$aslh. 

Tubular, projecting inwards: / ^ ^ or( ^ a ' Q — 4 ' 2 as/k 

\(^) Bidone. Q = 6 aJ/i. 

Circular orifices, sharp-edged : 

0-018 

C = 0*5952 + 


3 ^VH ' 
Correction for velocity of approach : 
r 0-485 f //z 2 -iY 2 ] 

Ci = 77i( i+ («•-) / 


r d 

LInches 

(see p. 144) 


1 


n* 


n 0*97 « 2 

or C x = —-- .. 

V2’62« 4 - 1 *62 

Correction for partial suppression of contraction : 

C^C^i + 0-128^). 

Submerged Discharge : Q = CasjLghd. 

Values of C s^2g, are on the average 1 per cent, less than those given above (see p. 146). 
Fountain Discharge : Q = 5-6D 2 \//z (see p. 152). 

Rectangular Orifices : 

Sharp-edged : Q = 4-8 to 5 asjk (see p. 154). 

Contraction suppressed on three sides : Q = 5-3 to 5 "fajh (see p. 158). 
Thick-walled orifices : Q — 6 to 6 4 asjTi. 

Square orifices : C = 0-598 ° OI ^ .J ..... [Inches] 

’sjd ' 2 QH (seep. 156) 

Sluices—(i) Submerged : 

W B ° rnema nn : Q = Cwk ^2g (*, - h 2 + ( see p. 165). 

With w = 3 feet. 

sjk 


C = 0-664 + 0-053 
or, with iv = 1 foot to 2 feet. 


/ 1 k ' 

tin + — 











DISCHARGE OF ORIFICES 


137 


■■ -K 

s. 


C — 07201 + 0.0074 w (see Table, p. 167). 

( c ) Chatterton : Q = C wkf^ghd. 

c = 0-83-0-11 h a (see p. 168). 

(ii) Unsubmerged : Q = 5 -o$w (H 2 15 - H^- 5 ). 

Discharge of Orifices.— For simplicity’s sake, let us consider an orifice 

under a constant head, which is the same at all points in the area of the 
orifice. 

The pressure at the orifice, if it were closed, being that corresponding to 

7 i, feet of water, the theoretical velocity of efflux of water through the orifice is 
given by : 

v 2 ----- 2 gh 

Thus, the quantity discharged should be : 

Q = area of orifice x v = a\/ / 2g1i 

Actually, we find experimentally that the maximum velocity attained near 
the ori fice (so that the question of free fall may be neglected) is never 
quite V 2 ~gh, but is represented by : 

v—c v \J 2 gh 

where c v , is “ near to 0-97 ” (although modern results for sharp-edged orifices 
indicate 0-98 to 0-99), and is termed the velocity coefficient. Also, at the 
point where this velocity is attained the area of the jet is not equal to that of 
the orifice, but is equal to the area of the orifice multiplied by c c , where c c , is 
termed the coefficient of contraction, and for a sharp-edged circular orifice is 
not far off 0*62. We thus get for the quantity discharged : 

Q — c v x theoretical velocity xc c x area of orifice 

Q = c v c c a V 2 gh ~ D# V 2 gh 

where C = c v c c , and is termed the coefficient of discharge of the orifice. 

The above is a summary of the explanation of the question usually given. 
I assume that it tends to elucidate the subject, since it bears little relation to 
the physical facts. 

It is possible to measure c v , and c c , for a circular orifice. It is also 
absolutely certain that c c , cannot be measured with any degree of accuracy for 
any other orifice, and that c v , can only be defined by referring it to the mean 
velocity over the area of the jet. 

Sketch No. 36 shows the cross-section of jets from circular orifices of 
various diameters, and is taken from a paper by Messrs. Judd and King 
(.American Assoc, for Advancement of Science , 1909) with the addition of 
Bazin’s general contour (. Recherches Hydrantiques). 

For orifices of any cross-section, other than circular in form, the shape of 
the jet is very complicated, and can only be described as longitudinally ribbed, 
and swollen at regular intervals. 

These forms have been studied by many experimenters (particularly by 


C = 0-541 + 0-15 


\J k 


K + 


k' 


(6) Benton : Q =■ C wk sl 2 gh d . 










138 


CONTROL OF WATER 


Rayleigh, Proc. Roy. Soc., vol. 29), but they concern engineers only in so 
for as they afford proof of the impossibility of measuring c c , with any 
accuracy. 

Practically, the coefficient of discharge C, is the important figure (except 
occasionally c Vl for such matters as Pelton wheels). I shall therefore in future 



Sketch No. 36.—Longitudinal Sections of Jets from Sharp-edged 

Circular Orifices. 


call C, the coefficient. As will later appear, c c , possesses a certain somewhat 
limited theoretical importance. 

It is stated in many text-books that when Ji , is less than 3 cl (where r/, 
represents the vertical height of the orifice), more accurate formulas than 

Q = C area V2 gh 

can be obtained by considering the variation in the pressure from point to point 















































VELOCITY OF APPROACH 139 

of the orifice. These formulae are complicated, and the theory upon which 
they rest is of doubtful accuracy. I have altered the figures (wherever they 

have been employed by experimenters) so as to cause the simpler formula to 
be applicable. 

Causes of Variation of C. —Boussinesq has proved mathematically that C, 
is constant for all cases hitherto investigated. (For a very excellent precis see 
Boulanger, “ Hydraulique Generale.”) We find by experiment that C, varies 
somewhat both with /z, and a. These variations are most marked when 
/^, and a , are small, and this is especially the case when both are small. As 
they increase C, tends to become constant, and (in cases hitherto investigated) 
this constant value is slightly less than 
that obtained theoretically. 

I therefore believe that true con¬ 
stant values exist for C, and that the 
divergences occurring at low heads 
and for small sizes of orifices, are due 
to extraneous influences, such as vis¬ 
cosity, capillary adhesion at the edges 
of the jet, and also (very probably) to 
errors in workmanship due to the 
difficulty of making a small orifice 
which is truly “ sharp-edged ” under 
small heads. 

Sketch No. 37 also shows how 
(when the head over the orifice is 
small) the measured head may differ 
from the head producing the velocity 
at the vena coniracta , or area where 
the velocity is a maximum. 

For this reason, I have in some 

cases added the supposed constant value towards which C, tends, as h, and a , 
increase. 

« _ , j . - 

Velocity of Approach. —Theoretically speaking, if the water flows 
towards the orifice with a velocity zz, we have : 

7/ 2 = 2 gk-\-U 2 

Q=o \/ 2 ^+$) 



Sketch No. 37.—Effect of Surface Con¬ 
traction on the Head observed over 
an Orifice. 


so that, 

As a matter of fact, the most useful expression is : 


Q = Cx« V 2 gh 

I shall later discuss this equation as applied to several particular 
cases. 

Circular Orifice. —General Rules .—Consider a circular orifice, and in future 
define /z, as measured from the geometrical centre of the orifice to the surface 
of the water above it. The following table of Bellasis gives a general idea of 
the approximate values of C, for various forms of the orifice. The values are 
selected as leading to a first approximation to the size of orifice required, and 
in accurate work they should be corrected by the rules given hereafter. 








I 


"CONTROL OF WATER 


Sketch 
No. 38. 

Description. J 

| 

. 

Remarks. 

c. 

Cc 

Cv 

Fig. No. 

I 

Orifice in a wall whose 

Theoretical 

0-607 

• • • 

• • • 


edges are so thin in 
comparison with the 

value 

Fair average 

o*6i 

0*63 

0-97 


head and the diameter 
of the orifice that the 
jet springs clear and 
does not wet any portion 
of the boundary of the 

for h , about 

1 to 6 feet; </, 
about 0*07 to 
0*20 foot 
Constant value 

0-598 


- 

* 1 

• • • 

2 

orifice 

Bell-mouthed tube shaped 

to which C, 
tends 

• • • 

o*97 

I *o 

!,t • 

0-97 

J 

so as to conform to the 
shape of a free jet as 
per Fig. 36 

Conical convergent tube, 


o*94 

0-98 

0*96 

4 

measured on small end 
of cone, values accord¬ 
ing to angle of cone up to 

Cylindrical tube, length not 

Fair average, 
say, 

♦ • • 

0*90 

0*82 

• • • 

1*0 

• • • 

0*82 

. u t. . 

5 

more than three times 
the diameter 

Ditto., projecting in- 

Theoretical 

1 

7t — 

0-707 

• • • 


wardly, with jet ad¬ 
hering 

Experimental 

v 2 

075 

075 

1*0 

6 

Ditto., ditto., with the 

Theoretical 

1 

k ■ 



jet springing clear 

Experimental 

0-51 

0-52 

0-98 

7 

Divergent conical tube; 

Varies, Bel- 

1-46 

• • • 

• • • 

Sketch 

calculated for area of 
the smallest section 

Divergent bell-mouth; 

lasis’ sugges¬ 
tion 

c ^ : ' , j J 

2 ‘o 

1*0 

2-0 

No. 40. 

ditto. 

p , 



i . . 



The values of c v are probably somewhat less and those of c c proportionately 
greater than the truth. c v was obtained by observing the path of the jet and is 
therefore affected by air resistance, and given for use in similar calculations only. 

All these figures refer to orifices in a vertical plane. Where the orifices are 
in a horizontal or inclined plane, the figures are not appreciably altered, but 
the head should usually be measured from the centre of the jet at the point 
where it first springs free from the walls of the tube or orifice. 





































SHARP-EDGED ORIFICES 


Sharp-edged Orifices .—An orifice is defined as sharp-edged when its edges 
are so thin that the jet springs free without wetting them. The absolute 



Sketch No. 38.—Typical Forms of Orifices. 


sharpness required entirely depends upon circumstances. For example, Bilton 
( Proc. of Victorian Inst, of Engineers) found that for holes ^th of an inch in 


Thejet boundanes,exceptin N°i,k, less certainlyfl°6,are 

me ref con op indications■ 

















142 


CONTROL OF WATER 


diameter, a thickness of 0*005 inch was necessary. Whereas for orifices say 
6 inches across, under a head exceeding 4 feet, y#th of an inch plates are 
sufficiently thin. For orifices 2 feet square, under a head of 20 feet, angle irons 
3 inches thick act like sharp-edged plates. 

Now, let h, be the head in feet, measured from the still water surface to the 
centre of the orifice. 

Let a be the area of the orifice in square feet. * 

The discharge in cubic feet per second is given by : 

O = 8*02 C a\f h, where 8*02 is a mean value for V 2 g 

Hamilton Smith ( Hydraulics , p. 59) gives the following table for vertical 
orifices, discharging into air with complete contraction. His original figures 
have been modified where necessary, in order to permit the use of the above 
formula in all cases. 

We may also add the experiments by Ellis (Traits. Ain. Soc. of C.E. , vol. 5, 
p. 19) on an orifice 2 feet in diameter, which indicate that : 

C = 0*588 for h = 1*77 feet, rising to 

C = 0*615 for ^ = 9*^4 f eet * 

At first sight these results appear to be high, but as Hamilton Smith points 
out, contraction was slightly suppressed, so that our present evidence justifies 
the assumption that the values for d — 1 foot hold for larger orifices. 

The figures given in this table were considered to be liable to 1 or 2 units 
error in the third place of decimals ; but, unfortunately, later experiments do 
not altogether confirm this view. 

The most careful work is that by Bilton (ut supra), supplemented (for heads 
exceeding 8 feet) by the accurate work of Judd and King, and Strickland. 

The following statements appear to be correct for diameters up to 0*20 foot. 

In orifices of less than 0*20 foot in diameter, contraction is never complete 
(due to viscosity and capillary actions) ; but for heads exceeding a certain 
magnitude the coefficient of discharge is constant. Below this value it in¬ 
creases. This value is termed the critical head (see p. 144). 

The following table is given by Bilton (ut supra) : 


Head in 


Diameter of Orifice in Inches. 


Inches. 

i 

i 

* 

1 

ii 

2 


2 

3 

0*683 

o*68o 

0*663 

0*657 

0646 

0*640 




6 

0*669 

0*643 

0*632 

0*626 

0*618 

0*612 

o*6io 

9 

o*66o 

0*637 

0*623 

0*619 

0*612 

0*606 

0*604 

12 

°' 6 53 

0*630 

0*618 

0*612 

0*606 

o*6oi 

o*6oo 

17 

0*645 

0*624 

0*614 

0*608 

0*603 

°’599 

0*598 

18 

0*643 

0*623 

0*613 

0*608 

0*603 

°’599 

0-598 

22 

0*638 

0*621 

0*613 

0*608 

0*603 

°‘599 

0-598 

45 

and over 

.. . i » 

0*6285 

0*621 

0*613 

0*608 

0*603 

°‘599 

--.—.- i . 

0-598 

-:a ». • J 1 






























CIRCULAR ORIFICES 


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144 


CONTROL OF WATER 


For orifices smaller than J inch, the critical head increases more rapidly, 
and so does the constant or normal coefficient for heads greater than the 
critical. 

.) c : ' •„ C _ .. • - -' v • 


Bilton tabulates as 

follows : 





Diameter in^ 

■ inches . .) 



>' 


0 

c> 

q 

si 

Sri 

r " 

o*i 5 

0-2 0-25 

o *3 

o*4 0-5 

TOO 

Critical' 








head in 

- 

65 

55 45 

32 

25 22-5 

20 l8 

17 

inches . ., 



C 1 1 • . #*) 

O 0 G 




Normal co-~ 
efficient .. 

[. 

0 

0-631 

0*630 0*628 

0*627 

0*624 0-621 

o*6i8 0*613 

. - j 

0*608 

Bilton’s work was 

. ' W*'* ' v 

extraordinarily accurate, but did 

not extend to 

heads 


exceeding ioo inches. 

Judd and King (ut supra ) experimented with heads varying from 4 feet to 
80 or 100 feet. They find as follows : 

* « r • 1 * C. . 1 f t 1 ■ * > !T*‘ 


Inch. Inch. Inch. Inches. Inches. 



Mean value of C = o*6iii 0-6097 0*6085 0-6083 0-59.56 


The individual values show slight variations, indicating a rise as the head 
increases ; but the variation is probably well within the limits of observational 


error. 

Strickland ( Proc . Canadian Soc. of Civil Engineers, 1909, p. 183), finds that 
for circular orifices less than 3 inches in diameter, under heads of from 1 to 


20 feet : 


0 = 0-5925 


o-o 18 

3 x /T 2 ^h ’ 


. [Inches] 


where H, is the head in feet, and d, the diameter in inches. 

Mair ( P.I.C.E ., vol. 84, p. 424), for orifices of 1 to 3 inches in diameter, 
under heads from 0-75 foot to 2 feet finds that: 

, v ✓ - - •. '' - d **• 

■ / " ‘ o - o . oo g 

0=0*60754-t= -0*0037^.[Inches] 


j c I do not consider that a more accurate presentment of the subject is likely 
to be attained. All experimenters remark that while it is quite easy to get 
regular results for the same orifice discharging under various heads, it is very 
difficult to construct a duplicate orifice which will yield the same value 
of C. 

It appears that small differences in the condition of the edge of an orifice, 
such as are hardly appreciable under a microscope, are (in the case of orifices 
of less than 3 inches in diameter, at any rate) quite sufficient to produce 
such variations in the value of C, as 0*002, or o 003 (see especially Mair’s 
remarks). 

The effect of similar differences may be traced in the value given by 
Judd and King for a 2^-inch orifice. Bilton’s values appear to be free 







EFFECT OF WORKMANSHIP 


r 45 


from such irregularities, so that his workmanship must have been unusually 
good. 

We may therefore state that in orifices of this size, the errors in workman¬ 
ship (not in measurement) during construction are more important than the 
errors of good observations. Thus, for orifices less than 0*20 foot in diameter, 
we may consider that the values stated by Bilton, or Mair, for small heads, and 
those given by Judd and King, or Strickland, for larger heads, will probably 
permit the discharge to be calculated with an accuracy of 0*3, to 0*4 per 
cent. 

In the case of larger orifices, the table drawn up by Hamilton Smith gives 
the best available information, but is probably subject to errors of 1 per 
cent. 

It may also be remarked that all modern experimenters find that c v = o’gg, 
or even o f 999. The difference from the older work is entirely due to the fact 
that in modern practice c v , or c c , are measured directly. In older work, c v , was 
obtained by observing the path of the jet, and was in consequence diminished 
by air resistance. 

Temperature. —The effect of the temperature of the water on C, is 
principally due to the diminished action of capillarity. We may consequently 
consider that it will be most marked at low heads, and with small values 


of d. 


Hamilton Smith, with d= o’02 foot, found that C, was diminished to the 
extent of 1*5 per cent, by a rise from 48 degrees to 130 degrees Fahr. 

Unwin, with d=o’o ^2 foot, found that C, diminished to the extent of 1 per 
cent, by a rise from 61 degrees to 205 degrees Fahr. 

It can hardly be. said that any diminution has yet been measured in the case 
of larger diameters, although some diminution probably occurs. 

Horizontal Orifices. — There is no certain evidence to show that a 
horizontal orifice has a C, differing from that of a vertical orifice of the same 
size under the same head. Bilton’s results for heads greater than the critical 
are generally obtained on horizontal orifices. He also observes orifices inclined 
at 45 degrees discharging upwards. Where all three cases do not give identical 
values, the differences are so small, and are so irregular, as to suggest that they 
are entirely due to errors of observation, and they certainly fall within errors of 
workmanship. 

Effect of Velocity of Approach .—Consider a circular orifice in a diaphragm, 
at the end of a circular approach channel. Let the ratio of the diameter of the 
approach channel to the diameter of the orifice be n. Rankine gives a formula 
for c c , as follows : 


o'gyn 2 



whence C — 



since he appears to have deduced these values from observed coefficients of 
discharge, under the assumption that c v = crgy. 

Goodman ( Engineering , March n, 1904), by a method which is partly 
experimental and partly mathematical, obtains : 



10 








146 


CONTROL OF WATER 


With the assumption that a> = o* 97, we get the following table : 


n. 

Q from Rankine. 

C x from Goodman. 

2 

0*652 

0*645 

3 

0*621 

0*622 

4 

0*612 

0*615 

5 

0*607 

o*6i 2 

6 

0*605 

o*6io 

8 

0*603 

0*609 

10 

o*6oi 

0*608 

100 

o*6oo 

o*6o 6 


For orifices where Hamilton Smith’s coefficient corresponding to complete 
contraction (i.e. n—\oo) differs from the value 0*606, we may proportionally 
increase or decrease the coefficient for other values of n. 

The difference between the values given by Rankine and Goodman for « = 2, 

probably arises from the 
fact that Rankine takes 
account of the partial 
suppression of contraction 
which occurs, which Good¬ 
man’s theory neglects. 

Where the approach 
channel is not circular, we 
take n 2 , as equal to the 
. Area of channel 
rat ’° : Area of orifice ’ and 
if any portion of the borders 
of the channel and orifice 
are close together (say 
nearer than 3^/), a certain 
increase must be allowed 
for the partial suppression 
of contraction. 

Submerged Dis¬ 
charge (Sketch No. 39).— 
method adopted is simples/' appropriate formula is 

nhen large orifices are Q = C ad 2 gk dj 

where h d , represents the 
difference in the level of the 
water surfaces above and 
below the orifice, corrected 

if necessary for differences 
in the pressure of the air above the water if the reservoirs are closed. 

F01 shaip-edged onfices, when the jet discharges into water, the coefficient 
of discharge appears to be diminished by about 0*5 per cent, at high heads, and 
up to 2 per cent, at low heads, from the coefficient appropriate to the effective 



Note, h, bfi 2 nvghtbe measured 
from any fixed level. The 


considered. 


Sketch No. 39.—Submerged Orifice 




































BELL-MOVTB ORIFICE 


147' 

head h d ; an equal diminution is believed to occur in other types of orifices. 
It also appears that this difference diminishes as the area of the orifice increases, 
the figures given corresponding to d=o’2o to 0*30 foot, but there is a great deal 
of uncertainty on this matter. I believe that the uncertainty is explained by 
the difficulties of correctly measuring the effective head owing to waves set up 
in the lower reservoir. 

Partially Suppressed Contraction.—Since the difference between the area of 
the vena contracta of the jet and the area of the orifice is caused by the con¬ 
vergence of the streams of water approaching the edge of the orifice from the 
interior of the vessel in which the orifice is made, any border or thickening 
of the edge of the orifice will partially prevent this convergence, and will 
consequently increase the value of c c . Orifices thus situated are said to have 
“ partially suppressed contraction.” 

Bidone (see Unwin, Ency. Brit ., article on “ Hydraulics ”) states that: 

^=0-62(1+0-128 |) 

where is the ratio the length of the perimeter over which contraction is 

suppressed bears to the total perimeter of the orifice. I have been unable to 
trace the reference, but Bidone experimented on small orifices only. The 
formula is known not to be very reliable, but the value 


C 1 = c(i+o*I 28 


P 

may be used in default of anything better, where C, represents the coefficient 
of discharge for an orifice with complete contraction, of the same size and under 
the same head. 

In cases where the border, or thickening, which suppresses the contraction 
does not coincide with the edge of the orifice, no formula can be given. The 
ratios given under “ Weirs” form the only available information, and the results 
thus obtained are probably not all accurate. 

Bell-mouthed Orifices. —Sketch No. 40 shows the dimensions usually 
given as appropriate. Reference to the actual forms of the jets as given in 
Sketch No. 36 shows that the 
form should vary with the 
diameter of the jet, but that 
the above form is correct, or 
nearly so, for a diameter of 
2 \ inches. For greater dia¬ 
meters it is probable that a 
somewhat larger ratio of ex¬ 
pansion and a shorter length 
may be correct. However, 
bell mouths of the above 
proportions up to 4 feet in 



diameter, were employed at Staines with very satisfactory results, 
gives the following table : 

1-64 11-48 5577 337 ' 93 feet 


Weisbach 


h o*66 
C 0*959 0*967 0*975 


0*994 


0*994 











148 


CONTROL OF WATER 


Experiments carried out at Amritsar with a probable error of 0*4 per cent, 
confirmed this table up to 5*0 feet head on a bell mouth 6 inches in diameter. 

Conical Converging Tubes. —The following table is given by Castel 
(Annales des Mines, 1838), where C, is referred to the area of the smallest 
section (see Sketch No. 38, Fig. 3) : 


For ^=0*05085 Foot, and a Length of Tube equal to 2 ' 6 d. 


Angle of convergence 
in degrees and 


minutes 

O 

O 

i° 3 6' 

0 / 

3 10 

0 / 

4 10 

5° 2 6' 

7°5 2 ' 


C = 0*829 

o*866 

0*895 

0*912 

0*924 

0*930 

5) 

8° 5 8' 

0 t 

IO 20 

I2°4' 

0 t 

13 24 

i4° 2 8' 

i6 ° 3 6' 


C = 0*934 

0*938 

0*942 

0*946 

°'94 I 

0*938 


i 9 e 2 8' 

21V 

0 / 

23 0 

29*58' 

4Q°2o' 

48*50' 


0 = 0*924 

0*919 

0*914 

0-895 

0 

00 

•<1 

0 

0*847 


For ^=0*05085 Foot, /=2* 3 <7. 
Angle of convergence in 


degrees and minutes . 9 0 14' 

IO° 28 ' 

I2°42' 

f 

IO 02 

i9°o6' 

C = 0*929 

°’945 

0*95 1 

0*940 

0*926 

For <7=0*0656 Foot, /= 

2*5 d. 



Angle of convergence in 





degrees and minutes . 2°5o' 

5° 2 6' 

6°54' 

0 / 

10 30 

I 2°10' 

C = 0*914 

0*930 

0 

M3 

GJ 

00 

o‘945 

0*950 

„ I 3°4° / 

i5°° 2 ' 

i8°io' 

2 3°04' 

33° 5 2 ' 

0=0-956 

0*949 

°*939 

0*930 

0*920 


For <7=0*0656 Foot, l—$d. 
Angle of convergence in 

degrees and minutes . n°52' I4°i2' 16*34' 

0 = 0*965 0*958 0*951 


The heads varied from 9*84 feet down to o*66 foot and C, increased very 
slightly for the larger heads. It is doubtful whether these experiments are as 
reliable as they appear. Taking them at their face value, we might predict 
better results for larger tubes, and this is confirmed by Hamilton Smith’s 
results of 0 = 0*986 to 1*04, under heads of 300 feet approximately, with 

/=o* 83 foot, and ^=0*053 foot to 0*102 foot. 

I consider that better results are obtained by calculating the coefficient as 
for a cylindrical tube, and correcting for skin friction, by the rule given on 
page 81. 

In Castel’s experiments, the cone has a sharp inner angle. When this is 
rounded off, and /—3^, Unwin ( Hydraulics ) states as follows : 


Angle of convergence of sides 
)) 


C 

O 

O 

5 ° 45 ' 

0 # 

11 15' 

= 0*97 

o *95 

0*92 

. • , 

2 2°3o' 

45 °°' 

9o°o' 

C: 

= o*88 

075 

0*63 


* 


)» 


CYLINDRICAL MOUTHPIECE 


Cylindrical Mouthpieces projecting Outwards. —The discharge 
in such cases is greatly influenced by the form of the corners of the junction of 
the mouthpiece and the reservoir. If these are sharp and rectangular, the 
discharge of the orifice is the same as that of a sharp-edged orifice, provided 
that the length of the mouthpiece does not exceed 1*5 time its diameter. If 
this length is exceeded, the issuing jet first contracts in a manner very similar 
to a jet from a sharp-edged orifice, and then expands, and adheres to the sides 
of the tube (Sketch No. 38, Fig. 4). 

The case should be theoretically investigated, in order to produce the best 
results. 

Unwin gives the following equation : 


Cv — 


v^+Qr 1 ) 


where c Ci is the coefficient of contraction for a sharp-edged orifice. From 
this, taking the approximate value of c e , as equal to 0*608 (not 0*64 as Unwin 
does), we get ^=0*840 ; and in this case c v , is probably very nearly equal to C. 

Castel (as already stated) finds that 0 = 0*829, which would correspond to 
^=0*599, which is a lower value than is probable. The difference between 
theory and experiment can possibly be explained either by friction, or by the 
small size of Castel’s orifice, which may cause c c , to have a value differing 
from 0*608. 

The full theory would indeed show that in a length equal to the diameter 

of the pipe, a head equal to — —, is lost in skin friction, if v=qo v rs be 

302^ 

assumed as the friction equation of the pipe. 

The velocity would thus be diminished by at least 1*5 per cent, assuming 
that the water is in contact with the pipe only over the length 

KH = vid=( k 2’!b—r$)d. 

This correction will bring theory and experiment into almost exact agreement, 
the value 0*840 being reduced to 0*827 (see Sketch No. 41). 

Thus, I believe that for pipes of lengths greater than 1*5^, Unwin’s formula 
with c c — 0*608 (as capillarity does not now influence the value), corrected for 
the friction of a length of pipe equal to the actual length minus 0*8 to v%d will 
give better results than any experiments which are not specially carried out. 
The formula proposed is therefore : 

1 + 4 (/ — 1 * 5 ^ 0 ) 

1 2 gc v 2 C pd J 


where C p , is the coefficient in the pipe equation v=C p Jrs , appropriate to the 

TT(i 2 

size of the pipe (see p. 427). The discharge is Q=— 

The resemblance to the usual pipe discharge formula is obvious. With the 

figures already given we find that — 1 * 45 - Experimental figures are rare, and 

in large pipes the difficulties discussed on page 424, probably manifest them¬ 
selves. To Castel’s result may be added those of Weisbach, with /= 3d, as follows: 

d, equal to 0*032 0*066 0*098 0*131 foot. 

C, „ 0*843 0*832 0*821 o*8io 







l 5o CONTROL OF WATER 

Unwin states that the coefficient is also affected by the length of the 
mouthpiece, and gives as average values : 

—, equal to i 2 to 3 12 

C, ,, o*88 0*82 077 

It will be noticed that the pressure at any point between L and K, Sketch 
No. 4r, is theoretically less than atmospheric, by approximately o’joh. It 


H. 


JL 


Hot to Scale . 

— 1 . — 


about 0&to!2d. 


\' 


K. 


about 07h. 


r 




L. 


Sketch No. 41.— Discharge through Cylindrical Pipe. 


would thus appear that water can be raised, or air sucked in through an orifice 
constructed in the tube along this length. This principle is employed in jet 
pumps, and hydraulic compressors (see p. 813). 

It would also appear that if h exceeds 1-4 times the height of the water 
barometer, say 45 feet, the coefficients of discharge above obtained will no 
longer hold. Russell ( Text Book of Hydraulics ) states that when h , exceeds 
42 feet the flow is “troubled and pulsatory.” It is therefore probable that the 
water jet ruptures, or springs free from the sides of the tube, and that the 
coefficient of discharge momentarily changes to that of a sharp-edged orifice. 





















































BORDA AND BID ONE 


151 

My own experiments lead me to believe that this effect becomes manifest at 
lower heads, especially if the tube is anything but perfectly smooth. If the tube 
is shaped internally so as to conform to the form of a jet, the discharge is 
increased by about 10 per cent. 

Cylindrical Mouthpieces projecting Inwards. —Here we have two 
cases as follows : 

(1) That generally known as Borda’s mouthpiece (see Sketch No. 38, Fig. 
6), where the jet springs free, and does not wet the tube. 

Theoretically, if <?, be the thickness of the inner end of the tube, and r, its 
radius, then : 

C = 


or C, is 0*50, or slightly greater, Borda finds that C = 0*515, with r = 0*04 foot 
approx. Bidone (Recherches exfierimentales\ with r = 0*06 foot approx., or 
d = o’ 12 foot finds that C = 0*555 5 while the theory would give C = 0*557. 
Weisbach finds that C = 0*532. 

(2) In the second case (Bidone’s mouthpiece, Sketch No. 38, Fig. 5) the jet 
expands, and wets the sides of the tube, so that at the outer end the tube flows 
full bore. If we put p for the value of C, for Borda’s mouthpiece, as calculated 
above, i.e. 

{r+O 

* 2r* 


we see that theoretically (Bidone, Recherches , p. 63) : 

1 


C = 


V 


■ + (" 
V 


y 


or if /x=i, C = 0*707 


As a rule C, is greater than 0*707. 

With r — 0*06 foot, or d = 0*12 foot, Bidone finds that C = 0*767, the 
theory leading to 0*781. 

Bilton {Proc. Victorian Inst, of Engineers , 1909) for sharp-edged square cut 
orifices, with the pipe 2 \d in length, finds that : 

s i f \ 4 1 2 2 \ inches. 

C, 0*91 0*87 0*85 0*83 o*8i 0*79 0*77 0*76 0*75 


V 

In very large orifices, where -, is small, 0*71 maybe assumed as correct. 


In a 12-inch pipe, with e = \ inch, we get fx = 0*587, and C = 0*818. Ex¬ 
perimentally, under a head of 14*3 feet, I found that C = 0*79. The accuracy 
of the experiment does not justify corrections for friction being applied. 

Fountain Flow from Vertical Pipes.— The calculation of the discharge 
through a vertical pipe is of importance, as the volume discharged by artesian 
wells and in other cases of fountain flow can thus be easily determined. 

The question has been investigated by Lawrence and Braunworth {Trans. 
Am. Soc . of C.E ., vol. 67, p. 265). The conditions of flow may be divided 
into the two following distinct types : 

(a) Weir flow, occurring under small heads when the discharge resembles 
that over a circular weir. 

(h) Jet flow, where the discharge occurs in a jet or fountain. 

If d , represent the diameter of the pipe in inches, and H, is the head in fee 






i 5 2 


CONTROL OF WATER 

over the horizontal orifice of the pipe, for pipes of 2, 4 > 6, 9 > an< ^ 12 inches in 
diameter, we find that : 

Type (a) occurs so long as H, is less than o'o28^ 104 . . • [Inches] 

Type (£) occurs if H, is greater than o’ic>7d 1 - 03 . • [Inches] 

During the intermediate range the discharge bears a fixed relation to the 
head, but [the investigators were unable to deduce a formula, and found it 
necessary to prepare a table which gave Q, in terms of H. 

Putting Q = the discharge in cubic feet per second. [| 

D = the diameter of the pipe in feet. 
h — the head over the orifice in feet. 

The experimenters found that: 

I. When /z, was observed by a pressure gauge in communication with an 
opening in the side of the pipe 1^90 inch below the top of the pipe : 

The weir discharge was represented by Q = S'SD 1 - 29 /* 1 - 29 . 

The jet discharge was represented by Q = 5*84D 2 - 005 /z°- 53 . 

II. When /z, was observed by sighting across the top of the issuing water : 

The weir discharge was represented by Q = 8'8D 1,25 /P- 35 . 

The jet discharge was represented by Q = 5'57D 1 -"/z°- 63 . 

The resemblance between the jet formula and the theoretical formula 
_ ttP ) 2 

Q = C V 2 gh -is obvious. 

v a 4 > 

It is plain that the second jet discharge formula is that which corresponds 
best with the conditions usually occurring in practice, and for this case C, is 
not far removed from 0*90. 

In some field experiments, where the discharge was measured over a weir and 
compared with the discharge calculated by the weir discharge formula, indicated 
that the weir condition is not adapted for securing accurate measurements under 
field conditions (probably owing to the large errors in Q, caused by small 
errors in the determination of h ). Thus, the best results will be obtained by 
decreasing the diameter of the tube until a jet discharge is produced. The 
original experiments indicate that if the jet discharge condition is produced by 
fixing a smaller pipe inside the casing of the well, and blocking up the annular 
space between the two pipes, an 8 to 10 foot length of the smaller pipe will 
suffice to wipe out any irregularities of flow which might cause an application, 
of the formulae to produce erroneous results. 

Discharge of Water through Orifices of other than Circular 
Form. —The figures given in the following discussions are by no means as 
accurate as are those which relate to circular orifices. 

In practice, circular orifices of a size larger than those considered in the 
tables are not of frequent occurrence, since engineers rarely employ such 
orifices except for measuring volumes of water. 

Square, or rectangular orifices of very large size, frequently occur in 
practice ; and our knowledge of the coefficients of discharge of such orifices is 
very vague. The available information has been collected. 

For preliminary designs, the following simple rules may be used. 

The coefficient of discharge of a sharp-edged orifice with complete con¬ 
traction, is o‘6, and increases as the contraction becomes more and more 



i 53 


SQUARE ORIFICES 


suppressed. The value §, may be taken for a case where borders exist around 
three-quarters of the perimeter, and the value J, for completely suppressed 
contraction, or a thick-edged orifice. 

All these values are low, and §, might be used in place of o’6 ; 07 in place 
of 0^67, and o'8o in place of 075. 

In practice, however, the total cost of a large sluice gate and the surrounding 
masonry is probably not increased by making it a little larger, and there is no 
doubt that too small a sluice capacity is always troublesome, if not dangerous. 

Square, or rectangular orifices are not well adapted for measuring purposes. 
The experiments of Benton (see p. 167) were intended to form a basis for 
systematic measurements, and very excellent tables were drawn up and 
officially promulgated. In practice, however, it was found that the engineers 
and supervisors preferred to carry out rod float gaugings. The standard of 
theoretical knowledge in the Punjab Irrigation Branch is high, especially when 
the overseer or sub-overseer is compared with men performing similar duties 
elsewhere. Thus, it may be inferred that the complication introduced by the 
corrections and double entries which are required with even the best system of 
tables, renders the method unfit for practical purposes. 

Square Orifices, —For square orifices the formula is : 

. Q = C X area V 2 gh 

where h , is the head measured to the centre of the orifice. 

Hamilton Smith ( ut supra) gives the following table (p. 154) for sharp-edged 
square orifices, in a vertical plane with full contraction, discharging into the 
air, his values being corrected so as to permit the simple formula given above to 
apply in all cases. 

These figures are known to be less accurate than those for circular orifices 
(being subject to at least 1 per cent, of error), principally due to the difficulty 
of making a really sharp-edged square orifice of small size. 

In view of our present knowledge of the accuracy of the table for round 
orifices, it is probable that this table is accurate to two figures. The third 
figure is retained, as Smith’s coefficients are so often referred to in ex¬ 
periments. 

Rectangular Orifices.- —The typical case is an orifice with vertical sides. 

Let w = the horizontal width of the orifice, in feet. 

Let H x = the depth of the top of the orifice, in feet, below the water level. 

Let H 2 = the depth of the bottom of the orifice, in feet, below the water 
level. 

The area of the orifice is : 

i w(H 2 — HO = wk square feet, where k = H 2 — H x 
and the theoretical formula is : 

Q = <Zw^Igh{ H^-Hi 1 - 5 ) 


Now, if H 2 — Hj be small compared with H 1? this is approximately equal to : 

q=cmh 2 -h 1 )v / 


or, 

where h — 


Q = C X area V 2 gh. 




and h, is the head measured to the centre of the orifice. 


2 





r 54 


CONTROL OF WATER 





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RECTANGULAR ORIFICES 155 

In practice the more complicated formula is only applied in cases where 

the ratio ^ 1 is greater than ^ The coefficient of discharge is not well 

2 5 

known, but (see p. 168) C = 0*63 is probably a fair average for sharp-edged 
orifices. 

The typical formula is : 

Q = Cxarea.y/ 2g * - H T± H l = Cw(H 2 - H x ) ^2gh 

and the following table is a condensation of Fanning’s values ( A Treatise on 
Hydraulic and IVater Supply Engineering) for rectangular orifices with vertical 
sides. The third figures may be regarded as of little, if any, significance. 


VALUES OF C FOR RECTANGULAR ORIFICES i FOOT WIDE. 


Head to 
Centre of 
Orifice. 

Vertical Height of Orifice. 

4 feet. 

2 feet. 

1*5 foot. 

1 foot. 

o *75 

foot. 

0*50 

foot. 

0*25 

foot. 

0*125 

foot. 

°*4 





• • • 

0*614 

0*631 

0*633 

o*6 


• • • 

• • . 

0*598 

o*6o 6 

0*616 

0*632 

0*633 

0*8 


• . . 

0*613 

0*600 

0*608 

0*617 

0*632 

0*633 

1*0 


• • . 

0*614 

0*601 

0*609 

0*617 

0*632 

0*632 

I *S 


0*619 

0*614 

0*603 

o*6io 

0*617 

0*631 

0*630 

2*0 


0*618 

0*614 

0*604 

o*6io 

0*617 

0*630 

0*629 

2*5 

0*629 

0*618 

0*614 

0*604 

o*6io 

0*616 

0*628 

0*628 

3 *° 

0*627 

0*617 

0*613 

0*605 

o*6io 

0*615 

0*627 

0*627 

4 *o 

0*625 

0*615 

o*6i 1 

0*605 

0*609 

0*614 

0*624 

0*624 

5 *o 

0*621 

o*6i 2 

0*609 

0*604 

0*606 

o*6i 1 

0*620 

0*620 

6*o 

0*616 

0*609 

0*606 

0*602 

0*604 

0*609 

0*615 

0*615 

8*o 

0*609 

0*604 

0*602 

o*6oi 

0*602 

0*603 

0*607 

0*609 

10*0 

0*604 

0*602 

0*601 

0*601 

o*6oi 

0*601 

0*603 

0*606 

20*0 

0*605 

0*602 

o*6oi 

o*6oi 

o*6oi 

0*602 

0*604 

0*607 

5°’° 

0*609 

0*606 

0*603 

0*602 

0*604 

0*605 

0*607 

0*614 


If we compare the fifth column with Hamilton Smith’s coefficients for an 
orifice i foot square, the agreement is fairly good ; but the figures for heads 
exceeding io feet do not follow the law of steady decrease which Smith 
considered to be correct for square and circular orifices. The figures for 
orifices, the vertical side of which is less than the horizontal were subject to 
special and constant errors, which usually tended to slightly increase the value 
of the coefficient. 

It is therefore probable that the following reasoning leads to values of C, 
which are quite as accurate as those given by Fanning. 

Bazin {Mem. de VAcademie des Sciences, tome 32, 1896) finds that for a 
square of 0*656 foot, under a head of 2*96 feet to 3*27 feet, C = 0*607. For a 
rectangular orifice 2*62 feet long, and 0*656 feet high, without lateral con¬ 
tractions (i.e. practically of infinite length), under the same heads, C = 0*627. 










































CONTROL OF WATER 


156 


We may therefore deduce that the coefficient for a rectangular orifice, 
0*656 foot in breadth, with a length equal to nx 0*656, with lateral contractions, 

is not far off 0*627—^-^—. This value is correct to two places of decimals, and 

n 

probably holds for all heads over 3 feet. For widths other than 0*66 foot, we 
may add or subtract, as is indicated by Hamilton Smith’s tables ; eg. consider 
an orifice 1 foot x 0*125 f°°b we 8 et if h = 4 feet : 


0 = ^0*627—+(o*6o6 — o*6o7) = o*624 


which agrees with Fanning’s table. Similarly, C = 0*622, when h = 10 feet, as 
compared with Fanning’s value of 0*606, which is probably erroneous. 

Strickland ( Proc . of Canadian Soc. of Civil Engineers , 1909, p. 185) suggests 
the following formula for the coefficients of discharge of squares with a side of 
less than 3 inches, under heads of 1 foot to 20 feet: 


C = 0*598 


0*018 

Jh W 2 


» . J ! 

[Inches] 


where H, is in feet, and d ’, in inches. 


If we endeavour to express this in terms of r=-=-;- we get : 

r wetted perimeter 

„ 0*045 

0 = 0*598+ .. [Inches] 

which may be applied to rectangles, and does not markedly conflict with existing 
experimental results. 

Royd ( fourn. of the Assoc, of Eng. Societies , 1895) gives the following results 
for an orifice 6 inches wide, under a head of 6 inches : 


Length of orifice. 6 12 18 

C, . 0*593 0*607 0*615 


24 30 inches. 

0*621 0*626 


The orifice was peculiarly constructed, and it may be doubted whether it 
was really sharp edged. The values of the coefficients, however, indicate that 
it behaved after the manner of a sharp-edged orifice. The top and bottom 
edges were formed of 2-inch, and the sides of i-inch planking, the latter being 
laid against the water face of the 2-inch planks, so that all four edges were 
not in one plane. 

Ellis {Trans. Am. Soc. of C.E,, vol. 5, p. 19) finds as follows : 

For a 2 feet by 0*5 foot orifice, C = o*6i 1, for H = 1*42 feet, 

falling to C = o*6oo, for H = 16*96 feet. 

For an orifice 2 feet wide, by 1 foot high, C = 0*597, for H = 1*82 foot, 

rising to C = 0*606, for H =;,11*31 feet. 

For a 1 foot square orifice, C = 0*582, for H = 1*48 foot, 

rising to C = 0*601, for H = 15*13 feet. 

When submerged, C, varies between 0*599 for h d — 2*32 feet, and 

C = o*611 for h d = 14*30 feet, but 
the mean between h d =ii'6 and 18*5 feet is C = 0*606. 






SUPPRESSED CONTRACTION 


*57 


The differences suggest partially suppressed contractions, 
h or a 2 feet square orifice, C = o*6i i to 0*597, H, varying between 2*06 and 
3*54 feet. The effect of suppressed contraction is very evident. 

Lespinasse (quoted by Fanning, ut supra) obtained the following values for 
an orifice 4*265 feet wide : V 


Height in Feet. 

Head in Feet to Centre 
of Orifice. 

c. 

1-805 

T 4‘55 

0*613 


1*64 

6*63 

0*641 


1*64 

.6*25 

0*629 


*' 5 1 

12*88 

0*641 


1 *5 75 

I 3’59 

0*647 


i ‘575 

6'39 

0*616 


I *575 

6*22 

o '594 


1 *5 7 5 

6*48 

0*621 



The values are probably affected by suppressed contraction, but are con¬ 
sequently more likely to be practically useful than experiments where contrac¬ 
tion did not occur. In any case, they are the best available results for really 
large orifices. 

Better results will not be easily obtained. The difficulties arising from 
errors in workmanship are exceptionally great; and the duplication of a square 
orifice with a side of less than 4 inches, so as to obtain accordant values of C 
(especially for low heads) is almost impossible. Thus, for practical calculations, 
the above values are sufficiently accurate, and it will also be plain that square 
orifices are useless for measuring water accurately. 

Suppressed Contractions.—Hamilton Smith {ut supra) calculates the 
following percentages of increase in C, from Lesbros’ results for an orifice 
0*656 x 0*656 foot. 


Description of Contraction. 

Head. 

1 foot. 

Head. 

2 feet. 

Head. 

3 feet. 

Head. 

5 feet. 

r » 

Nearly suppressed on one side. 

I *2 

I *0 

U r • 

1 *2 

i *3 

Quite „ „ • 

Nearly ,, two sides. 

3'8 

57 

3*3 

4*5 

3 ' 1 

4 *o 

3*5 

4 *o 

Quite on one, and nearly on 

5-8 




another .... 

5*3 

5*3 

5*6 

Quite suppressed on two oppos- 





ite sides .... 

7*3 

6*o 

5*6 

5*6 

Quite on one, nearly on two 




9*8 

sides . 

i 3‘3 

10*9 

9*9 

Quite on three sides 

* 5’ 6 

13*4 

11*9 

11 *6 






















i 5 8 CONTROL OF WATER 


For rectangular orifices, we have the following percentages of increase in C : 


Horizontal 

Side. 

Vertical 

Side. 

When the Contraction is 

| 

Suppressed at the 
Bottom. 

Suppressed at both 
Vertical Sides. 

/. 

w. 

Feet. 

H = 1. 

Feet. 

H = 3 * 

Feet. 

H = 5 - 

Feet. 

H — 1. 

Feet. 

h= 3 . 

Feet. 

H = S* 

0*656 foot 

0*656 foot 
0*328 „ 

0*164 „ 

0*098 „ 

°'°33 „ 

3*8 

5*4 

6*3 

7*8 

8*9 

3 * 1 

s; 2 

6*5 

7*6 

11 *i 

3*5 

5*4 

7*4 

8*5 

12*4 

5*7 

3*2 

i*6 

3*4 

4*5 

4 *o 

2*4 

i*4 

2*1 

5 *i 

4 *o 

3 * 1 

2*4 

2*4 

5*6 

Horizontal 

Side. 

Vertical 

Side. 

When the Contraction is 

Suppressed at the Bottom 
and partlyjon one Side. 

Suppressed at the Bottom 
and partly on both Verticals. 

/. 

w. 

Foot. 

H = 1. 

Feet. 

H= 3 . 

Feet. 

H = 5 . 

Foot. 

H = 1. 

Feet. 

H = 3 - 

Feet. 

H = 5 * 

0*656 foot 

0*656 foot 
0*328 „ 

0*164 „ 

0*098 „ 

0*033 „ 

5-8 

7*0 

7*3 

8*i 

8*5 

5*3 

6*7 

7*5 

8*8 

ii*i 

5*6 

7 *o 

8*4 

9*2 

12*2 

13*3 

10*7 

8*9 

9*6 

8-5 

9*9 

9*8 

8*6 

9*2 

11 * 1 

9*8 

10*0 

8*5 

9*5 

12*7 


These values are probably less accurate than the results for square orifices. 

The term “ complete suppression,” is employed when a side of the canal 
conicides with a side of the orifice. For sides where the term “partly 
suppressed” is used, the distance between the side of the canal and that of 
the orifice is o'o66 foot. The figures for the second case appear to be 
erroneous, and somewhat peculiar irregularities occur in all cases. 

Bidone (Recherches Hydrauliques) suggests the following (compare with 
circular orifices) : 

Ci = C ^1 + 0*152 — ^ 

The results are probably more accurate than those given by his formula for 
circular orifices, but they are obtained from experiments on small orifices only. 

Bellasis {Hydraulics) gives the following table for rectangular orifices with 
partial suppression round a portion of their perimeter, where G, is the distance 
of the side of the channel from the edge of the orifice, and : 

Ci = C x coefficient in table 


































































RECTANGULAR ORIFICES 


159 


where C», is the coefficient of discharge for the orifice with partially suppressed 
contraction, and C, is the coefficient under the same head, but with complete 
contraction. 


m 

T 

G 

d ~ 3 

2*67 

2 

1 

o*5 

O 

0-25 

1 ’ 

I ‘ooo 

I ‘002 

1 "oo6 

1-015 

1*04 

°'5° 

1 

I'001 

I‘003 


1-030 

1*08 

o*75 

1 

I ’OOI 

I ‘OO4 

1*019 

1*045 

I" I 2 

°'875 

1 

I'001 

1-005 

1-04 (?) 

i*io (?) 

I -40 (?) 

1*0 

1 

I ‘002 

i ’oo6 

i*°5 ( ? ) 

1*20 (?) 



I am not aware what experimental basis these possess. 

If a jet be bisected by a metal sheet, which is more than 0*04 inch in 
thickness, and is afterwards allowed to unite, Smith finds an increase of 
about 1 per cent, in an orifice with a length of 0*30 foot, and a width of 
0*03 foot. 

Orifices with Prolonged Boundaries. —The following results are 
given by Unwin (Ency. Brit ., article on “Hydraulics”). I am unable to 
discover the original source, which is probably French. 

The formula used is : _ 

. Q = Ct vkisj 2 g (Sketch 0.42). 



RII Openings 8 inches wide 


Sketch No. 42.—Sketch of Rectangular Orifices. 


H.J- H x in 
Feet. 



H] 

in Feet. 

1 -» 



0*0656 

0-164 0 328 

0*656 

1 640 

3*28 

4-92 

6-56 

9*84 

A | f 

B T -656 

cj 1 

A | ! 

B 0-164 

cj l 

0-480 
0-480 
o *5 2 7 

0-488 

0-487 

o' 5 s 5 

0-511 ’ 0-542 
0-510 ; 0-538 
o *553 | o '574 

o‘577 0*624 
0-571 o‘6o6 
0-614 0-633 

o *574 

0-566 

0-592 

0-631 

0-617 

0-645 

o *599 

0-592 

0-607 

0*625 

0*626 

0-652 

o - 6oi 

o*6oo 

o*6io 

0*624 

0*628 

0*651 

o*6oi 

0*602 

o*6to 

0-619 

0-627 

0-650 

o‘6oi 

0 " 6 C 2 

0*609 

0*613 

0*623 

0*650 

o*6oi 

o‘6oi 

0608 

0*606 i 
0*618 i 
0*649 



















































































i6o 


CONTROL OF WATER 



Plan 

dll planks ! s /& thick. 

Sketch No. 43.—Sketch of Rectangular Orifices. 

C for figure P. 


Head H l5 
above Upper 
Edge of Orifice 
in Feet. 

Height of Orifice, H 2 — H 1} in Feet. 

I ' 3 I 

o*66 

o*i6 

0*10 

0*328 

0*598 

0-634 

0*691 

0*710 

0*656 

0*609 

0*640 

0*685 

0*696 

0787 

0*612 

0*641 

0*684 

0*694 

0*984 

o*6i 6 

0*641 

0*683 

0*692 


[ Table continued 









































































RECTANGULAR ORIFICES 


161 


Table continued'] 


C for figure P. 

Head H x , above 

Height of Orifice, H 2 -H,, in Feet. 


Upper Edge of 





1 *3 1- 

066. 

0-16. 

o-io. 

Orifice in Feet. 

I '968 

o’6i8 

0-640 

0*678 

o-688 

3-28 

o'6o8 

0-638 

0-673 

o"68o 

4*27 

o’6o2 

0-637 

0*672 

0-678 

4-92 

0-598 

0-637 

0-672 

0-676 

5-58 

0-596 

0-637 

0*672 

0*676 

6-56 

°'595 

0-636 

0*671 

0-675 

9*84 

i °’59 2 

0-634 

o-668 

0-672 


C for figure R. 

Head H,, above 

Pleight of Orifice, 

H a - H x , in Feet. 


Upper Edge of 





i* 3 i- 

066. 

o*i6. 

o-io. 

j Orifice in Feet. 

1. - - . 

0*328 

0-648 

0*668 

o’666 

0*696 

0-656 

0-657 

0-675 

o"688 

0-706 

0-787 

0-659 

0-677 

0*692 

0 

0 

00 

0*984 

o"66o 

0-678 

0-695 

o*711 

1-968 

°* 6 53 

0*679 

0-697 

0-712 

3-28 

0-634 

0*676 

0-695 

o‘ 7°5 

4-27- 

0*626 

0-675 

0-694 

0-702 

4-92 

0*622 

0*674 

0-693 

0*699 

5 '5 8 

0-620 

0-673 

0-693 

0*698 

6- 5 6 

o*6i 7 

0*672 

0*692 

0*696 

9-84 

1 

0’6l2 

0*670 

0*690 

0-693 


f 


C for figure Q. 



Head H x , above 
Upper Edge of 

Height of Orifice, 

II 2 - Hj, in F'eet. 


o-66. 

0-16. 


Orifice in Feet. 

1 ' 3 1 - 

O'lO. 

0*328 

0-644 

0-665 

0-604 

0-694 

0*656 

0-653 

0*672 

0687 

0-704 

| 0-787 

0-655 

0-674 

0*690 

0*706 

0-984 

0-656 

0-675 

0*693 

0-709 

1*968 

0-649 

0*676 

0-695 

0*710 

3*28 

0*632 

0-674 

0*694 

0-704 

4-27 

O 624 

0-673 

0-693 

0-701 

4-92 

0*620 

0-673 

0*692 

0*699 

5*58 

0*618 

0*672 

0*692 

0-698 

6-56 

0-615 

0*67 I 

0-691 

0*696 

9-84 

o*6i 1 

0*669 

0*689 

0*693 



































































































162 CONTROL OF WATER 


Submerged Orifices. —The following table gives values calculated from 
Smith’s experiments : 


Effective 
Head in 
Feet. 

Circle 
^=0*05 Ft. 

Square 

Ft. Ft. 
0-05 x 0*05 

Circle 
o*i Ft. 

Square 

Ft. Ft. 

0*1 X 0*1 

Rectangle 

Ft. Ft. 
0*05 x 0*3 

o*5 

0*616 

0*620 

0*602 

0*609 

0*622 

1*0 

o'6io 

0*615 

0*602 

0*606 

0*622 

i *5 

0-607 

0*612 

o*6oi 

0*605 

0*621 

2*0 

0*604 

0*609 

o*6oo 

0*604 

0*620 

2 ’5 

0*603 

o'6o8 

o*599 

0*604 

0*619 

3 ’° 

0*602 

0*607 

o-599 

0*604 

0*618 

4 '° 

o*6oi 

0*607 

o'599 

0*605 

• • • 


Smith suggests that the difference between these coefficients, and those 
for similar orifices discharging into air under the same effective heads, is 
proportional to : Wetted perimeter 

Areax Vhead 

I have been unable to find any difference for orifices i foot square, under 
heads up to 4 feet. I was not able to gauge the quantity of water passing, 
but the effective heads over the orifices were identical. 

The rules given under “ Circular Submerged Orifices ” may be applied in 
default of better information. 

Coefficients for Orifices which are neither Circular nor 
Rectangular. —For orifices other than circular, square, and rectangular 
in form, no very definite information exists. Bovey (. Hydraulics , p. 40), gives 
a series of determinations of orifices 0*196 square inch in area, under heads 
up to 20 feet. The area is far too small to permit any practical application 
being made, and it is therefore sufficient to state that the mean ratios of the 
C’s, were as follows : 


Circular. 

Square. 

Rectangle Sides 4:1. 

Sides 

Vertical. 

Diagonal 

Vertical. 

Long Side 
Vertical. 

Short Side 
Vertical. 

I 

1*011 

1*013 

I-030 

1 '°33 


Rectangle Sides 16 : 1. 


Equilateral Triangle. 


Long Side 
Vertical. 


1*050 


Short Side 
Vertical. 


One Side 
Horizontal. 


1-050 




























































LARGE SUBMERGED ORIFICES 


163 

The arrangements for measuring were extremely accurate, and the figures 
may be relied on to about three units in the third place of decimals. It is fairly 
plain that large orifices will probably show no measurable difference. 

Large Orifices. —The most complete experiments are those of Stewart 
(■Bulletin of Univ. of Wisconsin , March 1908, and Eng. News , January 9, 
1908) on 4 feet square submerged orifices, under small effective heads. 

Here we have as follows : 

Where I. refers to square-cornered orifices, prolonged by a tube of a length l. 

II. refers to a similar orifice with contraction suppressed at the 
bottom by a bellmouth of elliptical form. 

III. refers to ditto, at one side, and the bottom by a similar bellmouth. 

IV. refers to ditto, at two sides, and the bottom by a similar bell¬ 

mouth. 

V. is as IV., but unlike all the other cases, the tube does not simply 
end in a sharp edge, but in a bulkhead, as though it passed 
through a thick wall. 

VI. is an orifice as No. IV., with contraction completely suppressed 
on all four sides, and no bulkhead at end of the tube. 

We have, Q = Ca\l2gh c i, and the following are the values for a tube of a 
length equal to / feet. 


Ei 

Feet. 

Case. 



/= Length of 

Tube. 



0-31 ft. 

0*62 ft. 

1 -25 ft. 

2-5 ft. 

5 *° It- 

10-0 ft. 

14-0 ft. 

0-05 

I. 

0*631 

0*650 

0-672 

0*769 

0-807 

0*824 

<>•838 

• • • 

II. 

0 ‘ 6 j 2 



0*742 

o"8io 

... 

0*848 

* * * 

III. 

0740 



0*769 

0-832 

• . . 

0*862 


IV. 

0-834 



0-769 

0-875 

... 

0-890 

• • • 

V. 

... ■ 



... 


... 

0-875 

.. . 

VI. 

0-948 



o '943 

0*940 

0-927 

0-931 

0*10 

I. 

o'6i 1 

0-631 

0*647 

0*718 

0-763 

0-780 

o *795 


II. 

0*636 



0-698 

0-771 

... 

o*8oi 


III. 

0-685 



0-718 

°* 79 I 

•.. 

0*813 


IV. 

0-772 

... 


0-718 

0-828 

... 

0*841 


V. 

... 



. • . 

... 

• • • 

0-830 


VI. 

0-932 



0-911 

0-899 

0*892 

0-893 

O-I 5 

I. 

0*609 

0*628 

0*644 

0*708 

o 75 8 

o *779 

0 794 


II. 

0*630 

. . . 


0*689 

0-767 

. . . 

0-803 


I III. 

0*677 

. . . 


0-708 

o-yS? 

... 

0*814 


IV. 

0-765 

. . . 


0-708 

0-828 

... 

0-839 


V. 

• • • 

• • • 


• V 


• . • 

0*829 

... 

VI. 

0-936 

• • • 


0-910 

0*899 

0*893 

0*894 


[ Table conlimied. 





































































164 CONTROL OF WATER 


Table continued J 




I 


1 = Length of 

Tube. 



ha 

Case. 

1 














Feet. 


0-31 ft 

0*62 ft. 

1*25 ft. 

2*5 It. 

5*o ft. 

10*0 ft. 

14*0 ft. 

0'20 

I. 

0*609 

0*630 

0*647 

0-711 

0*768 

0*794 

0*809 

. . . 

II. 

0*632 

• • • 

. . • 

0*694 

0*777 

• • • 

0*819 

• • • 

III. 

0*678 

• • • 

• . . 

0*711 

0*796 

• • • 

°' 8 33 

. . . 

IV. 

0*771 

... 

. . . 

0*711 

0*838 

• • • 

0*856 

... 

V. 

• • • 

... 

. . . 

• • • 

• • . 

• • • 

0*846 


VI. 

0*948 

... 

• • • 

0*923 

o-g 11 

0*906 

°' 9°5 

0-25 

I. 

o*6io 

0*634 

0*652 

0*720 

0*782 

0*812 

0*828 

. . . 

II. 

0*634 

• • • 

. . . 

0*705 

0790 

• • • 

• • • 

. . . 

III. 

0*683 

. . . 

. . . 

0*720 

0*809 

• • • 

• • • 

• • • 

IV. 

0*779 

. . . 

• . • 

0720 

0*854 

• • • 

• • • 

• • • 

V. 

• • • 

• • • 


• • • 

• • • 

• • • 


• • • 

VI. 

0*965 


... 

0 

'O 

OJ 

00 

0*928 

• • • 


0*30 

I. 

0*614 

0*639 

o*66o 

0*731 

0*796 

0*832 

0*850 

• • • 

II. 

0*639 

• . • 

• • • 

• • • 

• • • 

• • • 

• • • 

III. 

0*689 

• . . 

• • . 

• • • 

• • • 

... 


• • • 

IV. 

0*788 

• • • 

• • • 

• • • 

• • • 

... 


• • • 

V. 

• • • 

• • • 

• • • 

• • • 

• • • 



... 

VI. 

0*980 

• • • 

... 

... 


• . . 



These experiments were conducted with the help of a carefully calibrated 
weir, and may be regarded as possessing a very high degree of accuracy. 

The values given above are not corrected for velocity of approach, and 
the form is consequently that which is most useful in practical work. If a 
correction for the velocity of approach is introduced, the values of C; are 
reduced by ^ per cent, to i| per cent., the lesser reduction occurring for square 
corners, and h — 0*05 feet, and the greater for Case VI, and h = 0-30 feet. 

Sluices and Gates. —These may be considered as orifices, usually 
rectangular in shape, with completely suppressed contraction along the lower 
portion of the perimeter, more or less suppressed contraction at the sides 
and complete contraction at the upper portion. Also, the issuing jet, or 
sheet of water, is generally guided, and prevented from expanding on'the 
sides corresponding to those on which contraction is suppressed at entry. 

The complexity of the problem is indicated by a mere statement of the 
above facts. Existing experiments show that the coefficient of discharge 
varies markedly with the amount of opening of the sluice. The issuing jet 
often forms a standing wave, and, in such cases, we have the additional prob¬ 
lem of specifying where the head is to be measured. (Compare Sketch No. 33.) 

The problem is obviously that of a submerged rectangular orifice, and tlie 
following general statements can be made. 

When the sluice is first opened, the thickness of the bottom of the gate 





















































SLUICE GATES 


i 6 5 

is comparable with the width of the opening, and phenomena occur which are 
analogous to those of an orifice with a mouthpiece. Coefficients of discharge as 
high as i*2o, reckoned on the gate opening, have been observed, and there is 
little doubt that higher values are met with, but are masked by the leakage 
that takes place at other portions of the gate, and by experimental difficulties 
connected with the measurement of the head. When this stage ends, (which 
both theory and experiment indicate occurs when the width of the opening 
is equal to about three-quarters of the thickness of the bottom of the gate), 
the flow resembles that through an orifice with partially suppressed contraction, 
and a coefficient of 0*65 would appear to be approximately correct, although 
reliable observations occasionally indicate lower values, such as o*6o. These 
values may be explained by the fact that when the seat of the gate is some¬ 
what raised above the rest of the floor, and the width of the opening is not 
too great, marked contraction at the bottom of the orifice is produced. Theory 
then indicates a value of about 0-63, so that the observations are probably 
accurate. As the gate rises, this bottom contraction has less effect, the 
coefficient increases, and values ranging up to 0*85 occur. 

The only systematic observations are those of Bornemann. Those by 
Benton, and Chatterton, are more practical, but are less suitable for ascertaining 
the general laws. 

Bornemann ( Civilmgenieur , vol. 26, p. 297) experiments with sluices in open 
channels. His table shows the following particulars : 


No. of 
Experiments. 

Width of 
Sluice. 

Width of 
Channel. 

Height of 
Opening in F'eet. 

Effective Heads 
in Feet. 


Feet. 

Feet. 

Max. 

Min. 

Max. 

Min. 

16 

3 ’ 3 ° 

3*73 

o- 5 8 

O'l 1 

073 

0*06 

28 

1*70 

178 

0-84 

0-30 

o’6i 

o"o6 

I 9 

2 ’54 

2-83 

°’43 

0*22 

°‘57 

0*06 


With the formula Q = C X area of opening 2 g {^Ji x — ^ 

where /q, is the depth of the top of the opening below the upper water surface, 
h 2i is the depth of the top of the opening below the lower water surface. 

Thus, h x —h> 2 — h ( i — effective head. 

и , is the velocity of approach. 

к , is the height of the opening. (Sketch No. 44.) 

Bornemann gets for the 3-30 feet sluice : 

~ cc. , . k 

C — 0-664+0-053 ——y 


h. 2 -\- — 


and for all the experiments : 


C = 0-541+0-150 


yk 

1 _i _ k 

ho H— 

" 2 


The range of these experiments is by no means as wide as is desirable. 
Large values of h, are almost universally accompanied by small values of the 





























i66 


CONTROL OF WATER 


effective head, but this connection is far less marked than in the case of the 
experiments which are later discussed. The form arrived at by Bornemann 
must therefore be considered as the best which is at present available. 

Benton (.Punjab Irrigation Branch Papers , No. 8) experimented on the 
ordinary sluice gate used for regulating the discharge of irrigation canals. 


~i\ - 




J 


-^3 


T 


Yiidlhof 
11 idth of 


Velo city of 'approac/i 
u ft. tier sec. 
sluice opening - W. feet. 
clmnePdfecforgrester. 


k.is measured to top of sill if if exists. 


Sill. 

r~~r~TL 


i 


Mam Stream 



Sketch No. 44.— Diagram of Discharge through a Sluice, and 
Type of Sluice experimented on by Benton. 


These gates were io feet wide in eleven cases, 8 feet wide in sixteen cases, 
6 feet wide in twelve cases, and 4 feet wide in seven cases. The discharges 
weie observed by rod floats, and are probably accurate to 1 per cent., the 
observer being unusually skilful. The discharge being submerged, and velocity 
of approach being neglected, the formula is as follows : 

Q = Czuk x V 2gh ( i 




























SLUICE GATES 


167 

The effective head h d is defined as the difference between the water levels 
upstream and downstream of the gate, as observed in stilling wells. 

We have the following table : 


iv, in Feet. 

Max. Q, 
in 

Cusecs. 

Min. Q, 
in 

Cusecs. 

Max. hd, 
in 

Feet. 

Min. hd, 
in 

Feet. 

Max. k, 
in 

Feet. 

Min. k, 
in 

' Feet. 

10 

113*0 

3 °* 7 

3*88 

0*07 

2 ‘55 

0*46 

8 

5 6 '7 

26*3 

i *47 

0*16 

3 * 2 ° 

0*42 

6 

49*3 

7*2 

4^5 

0*22 

0*92 

0*28 

4 

24*9 

10*1 

3 * 5 1 

2 ‘44 

0*71 

0*19 


Benton considers that C is solely affected by w, the width of the gate, 
and gives for all observations : 

C = 07201 + 0*00747^ 

For all cases where h d , exceeds 0*50 foot. C = 0*7162+0*0079so that: 


W — 

10 Feet. 

8 Feet. 

6 Feet. 

4 Feet. 

C (first case) 

0*794 

0 

--j 

00 

0 

0*765 

0*75° 

C (second case). 

0*795 

0*779 

0*763 

0*748 


The results agree very well with the experiments, but it must be remembered 
that the maximum ha, almost invariably occurs when k, has its minimum 
value, and vice versa, consequently, Q, as tabulated, varies far less widely 
than might be supposed. 

The experiments of Chatterton (.Hydraulic Expcrime?its in the Kistna 
Delta) are subject to the same objection. The gaugings were effected with 
a current meter, but are probably less accurate than are those of Benton. 
With one exception, the gates were from 6 feet to 5*25 feet wide ; but, unlike 
Benton’s experiments, the discharge observed was that of a number of gates 
(in some instances as many as 17) separated by piers 3 feet in thickness. The 
experiments are somewhat mixed in character, containing submerged orifices 
similar to those experimented on by Benton, and orifices with free overfall, 
where the theoretical formula is represented by : 

Q = 

Hj, and H 2 , being the depths of the top and bottom of the orifice below upstream 
water level. Velocity of approach, though neglected, had probably more effect 
than in Benton’s experiments, the circumstances being similar to Sketch No. 42, A. 

Chatterton gives the following equation : 

C — o*615 +0*007 x 2 5 ~ h <t 
for all cases where h d varies from o, to 5 feet. 


































i68 


CONTROL OF WATER 


I find approximately that: 

(i) For the cases where the discharge is submerged, and the formula : 

_ 

Q = C wks/ 2 gh& is applicable, 

C = 0-83 —o*i i h d 

where ha varies from o, to V2 foot. This compares very well with Benton’s 
experiments under similar heads, and the larger values of C, are plainly due 
to neglect of the velocity of approach. 

(ii) For cases where the discharge is not submerged, and the formula : 


with 


Hi -f~ Hg 

o 


Q = CW2* r (H 2 1 - 5 -H 1 1 - 3 ) 
C = 0-63, 

varying between 3, and 5 feet. 


applies, 


The results are not very concordant, although they agree well with the 
theoretical values. The experimental difficulties are great, so that these figures 
are the best that are likely to be obtained. 

The results obtained by Benton and Chatterton show that the shape of 
the approach channel, or the circumstances affecting side contractions, have 
extremely little influence on the coefficient of discharge in orifices of the size 
now under consideration. All these matters may be neglected in practice, 
without introducing serious errors. 

We may therefore sum up this obscure, but important subject, as follows : 

The general value of the coefficient of discharge of a submerged orifice 
with bottom contraction completely suppressed, may be taken from Benton’s 
experiments for heads exceeding o‘6, or 07 foot. For lower heads, the values 
given by Chatterton, corrected by Benton’s rule for the width of the opening, 
may be used. Nevertheless, it is inadvisable to take a greater value of C, 
than o*8o, although there is little doubt that in wide openings values such as 
o‘ 85, or even 0*90 occur. If the bottom contraction is complete (eg. the gate 
rests on a raised sill), and the orifice is not submerged, a coefficient of o’63 is 
safe, but is probably exceeded when the discharge is submerged. 

When actual observations have been made, a formula of Borncmann’s type, 
with properly determined coefficients, will probably be found useful, and the 
velocity of approach should be allowed for. 

Comparing these results with the general trend of the evidence afforded 
by small scale observations, we can rest assured that the application of 
coefficients derived from work on orifices say 1 foot wide, and 8 inches high, 
is not likely to lead to serious error, and that the large orifice will almost 
invariably discharge more than is indicated by the calculations. 

Non-circular Orifices , under Large Heads. —The only available 
experiments are due to Graeff (see p. 788). It appears justifiable to assume 
that the geometrical form of the orifice has no appreciable influence on the 
coefficient of discharge, which is determined entirely by the thickness of the 
walls and the amount of suppression of contraction. In calculations it is 
desirable to bear in mind that the higher the head the blunter (geometrically 
considered) the edges of the orifices may become before the orifice ceases to 
be “ sharp-edged ” (hydraulically considered). 




CHAPTER VI.—(Section A) 
COLLECTION OF WATER AND FLOOD DISCHARGE 


Collection of Water .—Connection between rain-fall and stream discharge. 

Average, or Mean Value. —Sampling—Application to rain-fall or stream discharge 
statistics. 

Definitions.— Mean annual rain-fall — Evaporation — Run-off—Rain-fall loss — Percola¬ 
tion—Periods of observation. 

Sources of Information. 

Rain-fall. —Importance of observations on rain-fall. 

Climate as affecting the Variability of Rain-fall. —Insular and Continental climates— 
Temperate and Tropical climates—Wet and dry seasons—Variability of the annual 
rain-fall—Binnie’s rules for the relation between the values of the mean annual rain¬ 
fall for a short and long period—Ratio of mean annual to maximum and minimum 
annual rain-fall— Binnie’s rules —Criticism—Exceptions—Indian and Californian 
examples—Probable explanation—Space variability of rain-fall—Large scale selection 
of the sites of rain-gauges—Liability to underestimate the average rain-fall of any 
area—Local conditions affecting rain-gauges—Effect of eddies—Gauges on hillsides 
—Nipher shield—Standard rain-gauge—Correction for elevation above the natural 
surface. 

Accuracy of Rain-fall Records. —Snow—Non-standard gauges. 

Water Year. —Period of minimum stream flow—Period of maximum water storage. 

Variation of the Rain-fall over the Year. —Summer and winter rains—Wet and 
dry season rains. 

Connection between Rain-fall and Run-off. —Disposal of rain-fall in the 
forms of: (i) Utilisation by vegetation ; (ii) Evaporation ; (iii) Topographical flow ; 
(iv) Stored rain—Ground water flow—Period over which the relations hold— 
Period of a year—Values of AR—Possible errors—Approximate estimation of the 
monthly run-off from evaporation statistics—Values for English catchment areas 
—For Elbe and Moldau. 

Observations supplementing the usual Stream Gaugings.—-Subsoil water levels 
—Survey of permeable beds—Chemical investigations—Seepage water inves¬ 
tigations. 

Case when rain-fall does not suffice to provide for vegetation and evaporation— 
Droughts. 

Climate in Relation to Run-off. —Effect of duration of the periods considered. 

Climates of the First Type. —Omission of the wetter years—Probable errors— 
Effect of abnormal winter and summer rains—Annual and mean annual rain-fall loss. 

Run-off of Catchment Areas .— Circumstances affecting the relation. 

Effect of the Absolute Magnitude of the Mean Annual Rain-fall .— 
Effect of errors in estimating the rain-fall—Example of Melbourne—General 
investigation—Deductions. 

Seasonal D.stribution of Rain-fall. 

Effect of Geological Structure.—Effect on topography—Permeable beds—Geological 
and topographic watersheds—Detection of springs, or leaks in stream beds— 
Detection of underground flows—Dew ponds. 

Effect of lakes and swamps.—White Nile—Aker. 

Glacier-fed Streams. —Monthly discharge curves. 

Daily Variations of Mountain Streams. 

169 


1 7 o 


CONTROL OF WATER 


Relation between mean Yearly Rain-fall and Run-off. —Keller’s results for 
German areas—Flat areas—Partly flat and partly hilly areas Hilly areas Alpine 
areas—Probable errors—British areas. 

Relation between the Rain-fall and Rain-fall Loss for Individual 
Years —Determination of the constant a —Examples—Wet districts. 

Distribution of Run-off during the Year. —Visible and invisible reservoirs 
Structure of the catchment area—Typical tables of rain-fall and run-off by months. 

Subtractive Method. —Monthly rain-fall losses—Summer rain-fall losses. 

J Run off 

Proportional Method — Monthly values of the ratio —Practical application. 

Third Method taking into Account the Effect of Ground Water Storage on 
Run-off —Vermeule’s investigation—Vermeule’s v —Tabulation—Connection with 
evaporation and rain-fall loss—Classification of catchment areas—Depletion—-Deter¬ 
mination of monthly run-off in terms of the initial depletion—Practical determination 
of the run-off and mean depletion curves—Criticism—Application to British catch¬ 
ment areas—Tables of y , and d{ —Example—Special monthly formulae—The run¬ 
off at end of a dry period is a geological phenomenon. 

Determination of Reservoir Capacity. —Accuracy of the predicted monthly and 
yearly run-offs—Three driest consecutive years—Hawksley’s rule— Rofe’s rule — 
New rule—Tabulation—German experience—United States experience. 

Mass Curve. —Description of monthly mass curve—Period of greatest depletion— 
Correction for evaporation—Equalising storage for driest year— Yearly Mass 
Curve —Storage capacity derived from the yearly mass curve—Determination of 
run-off during critical periods—Growing season—Replenishment season—Storage 
season—Consumption by vegetation—Equalisation of yield over five dry years ; 
probably represents maximum storage capacity—Gore and Brown’s investigations— 
Tables of yearly rain-falls and run-offs. 

Catchment Areas situated in Climates of the Second Type —Authorities— 
Strange’s table for India—Criticism—Accuracy of rain-fall records— Binnie’s 
Method —Criticism—Observations for a partially permeable catchment area — Table 
for daily run-offs—Table for flat and permeable areas—Correction for stored water. 

Variability of the Wet Season Rain-fall. 

Capacity of Reservoirs. 

Climates of the Third Type. 

Records of the Sweetwater catchment area. 

Records of Australian and Californian catchment areas. 

Victorian records of rain-fall and run-off. 

Secondary Catchment Areas. —Capacity of the diversion channel—Vyrnwy secondary 
catchment areas—Effect of silt—Coghlan’s rule—Artificial drainage—Impervious 
catchment areas. 

Collection of Water from Sources other than Stream Flow. —Underflow 
—Springs—Catchment galleries—Dune sand developments. 

Wells in Uniformly Permeable Strata.— Conditions in sand, chalk, and granite 
—Permeability—Slope of ground-water surface—Velocity of flow—Formulae for 
circular well—Catchment gallery—Effect of the size of the well—Variations in 
permeability—Effect of the well lining, or of a stream or lake near the well—Spacing of 
wells—Blowing of a well—Natural replenishment of the well—Preliminary studies— 
Correction in deep beds of sand—Probable yield of large schemes—Reversed filters 
—Well plugs—Mota wells. 

Artesian Wells.— Practical conditions—Thickness of permeable strata— Estimation 
of probable yield—Permanent diminution of yield—Quality of water — Typical 
example—Geological conditions as applied to individual wells. 


NOTATION FOR RAIN-FALL AND RUN-OFF 

The period to which the quantities refer is denoted by a suffix. A symbol without 
a suffix refers to the year. All quantities are expressed in inches depth over 
the catchment area. 

Suffix I, 2, etc., refers to calendar months. 
m, refers to the 30 or 40 years’ mean. 

/>, refers to any period in general. 

c, and h , refer to the cold and hot seasons. 



RAIN-FALL AND RUN-OFF 


171 


s, and w, refer to summer and winter. 

Capitals are occasionally used when two periods of different years are contrasted. 
a p + t>pX p = Vp is the vegetation and evaporation loss (see p. 185) during the period /, 
and a similar formula gives Vermeule’s v (see p. 219). 
a p + b (J Xq + b r xr is used to denote Vp, when the change in temperature during the 
period /, is too great to permit the simpler form to be used. 

A, and A w (see p. 222). 
c (see p. 200). 

d n , or di, is the initial depletion (see p. 221) of the month considered. While d n y x is 
the final depletion of this month, or the initial depletion of the next, and the mean 

depletion during the month, + ^ +I is denoted by D n . 

2 

D, 2D, 3D, as suffixes refer to the driest, two consecutive driest, and three consecutive 
driest years of a long period. 

e, is the evaporation from a free water surface, as observed in meteorological observatories. 
E (see p. 190). 

/> is the ground water flow as calculated on the assumption that ke v — V p . See p. 190 
and g, k , t, u, and v. 

gy is the water flowing out from the ground storage to the stream, as actually observed 
(see p. 187, and also/, t , and u). 

k — - (see p. 190). 

R, is the total quantity of water stored up in the ground. The depletion d, or D, is the 

difference between the maximum value of R, for the year, and the value of R, at the 
time considered, when AR, is calculated by Vermeule’s method. 

Also, AR = s-g, and f — — AR, on the assumptions explained under these symbols. 

S, is the maximum depletion ever found to occur, and theoretically, the difference 

Rmax - Rmin calculated according to Vermeule’s rules is equal to S. 

S M (see p. 222). 

s, is the flow to ground storage from the surface (see p. 187). 
ty is the topographic flow (see p. 186). 

Neither the Vs, g > s, nor Vs, are ever obtained by calculation, and different symbols are 
used for the calculated values in order to indicate that these values are only 
approximations. 

Uy is the value of^, calculated according to Vermeule’s rules. See^ - , and/. 

Vy is Vermeule’s value of a + bx (see p. 219). 

V, is the vegetation and evaporation loss. 

x, is the rain-fall. 

y, is the run-off. 

y 0 , and y n (see p. 222). 

z, is the rain-fall loss, z = x —y. 


Collection of Water.—Apart from a few somewhat doubtful exceptions, all 
fresh water occurring in nature has at some period of its existence fallen as 
rain. The present chapter is essentially an endeavour to deal with the following 
problem. The area of the surface drained by a natural stream, or artificial 
channel, and the average depth of rain falling on this surface during a given 
period being known from actual measurement and observation, the total 
volume of rain water falling on this area (which we shall hereafter term the 
catchment area of the stream or channel) during this period can be calculated. 
We wish to determine the relation between this volume and the total volume 
delivered by the stream in the same period. 

No precise solution can be given ; and it will be evident that the fact that 
the problem assumes this particular form is in reality an indication that 
observations of the discharge of the stream have been neglected. Thus, in a 
strictly scientific sense, the fact that 85 pages are devoted to a consideration 
of the question is almost discreditable. In practice, however, observations of 
rain-fall are made in all countries for many years before the discharge of the 




172 CONTROL OF WATER 

streams is systematically measured. Hence, engineers are obliged to consider 
the question. 

Average , or Mean Value. —The conception of the average or arith¬ 
metical mean of a number of quantities of the same kind is familiar to all 
practical men, and the belief that the average value of any quantity common 
to a class of individuals of not too variable a character (eg. individuals of the 
same biological species) can be ascertained with sufficient accuracy for practical 
purposes by selecting a certain number of the individuals at random, and taking 
the average of the quantity as observed in these individuals, is relied on in 
practical life to an enormous extent, since it forms the ultimate justification of 
sales by sample, and analyses by “quartering.” The mathematical difficulties 
attending any proof of this belief are very great, and there is little doubt that 
in some cases the geometrical mean of the quantity observed in the samples 
is a fairer representation of the value around which these quantities tend to 
range themselves when the whole class is considered. In practice, however, 
a sample of a material taken at random is usually a satisfactory representation 
of the sampled material, provided that the bulk of the sample is not too small 
relatively to the total bulk of the material, and that the selection is one made 
truly at random. 

Average Values. —In considering statistics of rain-fall, stream discharge, 
or other quantities observed by engineers, the problem usually presents itself 
as follows : 

Let P l5 P 2 , . . . . P N , say, represent the observed quantities, where N, indi¬ 
cates a very large number, say 10,000 if the symbols represent daily values, or 
100 if the symbols represent yearly values. The difference is obviously due 
to the fact that a yearly value is in itself a mean, or total (as the case may be) 
of 365 daily values. 

The mean value is : • - +Pn _ ^p N sa y 

Now, consider : Pi + etc - + I jt _ ^ 

n 

Pi + etc. + P w+1 _ 

n+i ~™r n+ 1 

P 1 + etc. + P M+2 


Where n is any number less than N. 

What is the relation between m P N , and the various quantities m P n , m P„ +2 , 
etc. ? 

As a matter of observation, we usually find that if /z, be not too small com¬ 
pared with N, the quantities are very approximately equal to each other. This 
property is specified by the statement that the “ P’s ” vary more or less regularly 
about a mean value, and the more regular the variation, the smaller the value 
of n, required to secure this approximate equality. The differences that still 
exist between m P ?! , mP»+i, etc., are called the residual irregularities. 

Meteorologists have a belief (it is not more) that if the P’s, be meteorological 
quantities observed yearly, n, must be approximately equal to 35. With con¬ 
siderably less justification engineers are accustomed to assume that if P, 






MEAN VALUES 


i73 

represents the twenty-four hour discharge of a stream, n, is about 7 x 365, i.e. 
a seven years’ record will suffice. 

As a matter of observation, we also find that if: 

P '-'w' P 13 13 

n m-t 74 + ] n +2 wia N 

Then also : 

p ^ P2 + etc. + P M+1 ^ P 3 -fete. + P, l+2 

m l n 

n 7 i 

P4 + e t c - + h > « + 3^ T etc. -j- P n+r—\ 

n n 

'r^C m^N 

From a purely philosophical point of view, the whole series of assumptions 
rests on very insecure foundations, and it is quite possible that when accurate 
statistics of 300 or 400 years are available, “ century long ” climatic changes 
will be found to have a real existence. At present, 100 years of accurate 
statistics of any climatic quantity do not exist, and all that can really be said 
is that some assumption must be made, and that the possibilities of error should 
be indicated. This has been attempted in the following treatment of the 
subject. 

Definitions. —We define as follows, all quantities being expressed in 
inches depth : 

The Rain-fall, or mean annual rain-fall, is the mean of the annual rain-fall 
observed over a period which is sufficiently long to produce a fairly constant 
mean value. In the British Isles we can state that this period is about thirty 
to forty years, and that the probable variation of this mean value {i.e. the 
residual irregularity) is ± 2*5 per cent, when compared with the mean of another 
record of equal duration for the same locality. 

The Evaporation, or mean annual evaporation, is the mean value, in inches, 
of the depth of water annually evaporated from a free water surface, the period 
of observation being of adequate duration to secure approximate constancy, 
as in the case of rain-fall. 

The Run-off, or mean annual run-off, of a catchment area, is the value of 
the annual volume of water discharged by the stream draining the area, 
expressed in inches depth of water over the catchment area, the period of 
observation being sufficiently long to secure a fairly constant mean. 

We also define the Rain-fall loss for a catchment area, as the difference 
between the rain-fall and run-off for any period, both being measured in inches 
over the catchment area. 

The Percolation, or mean annual percolation, is the depth of rain water 
measured in inches that annually soaks away through the earth ; it being 
presumed that the period of observation is of sufficient length to secure 
approximate constancy. 

As yet we are unaware how long a period of observation is required in order 
to produce fairly constant mean values of these last four quantities ; although 
it is highly probable that the periods are less than those for rain-fall in the case 
of percolation, but greater for evaporation and possibly also for rain-fall loss 
and run-off. 

Sources of Information .—Since the above defined quantities vary from year 
to year, and differ for every locality on earth, it is impossible to give any useful 






1 74 


CONTROL OF WATER 


table of their values. Records of rain-fall exist in every civilised country, and 
usually a very fair value of the rain-fall, and a less accurate one (since observa¬ 
tions of these quantities are not so commonly made, and have generally been 
recently initiated) for evaporation and percolation, is obtainable by consulting 
such records as : 

Symons’ British Rai?ifall , for the British Isles. The publications of the 
United States Weather Bureau, and reports of the various Meteorological Offices 
for their respective countries. 

I have tabulated, and, where possible, given the original references to all 
published values of the rain-fall loss that I have been able to ascertain, that are 
based on anything more than a vague assertion. 

For run-off statistics, the principal authorities are the publications of the 
United States Geological Survey, which refer only to the United States. For 
the British Isles, no complete record of the run-off of any river, except the 
Thames, has been published. Many must exist stored away in the various 
waterworks’ and engineers’ offices. A certain amount of information on the 
subject (especially values for yearly run-offs) lies scattered throughout the 
Proc. hist, of C.E., but it is small compared with that afforded by such papers 
as those by Fitzgerald, on the Boston Waterworks, in the Trans. Am. Soc. 
of C.E. ; or by Freeman, in his paper on the “ Report on the Water Supply of 
New York.” This latter work is a model example of the proper use of run-off 
statistics ; and, owing to Mr. Freeman’s careful discussion of this record, the 
possibilities of error remaining even in the case of such complete and carefully 
handled data, are clearly shown. 

In India, most of the big rivers are gauged, more or less systematically, 
by the Irrigation Department, and by the various railways ; and for such 
matters as the available low water supplies, the information is usually most 
complete. 

In the State of Victoria (Australia), Stuart Murray has instituted a very 
complete system of run-off records. The available rain-fall records are not 
very good, so that from the present point of view the figures are not of general 
interest. They form, however, a very excellent basis for all projects for water 
supply in Victoria, and, when compared with the available British information, 
are highly creditable to Mr. Murray. 

My own experience is that in most capitals, except London, a fair amount 
of accessible information exists, either worked up ready for use, or in the form 
of gauge readings ; and this, in conjunction with rain-fall records indicating the 
probable years of high and low values of run-off, enables a very fair idea of the 
capabilities of a catchment area to be obtained. 

I must here express my thanks to the many practising engineers in countries 
as far apart as Australia, Japan, the United States, and Great Britain, who have 
favoured me with copies of private statements of rain-fall and run-off. The 
rules put forward for British run-offs are avowedly capable of improvement. 
If I can obtain a careful criticism (even though hostile), supported by only one 
hitherto unpublished record, I shall feel amply rewarded 

Rainfall .—The amount of discussion devoted to this subject in a treatise on 
Hydraulics is, in reality, a measure of the absence, or non-accessibility, of long- 
period records of the discharge of streams and springs. It is to be hoped that, 
as the art progresses, discussions on the variability of discharge and water 
yield will gradually supersede the present methods, and that rain-fall will finally 


CUM A TE 


T 75 


be relegated to its rightful, and subordinate positon, which, in my opinion, is 
but little superior to that of the local temperature, as influencing the daily con¬ 
sumption in a town water supply, or the duty of water in the irrigation of crops. 

In the present state of the art we are forced to rely upon rain-fall observations, 
not so much because they are the most desirable records bearing on hydraulic 
questions, but because they are one of the few requisite observations that can 
be taken by an intelligent, but untrained man. Owing to the large influence 
that rain exerts on personal comfort, this work is undertaken by people who 
otherwise have not the slightest interest in, or knowledge of, hydraulics. Rain¬ 
fall figures indeed, form the one piece of definite information that the non¬ 
engineering world is generally able to give the hydraulic engineer when 
initiating a project. He therefore accepts it gratefully, and uses it to the best 
of his ability. It is, nevertheless, necessary to bear in mind continually that 
we are primarily, and almost exclusively, concerned with run-off or discharge 
statistics ; and that to neglect these—even when approximately accurate—for 
rain-fall records of far greater accuracy, is, as it were “ putting the cart before 
the horse.” 

Climate as affecting the Variability of Rain-fall.—It will be shown later that 
the annual rain-fall in any locality varies from year to year within certain limits. 
These variations are largely determined by the general character of the local 
climate, and, consequently, it becomes necessary to broadly define the types of 
climate that influence the probable variations. 

I therefore propose to classify climates as Insular or Continental. The 
distinction is primarily a geographical one. Localities close to the oceans 
have an Insular climate, while the Continental type of climate occurs either in 
the interior of Continents, or in places separated from the oceans by high 
mountain ranges. 

The characteristics of the two types are well known. Continental climates 
have a very hot summer, followed by a relatively cold winter, while the difference 
between the mean winter and summer temperatures in an Insular climate is by 
no means so marked, and in some cases is almost imperceptible. 

In the Temperate Zone, the climate of the British Isles is typically Insular, 
while the Middle United States, or Southern Russia, possess a climate of 
Continental character. The dividing line may be very practically illustrated 
by the fact that an Englishman’s wardrobe does not usually include either 
furs or white suits, while an American of the same class invariably possesses 
both. 

So also in Tropical Regions, such as the Punjab, fur coats are common in 
the cold weather, while in the hot weather punkahs, or electric fans, are 
necessities for Europeans, and are appreciated by all races. The contrast with 
say, Ceylon, where punkahs or fans are less essential, but are used all the year 
round by those who can employ them, is very marked. 

The distinction between a Tropical and a Temperate climate is somewhat 
difficult to define. Geographically, for instance, the Punjab is not in the 
Tropical Zone, yet the temperatures there obtaining are surpassed in very 
few localities, and, unless I am mistaken, these are also entirely extra 
Tropical, geographically speaking (i.e. the Persian Gulf and the Salton 
Desert). 

From the point of view of an engineer, Tropical climates may be defined 
as those in which the native workman is unable (during some seasons of the 


CONTROL OF WATER 


176 

year at any rate) to perform hard manual labour continuously during the 
hottest portions of the day. 

In all Tropical climates (except a few extremely Insular examples), and in 
most Temperate Continental climates, there are well defined rainy seasons, 
usually one each year, but in some cases two. In such instances, the major 
portion of the rain-fall, and all that has any practical influence on the run-off, 
occurs during well defined periods of the year, usually not exceeding four 
months in length ; and during the remainder of the twelve months the rain 
that does fall is insignificant in quantity and accidental in occurrence. 

Generally, it may be stated that an Insular climate is, (comparatively 
speaking) a wet one. 

A prevalent idea exists that Tropical climates are markedly wetter than 
Temperate ones. This, I believe, is principally owing to the fact that 
European habitation in the Tropics is somewhat closely confined to islands and 
sea coasts, possessing Insular climates. So far as our knowledge permits of 
any wide statement being made, I believe that when the areas of Tropical 
Continental climates are as extensively inhabited by civilised races as Tropical 
Insular climates now are, it will be found that the difference, if it exists, is but 
small. At present it can be definitely stated that the mean rain-fall of all India 
is very close to the mean rain-fall of the British Isles, and, so far as my own 
studies go, I believe that the actual distribution of rain gauges is such as to 
under-value the rain-fall of the British Isles, and to over-value that of India ; 
although I am well aware that the gentlemen who prepared the estimates of 
mean rain-falls did in each case allow for this possibility of error to the best of 
their ability. 

Variability of the Annual Rainfall .—As a matter of observation, the fall of 
rain at any locality, measured in inches per annum, varies from year to year. 
A study of rain-fall records extending over periods of many years, such as exist 
in England, Europe, and the United States, has led to the conclusion that the 
average of the yearly rain-fall tends towards a constant quantity, as the number 
of years over which the average is taken increases, and it appears that the 
average of 30 to 40 years’ rain-fall varies but little, whatever period of 30 to 40 
years in a long rain-fall record is selected. 

The exact figures as given by Hann and Mill (P.I.C.E., vol. 155, p. 368), 
are : 

AVERAGE VARIATIONS FROM THE MEAN FOR 70 YEARS AS 

GIVEN BY RECORDS OF 



10 Years. 

20 Years. 

30 Years. 

40 Years. 

Three European 
Stations 

Five British Stations 

Per cent. 

7*5 

47 

Per cent. 

5 ’ 2 

3'4 

Per cent. 
2*6 

2*2 

Per cent. 

2 '3 

17 


While Binnie, (. P.I.C.E ., vol. 109, p. 131) gives for 26 stations, with records 
of an average length of 53 years, the following : 












VARIABILITY OF RAIN-FALL 


i77 


DEVIATIONS FROM THE MEAN VALUE OF THE ANNUAL RAIN-FALL 
DURING THE WHOLE PERIOD OF THE RECORD, EXPRESSED 
AS PERCENTAGES OF THIS MEAN FALL FOR EACH LOCALITY ; 
WHEN THE PERIOD CONSIDERED IS 


1 

• 

5 

Y ears. 

10 

Years. 

15 

Years. 

20 

Y ears. 

25 

Years. 

30 

Years. 

35 

Years. 

Maximum positive 








deviation . 

23*2 

I 4’9 

9*2 

5* 6 

7*3 

5* 2 

4*5 

Maximum negative 








deviation . 

2 9’6 

16*1 

*2*5 

9*2 

9 ’o 

6*9 

4*7 

Average positive 
deviation . 

T 5 *35 

8-o8 

3* 8 7 

» ' > 

2*47 

2*56 

2*17 

i*73 

Average negative 


. 






deviation . 

I 4'5 2 

S'37 

5* 6 4 

4*08 

2*94 

2*36 

r86 

Minimum positive 
deviation . 

6*8 

1*0 

O’O 

O’O 

0*0 

1 

O’O 

O'O 

Minimum negative 








deviation . 

7-8 

4*7 

o -8 

o‘o 

cr’o 

0*0 

O’O 

Average deviation . 

14*93 

8*22 

4*77 

3‘ 2 7 

2 '75 

2*26 

1*79 

1 


These stations are distributed over a large portion of the globe, and may be 
regarded as including Insular climates, both Tropical and Temperate, together 
with 4 examples of what may be termed Semi-continental climates. We may 
therefore consider that these figures are applicable to all Insular climates, and 
probably, with a fair degree of accuracy, to all except the extreme Continental 
type. 

The results show that, even in so short a period as 15 years, the average 
annual rain-fall is unlikely to differ materially from the average values for a long 
period, such as 40 to 50 years. It must also be noted that such short period 
averages are more likely to be less than the long period average of rain-fall, 
than in excess of it. 

Binnie’s figures also indicate that the average deviation may slightly increase 
if the period exceeds 35 years ; the figures being : 

For 40 years 2T6 per cent. 

„ 45 years 2-03 „ 

„ 50 years 1*98 „ 

Rain-fall records extending for periods much above 50 years are somewhat 
rare and statements regarding the rain-fall values over such periods are 
consequently liable to error. It is nevertheless true that there is apparently a 
cycle in rain-fall, and that this cycle appears to have a period approximately 
equal to 36 years. 

In my opinion, the actual facts do not permit more than this to be stated, 
and the cycle is one which refers not to individual rain-falls, but to the average 
of 3 or 4 consecutive years. 

12 







































CONTROL OF WATER 


178 

We consequently define the mean annual rain-fall of a locality as : The 
average taken over a sufficiently lengthy term of years to ensure a fairly 
constant value, and may assume that 30 to 40 years are generally an adequate 
period. 

It is also evident that if we have a rain-fall record of say 10 to 20 years, 
which displays a fairly close relationship for this period with the rain-fall at a 
neighbouring place, where a long period record exists, it is only a matter of 
simple proportion to arrive at a fairly accurate value of the long period rain¬ 
fall for the first locality. In practice, in the case of places fairly close together, 
and separated by no very marked natural features, such as a range of hills, or a 
river, this proportional relationship holds with sufficient accuracy to justify its 
use in supplementing actual records. 

If the yearly rain-falls of localities distributed all over the globe are 
studied with respect to their absolute magnitudes, no rule is disclosed. If, 
however, we reduce this maze of figures to percentages of the mean annual 
rain-fall, for each locality, a very striking regularity will be found in nearly every 
case. 

These rules were first systematised by Binnie, in a paper on “ The Variation 
of Rain-fall” ( P.J.C.E ., vol. 109). 

I have taken the figures for some 80 long period records of places in Great 
Britain, selected by Mill, ( P.I.CE ., vol. 155) which may therefore be 
regarded as extremely accurate, and find that the rain-fall of the wettest of a 
long series of years is about 146 per cent, of the mean : 

The maximum value of this figure being about 170. 

The minimum value of this figure being about 125. 

.1 , 

The rain-fall of the driest year is about 66 per cent, of the mean : 

The maximum value being about 80 per cent. 

The minimum value about 55 per cent. 

Similar figures for the average rain-fall of the 2 consecutive driest years are : 

75 per cent. 86 per cent. and 60 per cent. 

and for that of the 3 consecutive driest years : 

80 per cent. 87 per cent. and 64 per cent. 

I have been unable to trace any relation between the variation of these 
ratios for British stations, and the absolute value of the mean annual rain¬ 
fall. 

46 per cent, of the years have a rain-fall above the average, and the average 
fall of these years is 119 per cent, of the mean fall ; while the remaining 54 per 
cent, have a fall below the average, and their average fall is 83 per cent, of the 
mean fall. 

Also periods of 4, 5, 6, and even 9 years in succession, may have falls less 
than the average, and the average annual fall of such a period of dry years is 
about 82 per cent, of the mean. 

Binnie’s selection of records, as given in Table VII. of the above paper, was 
obtained at localities distributed all over the globe, and the ratios are as 
follows. Taking the mean annual rain-fall as above defined, as 100, the value 
of the rain-fall in other years, on the average, is given by : 


RAIN-FALL RATIOS 


179 


Locality. 

Number of Stations. 

Wettest Year. 

Average of Two Consecutive Wet- ! 
test Years. 

Average for Three Consecutive 
Years. 

Average of Three Consecutive Driest 
Years. 

Average of Two Consecutive Driest 
Years. 

_ 

Driest Year. 

.___ 

Maximum Number of Consecutive 

Years with a Fall above the Mean. 

Average Fall of these \ears. 

---1 

Maximum Number of Consecutive 

Years with a Fall less than Mean. 

Average Fall of these Years. 

British Isles 

44 

T 45 

13° 

123 

78 

73 

66 

5-52 

117 

5'57 

84 

N. W. Europe . 

5 

148 

133 

126 

75 

66 

61 

3-80 

123 

5 ‘ 4 o 

83 

France . 

2 3 

I 161 

142 

I 3 1 

74 

68 

59 

5*22 

122 

5‘43 

81 

Italy 

15 

T 59 

139 

129 

76 

70 

55 

4*26 

121 

5-60 

83 

N. Germany . 

17 

139 

127 

121 

77 

70 

61 

5'53 

114 

5*59 

82 

S. Germany and 












Austria 

9 

144 

133 

127 

76 

68 

5 6 

6* 11 

120 

5*55 

81 

Russia 

12 

166 

146 

135 

68 

6 3 

53 

5 ’ 4 2 

122 

7-66 

78 

India 

9 

162 

142 

130 

72 

66 

52 

4‘77 

123 

5*33 

78 

Canada and 
Eastern Uni- 












ted States . 

10 

141 

!3* 

125 

79 

75 

1 

68 

5‘7o 

119 

6*90 

85 


Binnie also classes his stations by the absolute value of the mean rain-fall. 
The figures fall into two very sharply defined groups, over 20 inches and under 
20 inches mean rain-fall. The values are as follows : 


Over 20 inches . 

140 

149 

132 

126 

76 

70 

61 

5 *ii 

119 

5'73 

82 

Under 20 inches 

!3 

*75 

149 

i 37 

67 

62 

5 i 

5-62 

129 

7'38 

76 


The figures for the individual localities contained in the above table are 
remarkably concordant, and Binnie considered that the only exceptions likely 
to occur were those disclosed by the figures concerning rain-falls of less than 
20 inches. A study of the information at present available leads me to extend 
and slightly alter Binnie’s deductions. The variations of the individual annual 
rain-falls from the mean rain-fall are of the order of magnitude indicated by 
Binnie’s figures in the case of Insular climates only. For typically Insular 
climates, the figures given for the British Isles and N.W. Europe may be taken 
as very close to the truth for all portions of the globe. For Continental climates, 
however, the variations are larger, and the ascending scale shown, in the above 
table, by the graduation through Italy, France, India, and Russia, admirably 
illustrates the general law. Also, the greater the absolute magnitude of the 
rain-fall, the smaller is the variation (when expressed as a percentage of the 
mean annual rain-fall); and vice versa , the smaller the absolute magnitude of 
the rain-fall, the greater the percentage variations. It will be seen that I have 
been led to attribute more influence to the character of the climate than to the 





















































































i8o 


CONTROL OF WATER 


absolute value of the rain-fall. As an example, the following figures hold for 
the rain-falls of the years 1879-1908, at Amritsar (Punjab), which possesess a 
typically Continental climate, and a mean rain-fall of 25*26 inches. 

Wettest year—309 per cent, of the mean. 

Average of two consecutive wettest years—237 „ „ 

Ditto, of three consecutive years—214 „ „ 

Average of three consecutive driest years—52 „ „ 

Average of two consecutive driest years—48 „ „ 

Driest year—34 „ „ 

Maximum number of consecutive years with a fall above the mean—5 
Average fall of these years—170 per cent, of the mean. 

Maximum number of consecutive years with a fall less than mean—5. 
Average fall of these years—54 per cent, of the mean. 

Similar cases exist in India, where the average fall is even greater than 
at Amritsar, and several stations in Siberia and China show even larger 
variations. 

Even if we confine ourselves to Insular climates, the figures given by 
Grunsky {Trans. Am. Soc. of C.E. , vol. 61, p. 498) for the rain-fall at and near 
San Francisco are : 

Maximum annual rain-fall = twice the mean. 

Minimum annual rain-fall = one-third to two-fifths of the mean 
annual rain-fall. 

The probable explanation of these abnormalities is to be found in a considera¬ 
tion of the geographical distribution of rain-fall. Amritsar and San Francisco 
both lie between zones of comparatively heavier rain-fall (Orissa with 59 inches, 
and Oregon with 80 inches), and zones of far lighter rain-fall (the N.W. 
Frontier with 8 to 10 inches, and part of Southern California with 3 to 5 inches). 
While these zones are explained by the topographical features of the country, 
a study of large scale rain-fall maps shows in each case that a comparatively 
slight deflection of the rain-bearing currents would produce a considerable 
’ alteration in the absolute fall. 

We may therefore consider Binnie’s rules as generally applicable, but it 
will be wise to await further studies before accepting them as universally true. 
Exceptions are most likely to occur where the locality under consideration 
possesses a dry Continental climate, or lies geographically between regions of 
markedly lower and higher absolute rain-fall (see also p. 248). 

When mathematically regarded, the above facts are conclusive evidence 
that a yearly rain-fall sequence is not a matter of chance, in the sense that 
roulette or dice sequences are. In a series of rain-fall observations, negative 
variations are more frequent than positive, and negative variations {t.e. dry 
years) succeed each other more frequently than they should, if chance ruled 
the succession of wet and dry years. 

Space Variability of Rainfall. —Having discussed the variation of mean 
annual rain-fall in time, it is also necessary to consider its variation in space. 
We have already stated that the rain-falls of two localities, close to each other, 
and not separated by any marked natural feature, will probably, in any year or 
series of years, depart from their mean values in much the same proportion. 
But, it by no means follows that their mean values are likely to be the same. 


LOCATION OF RAIN-GAUGES 


181 


As a matter of experience, in the British Isles, water-works’ engineers prefer to 
have one rain-gauge to about every 1000 acres of gathering ground ; but it 
must be remembered that the rain-fall of the British Isles (and more especially 
that of England), varies from place to place far more rapidly, and more 
patchily, than is the case in countries possessing topographical features on a 
larger scale. The usual British gathering ground being a deep and frequently 
a winding valley, surrounded by high hills, possesses precisely the character of 
surroundings and relative elevation required to accentuate the space variation 
in rain-fall. 

Thus, in countries having large natural features, a wider spacing of rain- 
gauges is doubtless permissible, but, so far as I am aware, no watersheds 
except those of Great Britain have, in my opinion, been adequately provided 
with rain-gauges, the possible exceptions being certain cases in Prussia and 
Saxony. 

The problem of the selection of rain-gauge stations over an area, so as to 
arrive at a distribution which will approximately represent the average rain-fall 
over this area, cannot be reduced to general rules. If any records already 
exist, either in or just outside the area considered, valuable indications can 
be obtained by plotting these stations on a map, and drawing “contour” lines of 
equal rain-fall (iso-hyetal lines) across the map. As a rule, these lines will be 
found to be connected with the natural features of the country, and on a large 
scale map they are frequently almost undistinguishable from contour lines of 
equal elevation above sea level. On a small scale map this relationship is not 
so marked, but it is. frequently found to be of assistance in plotting the 
approximate iso-hyetals. 

The iso-hyetals being plotted, it will often be found that irregularities, or 
indications of irregularities, are disclosed, and these will naturally suggest sites 
for observation stations. 

In a range of hills, the rain-fall generally increases as we proceed towards 
the crest, but a small area of maximum rain-fall almost invariably exists, not at 
the exact crest, but a little below it, and to the leeward of the crest in relation 
to the prevailing rain-bringing wind. 

In plains, variation in rain-fall from place to place is generally accidental, 
due to summer thunder-storms of small extent in respect to area, which not 
only produce short but heavy and very local falls of rain over comparatively 
small areas, but tend to follow the track of the first storm of the hot season 
throughout each summer. This seasonal tendency should not be confused 
with the general habit of thunder-storms (whether covering a small area and 
following a sharply defined track, or covering a large and not well defined area) 
in an undulating country of following, year after year, some natural feature, 
since this will be more or less clearly disclosed in the mean summer rain-fall 
records. 

In a hill and valley country, it will usually be found that the floors of 
narrow valleys have approximately the same rain-fall as the adjacent hills, the 
difference, if appreciable, inclining towards a decrease in fall. 

Apart from this exception, and the one mentioned in the first rule, there 
is a general and undoubted tendency for the rain-fall to increase with the 
altitude, but such rules as have been proposed seem only to be applicable to 
limited areas. 

The above statements plainly indicate that, unless special precautions are 


182 


CONTROL OF WATER 


taken, the public will (as a rule) establish rain-gauges mostly in the relatively 
dry portion of any area, however small. Thus, the engineer should always 
supplement existing gauges by stations planned on a systematic basis. This 
usually entails the establishment of new stations in comparatively inaccessible 
positions, but gauges adapted to hold a month’s heavy rain-fall, such as are 
now procurable, do not throw much labour on the observing staff, and if 
read regularly every month, give sufficiently reliable information for such 
supplementary purposes. 

Having thus disposed of the result of the natural topography of the country, 
it becomes necessary to inquire what effect small irregularities, or artificial 
features, may have on the records of a rain-gauge. Here, a very general and 
comprehensive rule can be given. Anything likely to produce eddies in the 

wind near a gauge is liable to cause 
erroneous and deficient records, and 
the fewer the eddies, the more accurate 
the records will be. 

Thus, the neighbourhood of a 
steeple, a tall tree, or a high em¬ 
bankment, is to be avoided; and 
shrubs, trees, etc. should be removed 
at least their own height from the 
gauge. Also, a gauge should not be 
set on a roof, unless the roof is so 
large that the eddies produced by 
its edges have died out before they 
reach the gauge. 

It is as well to place gauges 
situated on steep hillsides in the 
centre of a small, level platform, of 
say 6 feet radius, and to surround the 
gauge by a wall about 2 feet high, 
and 3 feet distant from the gauge. 

For very accurate work, a Nipher 
shield (which consists of a large wire 
gauze funnel, 3 feet in diameter, with 
its rim at the level of the rim of the 
gauge) gives very good results. 

I append Dr. Mill’s drawing of a 
standard Snowdon gauge (Sketch No. 
45). It will be noticed that he specifies the rim of the collecting funnel as 1 foot 
above the ground ; but where, owing to local conditions, this elevation is 
impracticable, it should be remembered that every extra foot of elevation up 
to 9 feet, produces, roughly, 1 per cent, decrease in the rain-fall recorded. 

Accuracy of Rain-fall Records. —Excluding carelessness in booking, 
or measuring, which I consider to be more frequent than is believed, the 
principal sources of error in a Snowdon gauge are those due to snow being 
blown out of, or into the gauge. A valuable check may be made by measuring 
the depth of snow in sheltered places, and reckoning 12 inches of snow as equal 
to 1 inch of rain. 

A special warning is necessary against Glaisher gauges. These, when out 


Knife Edged 



Sketch No. 45.—Standard English 
Rain-gauge. 





































WATER YEAR 


183 

of order, are liable to collect more rain than has fallen, which is the very last 
thing an engineer wishes. It may also be noted that the “tube gauge,” so 
common in India, will usually collect more than the actual fall, even when 
in order. There are forms of rain-gauges which, when out of order, collect less 
than the true fall, and are therefore not so dangerous. 

Everything considered, it is believed that a good rain-fall record is liable to 
at least 2 per cent, of error ; and it is probable that the average record errs 
from 4, to 6 per cent., some of which could be adjusted if the whole local 
conditions of the gauge were known. 

Water Year. —As a matter of custom, rain-fall records are usually pre¬ 
pared, tabulated, and published, according to calendar years. From an 
engineer’s point of view this is somewhat awkward, since the water year, or 
period of time during which the total run-off is most closely related to the total 
rain-fall rarely, if ever, coincides with the calendar year. 

It is usual to assume that the water year should begin when stream flow 
is at its minimum, and should end at a similar period next year. 

The minima of stream flows do not succeed each other at rigid intervals 
of 12 months, far less 365 days ; but over a long period of years, it will be 
apparent that a month can be selected during which the minimum, or nearly 
the minimum, generally occurs. If the rain-fall and run-off are tabulated by 
years, starting with this month, or the next succeeding one, it will be found that 
the connection between these quantities is more regular than when they are 
tabulated by calendar years. 

Such a month is easily selected in any given, place, as for example : 

In the British Isles, and the Northern United States, it is September to 
October. In Northern India, it is May. 

The above statement as to the beginning of the water year may at first 
sight appear erroneous. I am of the opinion that if the period at which the 
water stored up in the ground (see p. 188) is at a maximum could be definitely 
observed, the relations of rain-fall and run-off for the intervals between these 
maxima would be more constant than for any other period. The difficulty 
lies in the fact that these maxima are, so far as present information exists, 
somewhat more irregular in time than the minima of stream flows, and are 
less easily observed. The error introduced by the selection of a date, say a 
month distant from the actual moment of the maximum ground water storage, 
is considerably greater than that caused by a month’s error in the date of 
minimum stream flow. Consequently, while agreeingthat the date of maximum 
storage of ground water has theoretical advantages, I believe that the time of 
minima stream flow is practically more useful as a dividing line for the rain-fall 
and run-off years. 

Variation of the Rain-fall over the Year. — So far we have 
regarded the year (whether calendar, or water year), as our unit of time. 
From a practical engineering point of view, this is too long a period, as when 
water supplies fail it is but little consolation to discover that the total volume 
flowing during the year would have sufficed if it had been equally distributed. 
We are thus face to face with the fact that however variable the annual fall may 
be, that of periods of less than a year is even more so. 

Many studies have been made, and in a given locality it is possible to state 
that a certain period of the year is usually the wettest, or the driest, as the 
case may be ; but in each individual twelve months the variations are such 


CONTROL OF WATER 


184 

that, with very few exceptions, the statements are useless for practical purposes. 
For an engineer’s requirements therefore, the best that can be done is to split up 
the year into periods during which the relations between rain-fall and run-off 
are markedly different. 

The calendar month is usually employed for purposes of convenience, but it 
is far too short for practical use. In the British Isles a satisfactory division is 
as follows : 

In the winter months (roughly December to April) a very large proportion 
of the rain-fall appears as run-off, while in the summer months (roughly May to 
November) the proportion appearing as run-off is but small. In the Northern 
United States, where the climatic differences are more marked, the following- 
threefold division has been used with advantage : 

Storage period, (roughly December to May). 

Period of vegetation growth, (roughly June to August). 

Replenishing period, (roughly September to November). 

In climates such as that of the Punjab, we have : The winter dry season 
(approximately October to May), when very little rain falls, and when that 
which does occur is practically without influence on the run-off. In the monsoon 
or rainy season (approximately June to September), almost the whole of the 
year’s fall occurs, and the year’s run-off depends entirely upon this monsoon 
fall. 

A similar division, varying only in regard to the months, holds in nearly all 
tropical climates, although in some cases, (for example, Ceylon, and S.W. India) 
there are two wet, and two relatively dry seasons in each year. 

These divisions cannot, however, be considered as more than approximate. 

The exact line of demarcation will be found (if the records are of sufficient 
length) to oscillate from year to year over a period of as much as three months, 
and it is a matter of common knowledge that “The weather of each year is 
abnormal in some respect.” Thus, it may be inferred that at least every fourth 
or fifth year must be abnormal as regards its rain-fall. 

Connection between Rain-fall and Run-off. —The nature of the 
relation between the rain-fall on a catchment area, and the discharge of the 
stream draining that area, is best realised by a general consideration of the 
manner in which the water which is produced by the rain-fall is disposed of. 

When rain falls on a land surface it first wets the upper soil, and it is only 
after this has become to some extent saturated that water appears in a visible 
form on the land surface. This visible water collects in small trickles, and 
runnels, and flows towards the stream channels ; but as it flows, a certain 
portion of it soaks into the ground. Thus, from the very start, we have a two¬ 
fold division of the rain,—that absorbed by the earth, and that which proceeds 
direct to the stream, without being absorbed. 

The fate of the absorbed water now requires consideration. A certain 
portion is consumed by vegetation, and a further amount is evaporated from the 
damp surface of the soil by the air ; the remainder slowly soaks into permeable 
beds underlying the surface, and is finally removed from the influence of 
vegetation or surface evaporation. 

The ultimate fate of this last portion depends on the geological structure ot 
the catchment area. As a rule, we may assume that it finally leaks away to 
the stream draining the area, although the existence of such phenomena as 


DISPOSAL OF RAIN-FALL 


185 

artesian wells is sufficient to show that exceptions occur, and that in some cases 
this ground, or subsoil water, never again comes to the surface, but escapes by 
underground passages (not necessarily larger than pores in the rock, gravel, or 
sand beds) to the sea, or possibly into the interior of the earth. 

We therefore see that the rain is finally disposed of in one or other of four 
forms : 

1 1 

(i) Utilised by vegetation. 

(ii) Evaporated from the surface of the catchment area, either from the 

earth, or from bodies of water included in the area. 

(iii) Appears in a time, measured by days at the most, as stream flow. 

(iv) Soaks into the ground, and either appears : 

(a) In a time that may be measured by months, or even years, as 

stream flow, or : 

(b) Seeps away through underground channels. 

The run-off is plainly the sum of (iii), and (iv), and in the normal catchment 
area (iv) ( b ), does not exist, so that considered over a sufficiently long period 
the rain-fall loss is the sum of (i), and (ii), only. But, over a short space of time 
the rain-fall loss is influenced either positively, or negatively, by (iv) ( a ). The 
effect of (iv) (a), may be compared to that of an invisible reservoir which at 
certain seasons temporarily increases, and at others diminishes the stream 
flow. 

Let us now consider each of these factors, and express the volumes of water 
which are thus disposed of, in inches depth over the catchment area : 

(i) The quantity of water consumed by certain species of vegetation is 
detailed on page 234, and these figures may be assumed to include the evapora¬ 
tion from earth surfaces which are sufficiently damp to cause such vegetation to 
flourish. We can therefore assume that, on the average, during any division 
of the year (the term division being used in default of anything better to express 
a period during which the demands of the vegetation do not vary sufficiently to 
prevent an average value from representing its effect with practical accuracy), 
the rain-fall loss under this head as approximately represented by a term such 
as a' p . 

(ii) The effect of surface evaporation is partly included in a term similar to 
the above quantity a' p . It is evident that the greater the rain-fall, the damper 
the earth becomes, and the more numerous will be the puddles and other 
shallow bodies of water exposed to evaporation. The loss by evaporation 
during a given division of the year is consequently represented by a term of 
the form a" p -\-b" p Xp ; where x p represents the rain-fall during the period 
considered. 

Thus, the first two causes combined may be regarded as producing a loss 
represented by a p -\-bpX p . Now, both a , and b, depend on the temperature, the 
amount of sunshine, the manner in which the rain-fall occurs, (i.e. in short storms 
or long drizzles, etc.), the movement of the air, etc., in fact, upon all the meteoro¬ 
logical circumstances united. On the average, it may be said that a, and b> 
are mainly dependent on the mean temperature during the division of the 
year under consideration. Bearing in mind that while growing vegetation 
to a certain extent stores up water in its tissues, it disposes of at least 
90 per cent, of the liquid by evaporation from its leaves, it may be safely 
assumed that a, and b, are dependent on the temperature in a manner 


i86 


CONTROL OF WATER 


approximately similar to that in which the vapour pressure of watei is affected 
by the temperature. 

Now, the relation between the temperature and the vapour pressure of 
water, is not even approximately a linear one. An examination of the curve 
expressing the connection as plotted in Sketch No. 46 shows that <%>, and b p , 
can only be considered as even approximately proportional to the duration of 
the period if the division of the year denoted by the suffix /, is so selected 
that the temperature of the water which wets the surface soil and is utilised 
by plants never differs materially from the mean temperature of the whole 
period during any portion of the interval denoted by p. 

For the sake of brevity I propose to term the total loss produced by 



Sketch No. 46.— Relation between the Temperature and the Vapour 

Pressure of Water. 


vegetation and evaporation the Vegetation Loss, and to denote it by V,,. We 
are justified in assuming that: 

Vp == cip d" b p x p 

if the weather during this division of the year is such that the mean tempera¬ 
ture can be regarded as in close connection with the probable total evaporation 
during the period. If this is not the case : 

V p — d p + b,jX q + b r x r +etc. 

where the suffixes q, r, etc., refer to less lengthy divisions of the year during 
which the momentary temperature varies but little from the mean temperature 
of each sub-period. 

(iii) The quantity of water that flows directly to the river or stream draining 


















GROUND STORAGE 


187 


the catchment area can, for conciseness, be called the topographical flow, and 
is denoted by t p . 


(iv) The quantity that soaks into the strata underlying the catchment area, 
and is there temporarily stored up in the form of ground water, can be called 
the Stored Rain, and is denoted by s p . 

Thus, we have : 


x p — a p -f- b p x p T t p -f- s p 

01 : Rainfall = Vegetation loss + Topographic flow + Rain stored in the 
ground. (See Sketch No. 47.) 


Case /. 



Sketch No. 47. —Diagram showing Relations between Rain-fall, Ground 

Storage, and Run-off. 

The two diagrams are drawn so as to represent the disposal of 2’5 inches of rain 
and the simultaneous production of a run-off of 1 inch. 

In Case I.—V = o’7 inch ; j=i*4 inch ; and/ = o’4 inch. 

Thus, g= 1 inch, and the water stored up in the ground is increased by 0^4 inch. 

In Case II.—V = I'25 inch; s = 0 ' 7 $ inch; t = 0*5 inch. 

Thus, g=o'9 inch, and the water stored up in the ground is depleted by 0-15 inch. 

• 

The run-off is plainly composed of the two following portions : 

(a) The topographic flow t p , and, 

(b) A contribution from the water stored up in the ground, which we shall 
term the ground water flow, and denote by^,. 

Thus,^ = t p +g P) and the connection between^, and s p , is not very evident, 








































i88 


CONTROL OF WATER 


for s p , is the quantity of water supplied to the invisible reservoir formed by the 
permeable strata ; and g Vi is the leakage from this reservoir into the stream 
channels. 

Now, g p is usually not equal to s p , and all we can definitely state is that if R, 
represent the total quantity of water stored in the permeable strata, then : 

AR P = Sp gp 

where AR J3 , represents the positive increment of R, during the period and 
AR ?) may be a negative quantity. 

Thus, jp = tp+gp = Xp — {a p + bpXp) — s p +g p 

= x p — (a p + bpXp) — ARp 

Or : Run-off = Rain-fall —Vegetation loss—Increment of ground storage. 

And z p = ap + bpXp +AR„=Vp+ARp 

The form deserves careful notice. The a* s, and b’s, are dependent upon the 
quality of the vegetation, and on the meteorological characteristics of the 
period, i.e. on the climate in its most general sense. But ARp, is influenced 
by the volume of the permeable strata forming the invisible ground water 
reservoir, and by the quantity of water stored up in them. Thus, while a , and 
bx , depend upon the climatic circumstances of the period under considera¬ 
tion, ARp, is almost exclusively dependent on the geological structure of the 
catchment area, and upon the rain stored up during all preceding periods of 
time ; the effect of each preceding period diminishing as we work backwards 
from the division or season of the year to which the equation refers. 

Now, ARp, being the increment of the volume of the water stored up in 
the ground, is plainly equal to the ratio of the area of permeable strata to that of 
the whole catchment area multiplied by the average rise or fall of the ground 
water level over this permeable area, multiplied by the percentage of void spaces 
in the permeable strata. As a matter of observation, the ground water level 
oscillates up and down during the year, performing cyclical variations about 
its mean level, and is found year after year to follow a fairly definite seasonal 
course. Thus, we may say that AR, approximately vanishes, or that the 
increment of water stored up during any water year is either nothing, or is 
comparatively speaking small. 

Thus, over a year, y—x— (a+bx), and still more accurately, if we consider 
a long term of years, it will be found that,=.*■„* — b in Xm). 

The assumption is best illustrated by examples. In an area which is 
underlain by granite, or other compact rocks, the maximum variation of R, 
when taken between the highest and lowest values of the year, rarely attains 
I inch, as is illustrated by the Nagpur catchment area (see p. 246). 

In a chalk, or sandy area, the maximum variation of R, during any year 
may amount to as much as 6, or 7 inches ; and in some cases R, has been 
observed to increase as much as 20 inches in a period of five years. The 
value of AR, i.e. the total change in R, during a year, is of course less than 
these values, and abnormal years apart, is not more than one-third of the 
maximum variation. 

The matter is of importance. In England we are fairly well aware that 
over a period of three dry years z m is approximately equal to 14, or 15 inches 
in impermeable areas. But values as high as 20 or 21 inches have been 
, observed during a period of three years in permeable areas, for which z m , 


GROUND STORAGE 


189 

taken over a long period, does not greatly exceed 17 or 18 inches. We may 
therefore consider that in these cases a quantity of water equivalent to 
9 or 12 inches is temporarily stored up ; so that the value of AR, for each year 
is about 3 or 4 inches. 

In certain chalk districts, a series of 6 or 7 dry years appears to produce a 
depletion of R, equivalent to 18 or 20 inches at least, and this is probably re¬ 
plenished during the following period of wet years. 

It is therefore plain that, so far as eliminating the influence of AR ; >, is 
concerned, accuracy is best attained by considering as lengthy periods as 
possible. But since a p , and b Py are both influenced by the temperature (and 
other meteorological quantities), the longer the periods considered as units, 
the less accurate their estimation becomes. As a p , and b p , are not linear 
functions of the temperature, it is impossible to express them over a long 
period even as functions of the mean temperature. 

The correct selection of the unit period therefore becomes a difficult matter. 

For general studies a year possesses certain advantages, since, (except the 
year be either abnormally dry, or wet) we may assume that the ground water 
storage is approximately the same at the same periods of successive years 
Thus, over a year, and more especially over a water year, we find that : 

y=x—a — bx, or, z—a-\-bx 

This equation holds very fairly well in practice, although in climates 
where a well marked cold season (winter), and a well marked hot season 
(summer) exist, greater accuracy can be assumed by using the equation : 

y — x ■ ci b $x g ■ b )i 'X k > 

where x s , is the summer, and x w , the winter rain-fall. 

The possibilities of error in the above equations are obvious. The assump¬ 
tion is that the sum of at least a dozen terms, of the form 

^.rj + ^a + etc. + ^^j may be replaced by a single term bx, 
where x=x l +x 2 + etc. . . .+.Ti 2 , 
or by two, b s x s -\-b lv x lv , 
where ^s+^w-Jx + etc.+.r 12 , 

where the b 1 s, are independent of the relative magnitudes of x l and x 2y etc., and 
this is obviously inaccurate. All that can really be said is that at least twelve 
years’ careful observations would be required to obtain the constants used in the 
theoretically more exact form. Preliminary studies of such magnitude are 
impossible. As will be shown later (see p. 232), when the catchment area 
contains a reservoir of a size adequate to equalise the run-off during the drier 
years, the assumptions are sufficiently accurate for practical purposes. 

The assumption regarding' AR, cannot be regarded as more than a first 
approximation. The ground water reservoir is apparently (in an average 
case) capable of temporarily storing up a quantity of water equivalent to as 
much as 5, or 6 inches (reckoned over the whole catchment area), and after¬ 
wards delivering it to the stream. Even if the water year is taken as the unit 
period, it appears that after a wet year at least one-third of this volume may 
be retained in the ground, and passed on to the succeeding year. In a dry 
year, an extra depletion of about one-quarter may occur, which has to be 
made up in the following year. Thus, from this cause alone, differences of 1, 
or even 2 inches may arise in the yearly run-off. 1 hese, in the case of a 


190 


CONTROL OF WATER 


catchment area of small mean run-off, but of large invisible storage, may amount 
to as much as 6, or 8 per cent, of the annual run-off On the average, however, 
the effect is not so great, but an error of 5, or 10 per cent, is quite possible, and 
may be expected after abnormally dry, or wet years. This error may be increased 
to 10, or 15 per cent, if there are two abnormally dry or wet years in succession. 

For studies of individual catchment areas, which do not contain reservoirs 
for water storage, we would naturally consider the day as a unit. This is 
impossible, and the calendar month is the smallest period for which any 
practical rules can be given. It will be plain that a calendar month is an 
artificial division, and that it does not accurately define the climate of the 
period. Thus, better results may be expected if a reservoir exists in the 
catchment area which is large enough to permit a consideration of seasonal 
periods only (such as are mentioned on p. 184). 

On page 218 I give Vermeule’s investigation. This method requires a 
very large amount of preliminary study before it can be practically applied. 
The following method obviously departs considerably from the truth, but it 
utilises observations which can generally be completed before the final designs 
are made. I therefore put it forward, not as a complete solution, but as the best 
that can be obtained under ordinary practical circumstances. 

We assume the following quantities, relating to the catchment area 
considered, as known : 

(i) The rain-fall loss for one year at least, and that this has been corrected 
for the nett ground water storage, or depletion during the year, by observations 
on the ground water level, taken at as many points as are possible. This 
we call z. Put z p =x p -~jy p , for each division (month, or season) of the year. 

(ii) A series of observations on evaporation from a free water surface such 
as are made at most large meteorological stations, for as many years as 
practicable, at a locality under as nearly as possible the same climatic condi¬ 
tions as those of the catchment area. Let the sum of these for the year under 
consideration be denoted by e. 

• z 

Take the ratio : /£=-. Then, I assume that the term \ p ~a p -\- bpX Pi for 

any period can be represented by ke p , where e v , is the total free water surface 
evaporation for that period. Thus, for every division of the year for which 
observations are taken, we can find : 

fp ~ kCp Z p 

where plainly f p , represents a nett flow of water from the ground, if ke p , be 
greater than z p , and a nett storage of water in the ground if ke p , be less than z p , 
and if my assumption be true : 

fp— ~AR p —g p —s v 

Thus,^, depends on the geological structure of the catchment area, rather than 
on the climate. 

For the same period of any other year, we have X P , the observed rain-fall, 
and E P , the observed free water surface evaporation, and we assume that Y ;) , 
the run-off, is given by : 

Y p = X p — k E ;) + f p 

where f p , is the value obtained for the same period of the year during which the 
run-off was observed. 

The method is subject to one obvious error. While A p , and B p , the values of a p , 


E VAPOR A TION 


191 

and b p , for the fractional period of the year now considered are probably propor¬ 
tional to E J; , we may be fairly certain that if X p , differs to a marked extent from x p , 

Ap+BpXp, will differ somewhat from 

£E p , which is probably fairly close to A p + BpX p 

This is the more likely because, while rain-fall does not in itself have much 
apparent influence upon evaporation, heavy falls are usually attended by cloudy 
weather, and the diminution of sunshine thus produced will decrease evaporation, 
while the term + is probably increased. (See Sketch No. 48.) 

The method is useful for the preliminary elucidation of the various factors 



Sketch No. 48.—Relation between the Mean Monthly Temperature, and the 
Evaporation from a Free Water Surface. 


concerned, and it may be said that it allows (with a very fair degree of 
accuracy) for : 

(i) The vegetation loss ; 

(ii) The influence of variations in the mean temperature of the divisions 

of successive years ; 

(iii) Ground water storage ; 

(iv) The duration of the rain-fall; 

but is liable to error if the absolute magnitude of the rain-fall varies greatly 
from that of the year of observation. Nevertheless, it tends to over-estimate 
the loss when the rain-fall is smaller than in the year of the original observations ; 
and to under-estimate the loss when it is greater. Consequently, the lesults 
thus obtained usually possess a certain margin of safety, which is advantageous 
for practical purposes. 

























i 9 2 CONTROL OF WATER 

The right half of Sketch No. 49 shows this method in a graphical form, as 
applied by Penck (Untersuchungen iiber Niederschlag und Abfluss ) to the catch¬ 
ment area of the Moldau. The emission of water in the spiing of the year to 
reinforce the stream flow, and its storage in the late summer and autumn, are 
characteristic of a large, and fairly flat catchment area, with a tolerably severe 
winter. In the case of a more Insular climate, such as that of the Thames, the 

figures obtained for the average of 9 years are : 

Storages, or negative values of f of 0*34 in September; 174 in October; 
r88 in November; ric in December; 1*04 in January; 0*17 in February ; 
o’12 in March, and : 

Emissions, or positive values of f of o’8o in April; ri 5 in May ; 2 13 in 
June ; 1*41 in July ; and 0-90 in August, 
giving a yearly variation in the ground storage of nearly 6*4 inches, which, in 
view of the large amount of permeable chalk in the I hames valley, is not 
surprising. The alteration in season, as compared with the Elbe, appears to 
occur in all markedly permeable catchment areas. If this method accurately 


- Monthly Rainfall' Losses at Redrmres in1905. 

——- Monthly Evaporati ons at Reevesby in1905. 
f||§f Storage. Emission. 


- Average Monthly Rainfall Losses in Moldau Drainage, y 

- Average Reduced Evaporation at Prague, k e. 

- Average Total Available Stored Ground Mater. R. 



Sketch No. 49.—Relation between Monthly Rain-fall Losses and Reduced 

Monthly Evaporations. 


represents the facts, some small and steep catchment areas have two storage and 
two emission periods during a year. (See left-hand side of Sketch No. 49.) 

The following table shows what I believe most closely represents the average 
values of ke p , given as percentages of an observed z, for English catchment 
areas, and probably also for any British catchment area, 

January 1 ; February 2 ; March 5 ; April 10 ; May 14 ; June 17 ; July 19 ; 
August 15; September 9 ; October 5 ; November 2 ; December 1. 

As an example, let the observed values for the whole year be : 
z — 18 inches, and for the month of May z s = 173 inches, and for October 
z 10 = 2-41 inches. 

Thus, during the month of May we have : 

/ 5 * — AR 6 = 18x0-14—1-73 = o*79 inch 
or the ground reservoir contributes 0-79 inch to the observed run-off. For 
October on the other hand : 

f l0 = — AR 10 = 18x0-05—2-41 = —1-51 inches 


or 1*51 inches 





































































RAIN-FALL LOSS AND MEAN TEMPERATURE 193 

are stored up in the ground, and the run-off during the month of October is 
diminished by that amount. 




Elbe. 



Moldau. 

1 

1 

X 

V 

r 

AJ 

ke p 

/ 

X 

y 

z 

kep 

/ 

February. 

1*24 

o-68 

076 

o’6o 

+ 0*04 

1*16 

0*64 

°"5 2 

o"6o 

4-o"o8 

March . 

176 

1-32 

o*44 

1*12 

+ o*68 

r68 

1*12 

0*56 

1 * 12 

+ 0*56 

April . . 

r88 

1*00 

o-88 

1*84 

4 -o ’96 

1*84 

o"8o 

1'04 

1 "84 

4-o"8o 

May . . 

2*52 

o*68 

1*84 

276 

+ 0*92 

2*48 

0*64 

1*84 

2*80 

+ o - 96 

June . . 

3’48 

0*52 

2 '96 

3' 16 

+ 0*20 

3-60 

°*5 2 

3’°8 

3‘ 20 

+ O’ 12 

July . . 

3'6o 

0*40 

3-20 

3‘ 2 ° 

O’O 

3*48 

0-36 

3’ 12 

3‘ 2 4 

+ 0"I2 

August . 

336 

°*44 

2*92 

2*84 

— o'o8 

3’44 

0-44 

3’°° 

2*88 

- O’ I 2 

Septem. . 

2"8o 

0*48 

2*32 

i *8o 

-0*52 

2*84 

o"6o 

2*24 

1’80 

-o*44 

October . 

2"l6 

0*48 

i-68 

1*04 

- 0*64 

2'08 

0*48 

1 '60 

1 "04 

-0*56 

Novem. . 

176 

0*48 

1*28 

0*64 

— 0*64 

172 

0-44 

I"28 

0^64 

- o"64 

Decem. . 

i*8o 

0^64 

1 *16 

0*48 

-o-68 

172 

! 0*52 

1*20 

0*48 

- 0-72 

January . 

1-32 

0*56 

076 

°' 5 2 

- 0‘24 

I "20 

°" 5 2 

o"68 

o* 5 2 

- o-i6 


Penck also states that the z , for each year, depends upon the mean 
temperature of the year, and is increased by 070 inch per degree Fahrenheit 
increase of the mean annual temperature (45'8°F.); so that regarded from this 
point of view, s', and E, to a certain extent increase together. 

Sketch No. 49 also shows that f varies very much as the flow from a 
reservoir might be expected to do, being small at first, when the streams are 
high, increasing rapidly as they fall, and again diminishing as the stored-up 
water becomes exhausted. 

The real importance of the method, however, lies in the fact that, to a certain 
extent, it permits us to take into account the effect of the topography and 
geology of the catchment area on the run-off. 

We may consider that ke Pf represents the effect of the rain-fall and 
temperature, and is therefore very much the same for all catchment areas in the 
same country ; f however, depends on the geology and topography of the 
catchment area, and is peculiar to each area. We may expect to find large 
values of/, in flat and permeable districts, while in steep, rocky regions they 
will be small. Regarded from this point of view, I believe that the method is 
valuable. If we have obtained the ke p , terms for a series of years, by actual 
observation, it is possible to apply them with very fair confidence to an adjacent 
catchment area. If only one year’s records of the second area are known, its 
monthly f may be determined, and the run-off by months for other years can 
then be considered as capable of very fairly accurate estimation. 

Observations supplementing the usual Stream Gaugings.—A careful con¬ 
sideration of the principles detailed above will suggest that a great deal of 
useful information, which is not at present usually obtained, could be secured 
by special and not abnormally costly observations. 

Thus a very fair idea of the magnitude of the term AR P , could be obtained 
by systematic observations of the subsoil water level, combined with a survey 
of the area of the permeable strata existing in the catchment area, and there is 

13 












































194 


CONTROL OF WATER 


little doubt that these observations alone would permit a very fair idea of the 
volume of the equalising reservoir required in the driest year (see p. 236). 
The matter is of extreme practical importance ; at present, areas largely under¬ 
lain by permeable beds are generally regarded as unfavourable for development 
for water supply purposes by storage reservoirs This idea may be correct, as 
the surface topography of such areas rarely affords advantageous sites for 
storage reservoirs, but there is but little doubt that if an impermeable reservoir 
site can be secured, studies of the size of the invisible ground reservoir might 
enable an engineer to feel satisfied with a smaller visible reservoir than is now 
considered advisable. Certain American studies {Trans. Am. Soc. of C.E ., 
vol. 27, p. 286) have shown that it is quite possible for the invisible storage 
to contribute about one-fifth of the supply drawn from the visible reservoir in 
dry years. 

Similarly, the chemical composition of the ground water, as compared with 
the chemical composition of the river water when the ground flow is known 
(from subsoil water level observations) to be a minimum, should enable a very 

fair idea of the value of the ratio — to be obtained. In my own work in the 

gv 

Punjab, I found that alkalinity determinations alone, permitted a very fair idea 
of the relative proportions of the ground water, and of the water coming down 
from the hills, to be obtained. Such determinations are useful, if it is desired to 
predict the flow that is likely to occur in a river-bed at some distance below the 
headworks of a canal which diverts the whole of the visible flow. 

Examples of “ seepage water irrigation ” with water thus procured are 
frequent in America, and a very large scale example is likely to occur in a few 
years in the Punjab. At present, in default of observations of the type 
suggested, these matters are settled by vague opinions, or by a comparison 
with similar cases, or, still worse, by legal discussions. 

Droughts. —A very important principle must now be considered. We find 
by observation that z, the rain-fall loss for a year, is very fairly represented by 
the equation : , 

z = a + bx 

and better still by : 

z = a +b Jv x h +b c x c 

where the suffix h, refers to the hot, or summer season, and the suffix c, to the 
cold, or winter season. We are therefore led to assume (and such observa¬ 
tions as do exist justify the assumption) that : 

V p = a p +bpXp 

where the a! s and are constants, or at any rate, are approximately so. 

Now, as a matter of observation, this vegetation loss has, as a general rule, 

“ priority of right ” over the topographic flow, and ground storage disposal of 
the rain-fall. Of course, exceptions exist, as may be observed wherever a 
torrential rain-fall occurs, but the statement is as nearly correct as any other 
that can be made regarding this complex subject. 

Now, let us assume that the rain-fall x p , happens to be unusually small. It 
is plain that during a dry season we may find that ; 

Xp is less than a p +bx p 


DROUGHTS 


i95 


Such conditions do occur in practice, and are indicated by the vegetation 
“ wilting,” or suffering from drought. The conditions are complex, and 
obviously depend upon the length of the period which is denoted by the suffix 
P • They also depend upon the character of the vegetation ; but it is plain that 
periods occur during which the rain-fall is insufficient to provide for the 
requirements of the vegetation, and for the evaporation which would occur from 
the surface of the soil if it were wetted sufficiently for these requirements. 

We thus arrive at a principle which is extremely important when 
climates are considered, and which may be stated in general terms as 
follows. 

If the rain-fall during any division of the year is insufficient to wet the soil, 
the vegetation or evaporation loss may be far less than that which is indicated 
by the other climatic conditions prevailing during that period. 

The case is best illustrated by taking the extreme example of a desert. 
The rain-fall is normally considerably less than is required to compensate 
for evaporation, and may be only 2 or 3 inches per annum, while the 
requirements of the vegetation and the evaporation, as found by observations 
on irrigated areas existing in the same climate, may be 20 or 30 inches per 
annum. Nevertheless, when a rainstorm occurs, it produces some run-off, and 
water can be collected in reservoirs, or can be drawn from the subsoil by wells. 

We are consequently led to believe that the relation between rain-fall and 
run-off in arid climates differs totally from, and is in some respects a simpler 
matter than, that which exists in Temperate climates such as those of Western 
Europe and the Eastern United States. 

Climate in Relation to Run-off. —The classification of climates, 
regarded from this point of view, is fairly obvious. If long periods of time 
alone are considered, the major portion (if not the whole) of the rain-fall loss is 
caused by vegetation and evaporation. Now, in Insular climates, and more 
especially in Temperate Insular climates, the amount of rain that falls in the 
year is sufficiently equably distributed to ensure that during all divisions of the 
year (abnormally dry years excepted), the rain-fall is always adequate to supply 
the requirements of the normal vegetation, and to keep the surface soil 
sufficiently damp to permit of some evaporation. For example, in symbols— 
x p is always greater than a p +bx Pi where the minimum duration of the division 
of the year expressed by^ may be taken as between one and two months, but, 
in any actual case, depends to a large extent on the thickness of the surface 
soil. In Continental, and more especially in Tropical Continental climates, 
this relation does not hold for all seasons, except in abnormal years, and the 
natural vegetation of these localities has adapted itself to droughts, either, as in 
the extreme example of the desert cacti, storing up water in its tissues, or, as in 
the less marked cases of wheat and cotton, being provided with long tap roots 
permitting it to draw on the subsoil water. 

It will therefore be plain that the general investigation given above is 
only directly applicable (for all seasons of the year) to climates in which the 
before-mentioned condition (which may be termed a vegetation and evapora¬ 
tion drought), does not normally occur. When such a drought takes place, 
the terms a and bx may be considerably smaller than the values indicated by 
the other conditions obtaining during the drought, and a certain depletion of 
ground water storage which does not appear as run-off, but is consumed by 
vegetation, may also occur. 


CONTROL OF WATER 


196 

It consequently appears logical to divide climates into three classes : 

(i) The standard class in which a drought, as above defined, does not 

occur in normal years at any rate. 

(ii) A class in which a drought occurs once a year at least, except 

in abnormal years. 

(iii) A class in which a drought is the normal condition of affairs. 

We may therefore have a climate such that the catchment area is normally 
never thoroughly dry, as (in this sense) is the case with all catchment areas in 
Temperate climates, except after very intense and long-continued droughts, 
such as take place at intervals of 30 or 40 years at least. 

The expression “ thoroughly dry,” is perhaps indefinite, but by that term 
I wish to indicate that the soil of the catchment area is so depleted of water 
in its upper layers as to reduce evaporation from the ground to a minimum, 
(I believe, as a matter of fact, that some evaporation, if only of night dew, 
always happens), which is quite independent of the last rain-fall that occurred. 

The second type of climate is the one found in most tropical countries 
which have a dry season. In such cases, once a year at least, the catchment 
area becomes thoroughly dry. 

The third type of climate, which occurs in its most representative form in 
desert regions, and in the arid zones of America, South Africa, and India, is 
one in which the catchment areas are normally thoroughly dry. 

Now, when rain falls on a perfectly dry catchment area, it is a matter of 
observation that the first portion is absorbed by the soil, as by a sponge, and 
neither runs off, nor soaks deeply into the ground, (in such climates ’it is 
very often customary amongst natives to speak of so many “ inches ” of rain, 
when the word “inch” does not mean rain-fall, but the depth to which the 
sides of a newly dug hole are found to be moistened after rain). 

Until the soil is soaked to an appreciable depth no run-off can occur, and 
if the rain is insufficient to effect this, the nett result will be a temporary 
wetting of the ground, which is sooner or later sucked up by the thirsty air. 

Thus, in a dry catchment area, the loss before any run-off can occur may 
be represented by a constant, which indicates the quantity of water consumed 
in saturating the surface layers of the soil. The loss that occurs thereafter is 
proportionally far less, and depends more on the time which the rain takes to 
fall, and on the distance which the water running off travels before it is collected 
into a river channel or reservoir, than on the absolute magnitude of the fall. 

When rain falls on a damp catchment area the initial loss is, relatively speak¬ 
ing, not large, and the influence both of time and distance factors is less. 

Thus, in climates of the first type, it is possible to consider the rain-fall 
of a month, or even of a season, as a unit; and, except towards the end of the 
summer season, it is rarely requisite to consider the rain-falls of individual days. 

In climates of the second type, however, we must certainly consider the rain¬ 
falls during the wet and dry seasons as independent, and, abnormal torrential 
downpours apart, can usually neglect the latter entirely. In the wet season we 
must consider not only the total rain-fall, but also the rain-fall of individual 
weeks, or, at most, months. As will be seen later, we are led to regard the 
rain-falls of the successive months, reckoning from the beginning of the wet 
season, as contributing in increasing proportions to the run-off. Consequently, 
a fall which had it occurred in the first month would have been regarded as 


CLIMATES OF THE FIRST TYPE 197 

unimportant, might towards the end of the season produce the major portion 
of the run-off of the season. 

In climates of the third type, we regard each rainstorm as a separate 
entity, and the practical rules will lead us to consider the run-off as produced 
only by heavy rainstorms, although it must not consequently be assumed that 
the run-off invariably occurs immediately after a heavy rainstorm. 

The general conditions are best illustrated by a detailed study of catchment 
areas in climates belonging to the first type, and I shall therefore discuss the 
effect of the geological and topographic structure under that head. 

It may be stated that the geological and topographic conditions are equally 
effective in climates of the second and third types, and that only the lack of 
detailed information prevents a discussion of their effect under these conditions. 

Climates of the First Type.— The rain-fall loss over a year may be 
represented with a very fair degree of accuracy by the equation : 

z = a-\-bx 

or, better still, by z — a 4- bsXprb^y^ where x Sy is the summer (hot season) 
rainfall, and x Wj is the winter (cold season) rain-fall. 

Now, theoretically, we should of course consider all years, wet or dry, 
in determining the constants a and bx. But, from an engineer’s point of view, 
it is better to take only the drier years. I have therefore neglected all years 
in which the annual rain-fall is much above 1*20 times the mean annual 
rain-fall. Subject to this condition, for catchment areas in Great Britain, 
Germany, and (less accurately) the Eastern United States, I find that b = o*i6. 

Considering the possibilities of error in the latter country, I am inclined to 
believe that the above statements are fairly accurate for all Temperate and 
Non-Continental climates, provided that the mean annual rain-fall does not 
greatly exceed 60 inches. 

As an example, I give the values of z, as observed by Ingham (Rainfall 
and Evaporation in Devonshire) at Torquay, for the years 1878-1900, and 
those calculated from z =97-f-o‘i6,r. 


x observed. 

2 observed. 

2 calculated. 

Difference. 

2 7‘5 

13 M 

i4’o 

+ 

0*9 

3 *'$ 

14*3 

I 4’5 

i*i 

3 2 ’3 

87 

14*8 

6‘i 

34 *3 

18*8 

I 5 ‘ I 

37 

35 ' 2 

18*0 

i 5*3 

27 

357 

14*4 

1 5’3 

o *9 

357 

18*4 

i 5‘3 

3 * 1 

3 6 '3 

10-5 

15*4 

4*9 

3 6 '3 

i6’o 


o - 6 

38*0 

12’8 

157 

2*9 

387 

14*8 

15-8 

1*0 

39’9 

5 "9 

16*1 

10*2 

42'8 

17-0 

16*5 

°*5 


[ Table continued 























CONTROL OF WATER 


198 


Table continued ] 


x observed. 

2 observed. 

! 

2 calculated. 

• ii * ' i ' 

Difference. 

> ■ .i 

43 ’° 

T 3’3 

t6*6 

+ 

3*3 

43 ' 8 

17*0 

167 

0*3 

447 

16*8 

16 *8 

0-0 0*0 

45*3 

167 

i6*9 

0*2 

45*5 

19*1 

17*0 

2 T 

45 ' 8 

21*6 

i7’o 

4‘6 

5°‘4 

2 I‘I 

17 *6 

3*5 

5 1 ’ 1 

2 5 ' 2 

17*9 

7*3 

5 2 '° 

17*0 

18*1 

IT 

5 2 ' 2 

I9’2 

i8t 

IT 

A 


The agreement for individual years is only rough, the average difference 
being 2*8 inches, or about 17*5 per cent, of the mean value of z, but it will be 
seen that (except in the case of the wetter years) the average loss in any three 
years is very close to that calculated. The divergence in the wetter years, and 
in the two with abnormally small losses, is explained by the fact that the 
expression s — a+bx is only a contracted form of: 

z —a s -\-b s x s -\-a w -\-b w x w 

and since b s , is far greater than b w , a year with abnormally heavy summer 
rain-fall may be expected to have a greater rain-fall loss than one of the same 
rain-fall with abnormally heavy winter rain-fall. 

The following table shows the agreement between : 

Z = J+O'^Xa+O'lXv, ;■■■■<! 

and the observed values for another British catchment area. 


Winter 

Rain-fall. 

' 1 

Summer 

Rain-fall. 

Observed 

Loss. 

Calculated 

Loss. 

Difference. 

X-iu 

x s 

%o 

2 

+ 


15-8 

20‘9 

15*9 

15*4 * 

... 

°*5 

26*1 

i8‘2 

187 

I9‘2 

0*9 

• • • 

20*3 

197 

16’4 

17*1 

°7 

• • • 

15*3 

18-4 

l6*2 

15-1 

• • • 

IT 

io*6 

18*9 

13*8 

I 3 * 1 

... 

°7 

16*9 

19*5 

I 5‘3 

i 5*7 

0*4 

• • . 

22 ‘5 

i 2 *3 

T 5*4 

17*2 

i-8 

. • . 

20*1 

2I - 4 

177 

i 7 *i 

. . • 

o*6 

21 *4 

13-6 

19*1 

17-0 

. . . 

2T 

2 2 *3 

22*2 

1 5 * 1 

i8t 

3 *° 

• • • 

187 

21*5 

16*6 

i6*6 

o - o 

0*0 

24*8 

217 

18*4 

i8t 

• . • 

°*3 

19*3 

24*2 

20T 

17T 

• • • 

3 "° 

17’6 

17*2 

15*2 

i 5*7 

°*5 

• • • 

26T 

19-4 

1 3*3 

19*3 

1*0 

• • • 















































MEAN RAIN-FALL LOSS i 99 

The agreement is somewhat closer, the average difference being ri inch, 
or, say 7 per cent, of the mean rain-fall loss. But it must be remembered that 
there are now 3 constants at our disposal, as against 2 in the first case ; so 
that a somewhat closer agreement might be expected in any event. It will, 
however, be observed that the wet years are no longer abnormally divergent, 
so that in all probability the three term relation is capable of including wet years 
as well as the drier ones. 

I • 

A somewhat important distinction must now be drawn. It has been stated 
that: 

z = a + o % \ 6 x 

for any individual year, and for any catchment area. It might therefore be 
supposed that if different catchment areas are considered the mean rain-fall 
loss over a long term of years z mj can be expressed in terms of the mean rain-fall 
over the same period x m , as : 

Zin == Cl -f- O I C)Xhi 

For some reason which is at present unknown, but which is probably 
connected with the fact that a heavy rain-fall shapes and cuts the topography 
of a catchment area into steep slopes, and thus favours a speedy arrival at the 
stream channels, where it is less exposed to evaporation, there appears to be 
very little doubt that the true relation for the countries enumerated above (so 
far as rain-fall determines the rain-fall loss), is : 

Z m = d-L + O'OSXm tO 0'12X m 

It is therefore plain that the value of a , ^"approximately : 

a = a 1 + o , nx m to o’04x m 

A discussion of the factors affecting a, is consequently necessary. 

This is best attained by a consideration of the mean annual run-off of 
catchment areas generally. 

Run-off of Catchment Areas. —The factors having the most influence 
on the mean yearly run-off of a catchment area, taken in their usual order of 
importance, are : 

(i) The average yearly rain-fall. 

(ii) The distribution of rain-fall by seasons. 

(iii) The character of the strata beneath the area, whether permeable, or 

impermeable ; and this influences : 

The general slope of the catchment area. 

(iv) The marshes, lakes, or other bodies of water existing on the catchment 

area. 

The last two have less effect upon the absolute quantity of the run-off than 
on its variability from month to month during the year. 

For catchment areas in which these four factors are approximately similar, 
the absolute magnitude of the area has a decided influence upon the variability 
of the run-off, the larger areas having (as a general rule) the less intense floods, 
and the more abundant dry weather flows. As a matter of experience, while 
the dry weather flow of a mountain valley, of say 10 square miles, often falls to 
nothing, the volume of a river draining several hundred square miles, is rarely, 
if ever, below o'2 of a cusec per square mile, in Temperate climates. This is, 
of course, explained by the greater likelihood of an extensive area (especially 


200 


CONTROL OF WATER 


if flat) including permeable strata to such an extent as to provide a large 
invisible reservoir. 

(i) Effect of the Absolute Magnitude of the Mean Annual 
Rain-fall. —The rain-fall loss can be expressed in the following form : 

b u is not far from 0*04 to o'H. Thus, since for the same country in¬ 
creases less rapidly than x m the heavier the rain-fall, the larger the run-off; and 
ceteris paribus , the fraction of the rain-fall collected each year increases far 
more rapidly than the absolute value of the rain-fall. 

A very important aspect of rain-fall in its relation to run-off is the extreme 
difficulty of ascertaining its correct value. The question of the location of 
gauges has already been dealt with, and it is there shown that the most usual 
mistake is to underestimate the rain-fall. This in itself is not very material, 
since engineers are principally concerned with the run-off. When, however, the 
relation between rain-fall and run-off is studied, and the determination of the 
values of a, and b, in the equation 

y — x—a — bx 

is attempted, a correct knowledge of the absolute value of x, is of the greatest 
importance. It is well known that older engineers invariably (and the practice 
is as yet by no means extinct), considered the relation as : 


y=px 


where/, was a more or less constant quantity. 

Now, both rules are avowedly approximate, but at first sight it appears 
obvious that it should be possible to determine whether a percentage, less a 
constant quantity, or a fixed percentage of the actual rain-fall, best represents 
the run-off in any given case, by forming the values of the rain-fall loss and the 
run-off percentage as given by : 


and, 


Rain-fall loss = Rain-fall —Run-off. 

Run-off 


Run-off percentage = ioox 


Rain-fall 


taking the mean values for the available series of years, and investigating their 
probable errors, by the method of least squares. 

A little consideration will show that this is only the cas’e if the “rain-fall” 
is the actual mean rain-fall on the catchment area. For, assume that, owing 
either to paucity of rain-gauges, or to a bad selection of their sites, the recorded 
rain-fall is not the actual rain-fall, but some proportion of this, say 

Recorded rain-fall = (1 —c) true rain-fall. 

It should be remembered that this error is likely, since, as already stated, 
the relation between the annual falls in adjacent localities is one of approximate 
proportionality, and not a constant, or approximately constant, difference, so 
that the relation : 

Recorded rain-fall = True rain-fall —a constant, is unlikely to occur. 

Then, if: . . . . y — the run-off. 

x = the true rain-fall. 
x 1 = the observed, or apparent rain-fall 

we have : 

The true rain-fall loss, z = x—y 



ERRORS OF RAIN-FALL 


201 


The apparent rain-fall loss z 1 = x x —y = x (i—c)—y — z—cx. 

While the percentages are : p = 

. _ iooy _ io oy _ p 
x 1 ~~ x(i — c) ~(i — c) 

Ihus, while z x , is more variable than z, owing to the inclusion of the variable 
term cx , p x is just as variable as p , and no more so. 

Thus, unless it is known that the observed rain-fall represents the actual mean 
rain-fall over the catchment area as accurately as the observed run-off represents 
the actual run-off, no valid argument regarding the relation between rain-fall and 
run-off can be based upon calculations of the mean square errors of^ and z. 

For this reason, the fact that the percentage method is still largely used by 
engineers in India and America cannot be considered as a weighty argument 
in favour of its general adoption. In these countries rain-fall statistics are less 
reliable than is the case in Europe, the actual observations being frequently 
less carefully taken ; and in nearly every case the duration of the available 
records is far shorter, and the distribution of the observing stations less satis¬ 
factory, both in number and position. 

Consequently, the employment of the percentage method merely indicates 
that the engineers have used unsatisfactory material to the best advantage, 
and does not in any way show the best method of utilising more accurate 
records. 

As an actual example, take the figures for the Melbourne (Victoria) 
catchment area, with which Mr. Ritchie, the engineer of the water supply for 
that city, has favoured me. The portion of his letter relating to the subject 
under discussion is as follows : 

“ The catchment of the Wallaby and Silver Creeks, and the Eastern 
branch of the Plenty River, are composed of mountainous country, ranging 
from a minimum elevation of about 700 feet above sea level, to a maximum of 
about 2700 feet. . . . 

“ There is one rain-gauge at 700 feet elevation, and another at about 
1700 feet elevation. Snow falls more or less in winter at the 1700 feet gauge, 
but does not lie for many days when the falls occur. I append for your 
information the annual rain-fall, and percentage run-off for stations (J.e. the 
700 and 1700) averaged, and also on the basis of the 1700 feet station only. I 
am inclined to think that the record .on the 1700 feet station basis would be 
the most accurate, as the larger portion of the catchment is at that level and 
over. Of course, to get a really accurate result, you require a number of rain¬ 
fall stations in selected sites, within the catchment, but I have no such records. 
The total catchment areas aggregate 23,000 areas.” 

If we examine the first series, i.e. those in which the average of the two 
gauges are taken, the method of mean squares gives as follows : 

Rain-fall loss = 2673 inches±4*30 inches = 2673 (1 ±0*16) inches. 

Run-off percentage = 3077 ± 370 = 3077 (1+0*12). 

That is to say, it appears that the assumption of a constant percentage 
represents the facts better than the assumption of a constant rain-fall loss. 

Taking, however, what Mr. Ritchie believes to represent the rain-fall more 
accurately ; that is to say, the 1700 feet gauge record only, we find that: 

Rain-fall loss = 34'6o inches ±5*45 inches = 34*60 (1 ±0*129) inches. 

Run-off percentage = 25*30 ± 3*05 = 25*30 (1 ±0*119). 




2o2 ; CONTROL OF WATER 

The almost complete agreement of the percentages of probable error (n'9 
and 12) of the run-off percentage should be noted, since it forms a confirmation 
of the theory. 

The rain-fall loss for the more accurate record is almost as steady as the 
percentage figure. 

I am therefore inclined to go somewhat further than Mr. Ritchie, and to 
state that I believe that even the 1700 feet record does not fully represent the 
rain-fall on the catchment area. 

My personal knowledge of the catchment area is confined to a 5 days’ 
camp in it, at a time when my experience of these matters was limited. I am 
not therefore prepared to make a more definite statement for this area, but if 
these figures related to Great Britain I should feel justified in assuming that 
the actual mean rain-fall was : 

Neither 3871 (mean of both gauges), 

r» * 

Nor 4679 (mean of the 1700 feet-gauge), 
but more like 52 inches, with a mean annual loss of approximately 40 inches. 

I trust, at any rate, that I have made it plain that the fair appearance of the 
percentage figures is misleading; although, of course, so long as these two 
gauges alone exist, Mr. Ritchie is perfectly justified in using the percentage 
method. 

• f » • f 

It also appears that another gauge is badly required to represent the area 
between 2000 and 2700 feet elevation. 

Treating the matter generally, and assuming that the relation : 

z — a + bx 

holds where x , is the true rain-fall, when the recorded rain-fall is x{ \ —c), in place 
of the true value z, of the rain-fall loss, an apparent value z ly is obtained where : 
Zi=x—cx—y = x—j'—cx = z-~cx=a + (b — c)x 
As definite examples, let us suppose that the correct relation is 

z = i2 + o*i6;r, 

but that the rain-fall is incorrectly observed, and 

(i) Is underestimated by 16 per cent. We have, 

z x — 12 + (o' 16 — o*i 6 )x —\2 inches. 

Thus, owing to underestimation, the value of the rain-fall loss has become 
apparently constant. 

(ii) So large an underestimation may seem improbable. Therefore, let us 
assume an underestimate of 6 per cent. only. The apparent value of z, is now : 

z 1 = 12 T o' 1 ox 

and if the mean rain-fall is 30 inches, in a long series of years the apparent 
mean loss is 15 inches, while its correct value is 16*8 inches. 

(iii) An overestimate of the rain-fall is usually improbable, unless the 
gauge-stations are very abnormally distributed. But assume an overestimate 
of 10 per cent., z, now becomes : 

Zj = I2-f-0'2&2- 

and the mean observed rain-fall loss is 19*8 inches, in place of the true value 
i6'8 inches. 

Hence, the following rules can be deduced : 

If the rain-fall is underestimated, the calculated value of b y is less than its 
correct value ; and if greatly underestimated, b, may appear to become 


SUMMER AND WINTER RAIN-FALL 


203 

negative. Consequently, in such cases as the Montaubry Reservoir, or (less 
markedly so) the Longendale Reservoir, or the Durance River, it would appear 
probable that the recorded rain-falls are considerably less than the true 
precipitation, and therefore that the rain-fall losses are underestimated. 

The term “ precipitation ” is employed to indicate the possibility that in 
some of these cases the water falling on the catchment area may not entirely 
arrive in the form of rain as collected in a rain-gauge (see p. 207). 

Similarly, (although with less certainty), it appears permissible to conclude 
that in cases where b , greatly exceeds the usual value 0*16, the recorded 
rain-fall and the rain-fall losses are overestimated. 

These rules are not of much value when applied to the study of existing 
observations of rain-fall and run-off, although they may lead to good hints for 
the location of new rain-gauges, and possibly, when some years’ of records 
have been accumulated, to certain corrections in the early figures. 

They are, however, very useful when it is desired to apply the records of 
existing reservoirs to neighbouring catchment areas for which no run-off data 
exist, but for which good rain-fall records are available. ) 

The rules are obvious. A record of s', which shows that z, diminishes as 
the rain-fall increases, should be regarded as underestimating the rain-fall 
loss ; while one in which z, increases very rapidly with the rain-fall, may be 
considered as overestimating the rain-fall loss. 

(ii) Seasonal Distribution of Rain-fall. —The effect of the seasonal 
distribution of rain-fall has already been indicated. It is obvious that rain 
falling during the colder months of the year, when evaporation is at a 
minimum, and vegetation is inert, will have a far better chance of reaching a 
stream, or permeable stratum, and appearing sooner or later in the form of 
run-off, than an equal quantity of rain falling in hotter months, when evapora¬ 
tion and the requirements of vegetation are more intense. 

This difference may be regarded as explaining many of the divergences 
between the observed and calculated rain-fall losses. 

Referring to Ingham’s table (see p. 197), the year specified by x= 36*3, z— 10*5, 
was one in which the major portion of the rain fell in the winter, while the 
seasonal distribution in the year given by x — 36’3, z— 16, was normal; but the 
year •*' = 39’9, 5 *9 cannot be thus explained. So also, taking the four years 

of heaviest rain-fall: 

.^ = 50*4, £=2t*i, was a year of fairly heavy summer rains ; 

jtf — 51 *r, z — 25*2, was a year of very heavy summer rains ; 

x— 52*0, z~'j 7’o, and ,r=52*2, z= ig’2, were years in which the distribution 
between summer and winter rains was more or less normal. 

Such abnormal results occur in every table of this character, and it will 
generally be found that some years of low rain-fall have an unusually low 
rain-fall loss (compared with the calculated values) owing to the year really 
having a dry summer, and a winter of normal rain-fall. Vice versa , in very 
wet years, the rain-fall losses are usually higher than the calculated figures, 
owing to the fact that a year can hardly be pronouncedly wet without having 
an abnormal amount of summer rain-fall. 

The worst possible case, from the point of view of run-off, is that of two 
successive years of exceptionally small winter rain-fall, when, even though the 
intervening summer is wet, a very small run-off must be expected. 


204 


CONTROL OF WATER 


The Hallington (Northumberland) reservoir, given on page 239, is a very 
striking example, and cannot be considered as the worst possible case, since 
the preceding year was exceedingly rainy. 

(iii) Geological Structure. —The effect of the geological construction 
of the catchment area is threefold : 

(a) The geological construction is the cause underlying and creating the 
topography, and therefore influences the run-off from this point of view. 

(1 b ) The strata, if permeable, absorb the rain-fall, and surrender it later, 
acting as concealed reservoirs. From this point of view, the geology 
influences the absolute value of the run-off to a certain degree, but its 
most important effect lies in the equalisation of the run-off over the 
whole year, as discussed on pages 188 and 220. 

(c) The geological structure may cause the true catchment area to depart 
widely from the area shown by the surface topography, and thus may 
influence the run-off to an abnormal extent. 

Considering these in order : 

( a ) From the purely topographical point of view, anything that assists rain¬ 
water to collect rapidly, increases the run-off. Steep slopes, bare rocks, 
and numerous well defined small runnels, all indicate a good run-off; whilst 
flat slopes, swamps, and bogs, or ill-defined topographical characteristics, 
are accompanied by a bad run-off. 

The question can be briefly summed up : An area underlain by impervious 
strata allows a large fraction of its rain-fall to run away on the surface, and is 
cut and shaped by the collected water into a topography favourable to a good 
run-off. An area underlain by pervious strata disposes of most of its run-off by 
ground seepage, and therefore is not cut or shaped into a favourable topo¬ 
graphy, and, in consequence, a certain additional loss is entailed in such 
topographic run-off as does occur, owing to evaporation during its slower 
journey to the streams. 

It is also plain that an impervious area will have more intense floods, and 
longer periods of low water than a pervious one, even though the mean yearly 
run-off is the same. This effect will be even more marked if the mean yearly 
rain-falls are equal. 

{b) Returning to the general discussion (see p. 190). The larger the 
proportion of permeable strata in a catchment area, the greater the individual 
fs (whether positive or negative), but apparently also the greater the in¬ 
dividual a's. This last statement may appear peculiar, but the explanation 
probably lies in the fact discussed when considering Droughts, namely : A 
large number of plants are capable of securing and utilising water lying in 
permeable strata near the ground level, and, where these strata exist, such 
plants being adapted to the local conditions, either grow naturally, or are 
cultivated. 

A further explanation may be that all, or nearly all, permeable strata com¬ 
municate with the sea, or with other catchment areas, by underground channels 
(in which may be included the flow of ground water which usually occurs in 
alluvial river beds, and which is rarely utilised, although it should obviously be 
included in the run-off in scientific discussions of the question). Be the 
explanation what it may, the extra rain-fall loss caused by permeable strata has 
a real existence in normal cases, and may be roughly estimated at about one- 


GEOLOGICAL STRUCTURE 


205 

sixth of the average yearly storage in the invisible reservoir, if that is known ; 
although (as is shown in the next section) permeable strata, under certain 
geological conditions, may increase the apparent run-off. 

I he above statement should perhaps be somewhat qualified. The records 
used to investigate the question nearly all refer to catchment areas the average 
elevation of which is greater than that of the country surrounding them, and 
the extra loss may be entirely due to leakage through permeable beds into 
neighbouring catchment areas. The only evidence which conflicts with this 
view is the fact that the permeable catchment areas with large average rain-fall- 
losses nearly always yield markedly larger run-offs at the end of a long period 
(two, or three years) of deficient rain-fall than other permeable areas with 
smaller average rain-fall losses. This fact suggests that the areas with the 
greater losses also possess the larger invisible reservoirs. It should, moreover, 
be noted that submarine discharges of large volumes of fresh water (which 
probably represent the leakage of permeable beds) are far more common than 
is generally supposed. Such phenomena are constantly being discovered both 
by submarine cable engineers, and by physicists studying questions relating to 
the distribution of deep sea fish. 

(c) From the purely geological point of view, the effect of permeable and 
impermeable strata is best illustrated by examples. 

If a permeable stratum occurs, which dips into a valley on one side at A, 
and outcrops again at B, across the topographical watershed W, as shown in 
section in Sketch No. 50, it is plain that some portion of the rain falling on the 
area WB, will appear at A. If conditions are favourable, as for instance 
if the stratum AB, is underlain by a bed of clay, this portion may be quite 
appreciable. 

The above circumstances generally give rise to springs at A, and an 
occurrence of this nature is unlikely to be overlooked. Cases exist, however, 
where such springs rise in a stream bed, and they may consequently be 
unperceived unless careful gaugings are taken. 

Similarly, a fault crossing a stream may greatly diminish its flow. It is 
therefore advisable, wherever faults or permeable strata are known to be present, 
to gauge all streams both above and below their outcrop. Since the loss or 
gain may be assumed as constant, the existence of the spring, or of the leakage, 
can generally be detected by a few observations. In my own experience I 
have found that two surface float gaugings will usually settle the question, 
because the stream being presumably of the same character above and below 
the outcrop, uncertainties as to the value of Harlacher’s ratio p, (see p. 61) do 
not materially affect the results. 

Fissured strata, or beds of sand and gravel, frequently provide invisible 
underground channels for the escape of water. The detection of such channels 
measurement of the flow in them is difficult. I his may be effected in 
a gravel bed by sinking a series of pipe wells across the supposed line of flow, 
and then one or two more some 100 feet above. A solution of some easily 
recognisable salt is poured into the upper pipes, and water drawn from the 
lower pipes is tested for this salt until it is detected. ^ 

letter but more complicated method is electrical. In this case, the 
upper pipe wells are dosed with ammonium chloride, or common salt, and its 
advent to the lower pipes is announced by a fall in the electrical resistance 
measured between plates immersed in two of the lower wells. 


206 


CONTROL OF WATER 

It is likely that any important flow of water of the above nature will be 
previously known, and such local knowledge should be utilised in arranging 
the tests. Where the quantity of water thus discovered is of sufficient value to 
justify the expense it may be collected by underground dams, or catchment 
galleries, or pumped from a series of wells. 



Sketch No. 50.—Effect of Geological Structure on*the Boundary of a 

Catchment Area. 


It should be remembered that such pervious beds may be utilised as 
reservoirs, if the intake of the scheme can be located below the point 
where they discharge above ground. They are, therefore, not necessarily 
detrimental. 

I shall later refer to the condensing effect which glaciers are believed to 
exercise, and there is little doubt that such condensations occur less extensively 
in many other cases. I am not, however, aware of any instance other than 


































































E VAPOR A TION FROM LARES 207 

glaciers, where the effect is so marked as to have yet been detected in 
influencing the run-off. 

The Dew Ponds of Sussex are worth describing, both as small, but quite 
practical examples of the possible utilisation of this effect, and as showing 
under what conditions it may be expected to occur. 

Dew Ponds are made as follows : 

A basin-shaped hollow is excavated in an open space, well exposed to damp 
sea winds. The hollow is covered by a layer of straw and twigs, or other non¬ 
conducting material, about 18 inches thick. On this is laid a continuous bed 
of puddled clay, about 2 feet thick, which in its turn is covered by a layer 
of broken stone. 

The object is to provide a surface of stone and clay which rapidly grows 
cold at night, and the dew thus collected is caught by the layer of puddle clay, 
and conducted to the central pond. 

Such a prepared area, about 200 feet in diameter, under favourable con¬ 
ditions, will keep the pond in the centre about 20 feet in diameter, and say 
3 feet maximum depth. So far as can be gathered, in default of systematic 
observations, the yield is about 0*01 inch per night during the summer, over 
the prepared area. 

(iv) Effect of Lakes and Swamps. —The presence of bodies of water in 
the catchment area has an equalising effect on the run-off. It is generally 
supposed that the evaporation from a free water surface, during the summer 
at any rate, is greater that the rain-fall on it. Thus, bodies of water, especially 
if shallow, and even more so if covered with vegetation, are regarded as 
tending to diminish the run-off. 

The most important example is the loss sustained by the White Nile in the 
swamps of the Sudd region, between 7 degrees and 9 degrees 30 minutes 
N. latitude. In this case, the reasoning is founded on approximate gaugings ; 
moreover, the rain-fall being small, and the evaporation intense, everything 
favours a loss of water. 

In more Temperate climates, such as that of Great Britain, the same effect 
has been assumed to occur. 

The later studies referred to on page 740, prove that the absolute magnitude 
of the evaporation from a free water surface has, until lately, been largely over¬ 
estimated, and since no actual gaugings showing the loss assumed to exist 
have ever been recorded, I am inclined to believe that in Temperate Insular 
climates at any rate, the loss is inappreciable, or even non-existent. Further 
evidence is required before this can be accepted as universally accurate, 
although it may be noted that the value assumed for the mean rain-fall loss 
{z m =io '6 inches) in the Aker (Norway) project {Tech. Ugeblad, 1907, p. 21) 
which refers to a catchment area of 86 square miles, containing about 18 square 
miles of lakes, is a very low one for the mean temperature of the locality, and 
is apparently founded on long-continued gaugings. 

Glacier-fed Streams. —The present state of development of water 
power schemes necessitates a consideration of the conditions of streams 
of which the catchment areas contain glaciers. 

Our knowledge on the subject is unsatisfactory. Such rivers as the Upper 
Rhone (which includes about 20 per cent, of glacier area in its catchment), are 
quite abnormal, and the run-off may rise to 90 per cent, of the recorded rain. 
As Forel has suggested, it is possible that the moisture of the air is 


208 CONTROL OF WATER 

condensed on a glacier surface in a form that cannot be recorded by a rain- 
gauge. 

As general rules it may be stated that: 

(a) The yearly run-off from a glacier is very heavy. Those feeding Lakes 
Como and Maggiore in Northern Italy give about twenty times the yield of 
equal adjacent areas where no glaciers occur. 

(, b ) Just as the melting snow causes a spring flood, so the more gradual 
melting of glaciers produces (in a purely glacial stream) a summer period of 
high water at the season when lowland, or hill streams, are at their smallest. 
A glacier thus acts as a reservoir, maintaining the summer flow. 

I append curves showing the flow of the Upper Rhone, and, as a contrast, 
that of the Durance, a mountain river which is not glacier fed. (Sketch No. 51.) 

Daily Variations of Mountain Streams. —As a glacier-fed stream is 
highest in summer, so streams issuing from a lofty mountain range are frequently 
found to possess a well-marked day and night variation in flow, especially in 
summer weather. Since this often amounts to as much as 20 per cent, of 
the daily flow, and is sometimes noticeable at points far removed from the 
mountains, it must be looked for in all such streams, and, if found, will 
necessitate the installation of a recording gauge, for since the variation occurs 
at approximately the same period each day, the results of daily, or even twelve 
hourly gauge readings, will be hopelessly erroneous. 

Relation between Mean Yearly Rain-fall and Run-off. —The 
most reliable observations on the relations between the mean rain-fall x m , and 
the mean run-off jy m , are to be found in the German and Austrian studies on 
the subject. 

Although very accurate run-off observations exist in America, the corre¬ 
sponding data for rain-fall are by no means so trustworthy. 

In view of the great regularity of rain-fall distribution in space existing in 
the Eastern United States, the fact that gauge stations are sparsely distributed 
is perhaps not of great importance ; but the records are mostly for short 
periods, and the local circumstances of the rain-gauges (judging by accessible 
information) are generally less favourable to accurate results than is usual in 
Europe. 

The British rain-fall records, thanks to the labours of Symons and Mill, 
are probably the best in the world, but the run-off records are usually kept 
secret. 

In Germany, run-off and rain-fall statistics are good, and publication is 
systematic and customary. 

Fortunately, we are able to state that the relations existing in Germany are 
very similar to those in Great Britain, except in the case of some British areas 
of unusually heavy rain-fall, so that the labour of comparison will not be 
wasted. 

Taking the results tabulated by Keller, in his paper Niederschlag, Abfiuss 
und Verdnnstimg in Mittleuropa , which are the means of a series of years 
varying between 6 and 30, and rejecting all observations marked by him as 
doubtful, we arrive at the following : 

Seventeen flat areas, with a mean rain-fall varying from 18*11 to 28*03 inches 
give a mean value for the mean rain-fall loss of 15*28 inches, with a probable 
error of ±7*4 per cent., and a maximum mean loss for individual areas of 
17*70 inches, with a minimum of 13*81 inches. 


GERMAN RAIN-FALL LOSSES 


209 


For six areas, partly flat, and partly hilly, with rain-falls varying from 
26*20 to 32*30 inches, the mean of all the mean losses is 18*09 inches with a 
probable error of ±4*9 per cent., a maximum mean loss of 19*30 inches, and a 
minimum of 17*03 inches. 

For twenty-four hilly areas, with rain-falls varying from 24*12 to 49*20 inches, 


—Rhone at SMaurice 



JLFM.fi. My. L. Jy. Ru. S. 0 M D. 

Sketch No. 51 .—Monthly Discharge of the Rivers Rhone and Durance. 


the mean of all the mean losses is 18*67 inches, with a probable error of ±8*3 
per cent., a maximum mean loss of 21*08 inches, and a minimum loss of 15*63 
inches. Rejecting the three areas which have rain-falls exceeding 40 inches 
and small rain-fall losses, the mean loss is 19*06 inches and the probable error 
only ±6*4 per cent., and the minimum loss is now 16*94 inches. 

For eight Alpine areas, with rain-falls varying between 38*80 and 68*10 inches, 

14 













































2 10 


CONTROL OF WATER 


the mean loss is 17*18 inches, and the probable error ±21 per cent. Here 
also, rejection of the two wettest areas reduces the loss to 15*62 inches, and the 
probable error to ±6*6 per cent. 

It may therefore be stated that, excluding very rainy areas (over 45 inches), 
the probable errors of the mean rain-fall loss are but small, and that the values 
obtained from areas of like configuration may be applied with a fair degree of 
confidence to those for which no records exist. 

For very rainy areas the values appear to be less consistent, but this may be 
ascribed to the fact that the areas are small in extent, with steep slopes, so that 
local influences have greater weight. 

It must also be recollected that the space variation of the rain-fall is 
accentuated in such cases. Therefore the mean value of the rain-fall is less 
easily obtained, and it is quite certain that the number of rain-gauges estab¬ 
lished in the above mentioned Alpine districts (on the average one per 400 
square miles) would not be considered sufficient in similar areas in the British 
Isles. 

When Keller’s results are applied to estimate the values of the rain-fall loss 
for areas of a size such as are usually developed for town water supplies, the 
fact that the average area of the catchment areas is : 


Flat. 

Partly flat and partly hilly 
Hilly . 

Alpine .... 


3180 square miles 
6020 „ 

34 oo 

5610 


must be carefully borne in mind. When town water supplies are considered, a 
catchment area of 20 square miles is large. The size of the area, per se, does 
not affect the value of the mean rain-fall loss, but the effect of any abnormal 
circumstance is likely to be relatively more marked in small areas than in the 
larger areas studied by Keller. 

A town water supply catchment area is usually at a relatively high elevation. 
Hence, invisible leakage out of the catchment area through permeable beds is 
more likely to occur than invisible leakage into the catchment area. Keller’s 
areas are so large that leakage by permeable beds is not likely to greatly 
influence the results either way. 

We must therefore consider Keller’s results merely as mean values, and 
should be prepared to make allowances for abnormal circumstances, if such 
exist in the catchment area, on a far larger scale than any of the figures given 
by Keller would indicate. I consider that all Keller’s results for wet areas 
probably err to a considerable extent, owing to the fact that the rain-fall is 
underestimated. The results, however, form a very useful practical guide for 
the estimation of the run-offs of wet areas, since, so far as can be ascertained, 
the rain-fall of all abnormally wet European areas is probably underestimated 
owing to the fact that the very wettest portions of such areas is usually but 
sparsely inhabited. Mill’s paper {P.I.C.E., vol. 155, p. 305), affords two very 
interesting large scale examples (t.e. Central Wales, and Western Northumber¬ 
land) of this fact. Keller’s original paper thoroughly deserves study by all 
hydraulic engineers. 

When the whole of Keller’s results are plotted with rain-falls as abscissae 
and rain-fall losses as ordinates, we find that the points form a group with well- 
marked boundaries. These agree very closely with straight lines, and translated 


BRITISH RAIN-FALL LOSSES 


2 I I 


into English measure, Keller’s results are as follows, where ,r m , represents the 
mean annual rain-fall in inches, and z m) the mean annual rain-fall loss in inches. 
The mean result is : 

z m = 0*05 8.r, H -{-15*95. Or, run-off= rain-fall— 16 inches. 

In no case is : 

z m less than 13*80 inches. 

In no case is : 

z m greater than o*n6.r w + 18*10 inches. 

Or, the run-off is always larger than § rain-fall—18 inches. 

Now, for other than German areas, such detailed figures cannot be given. 

The published British records are usually abnormal, being for a dry 
year, or for a series of dry years. Approximately accurate figures can be 
arrived at by a comparison with those available in Germany, and also by 
utilising unpublished data. The difference is almost entirely due to the fact 
that, owing to the more equable climate, the loss is somewhat less in Great 
Britain. By using Keller’s methods I find that the figures for areas of which 
the mean rain-fall is less than 60 inches are : 

Mean value of the rain-fall loss z m — o*o6.r m + 14 inches. 

Run-off = 0*94 rain-fall—14 inches. 

As minimum values I have been unable to find a reliable mean loss for any 
English district less than 12*5 inches, but, following Keller’s results, I believe 
that mean losses as low as 11 inches do occur, and I hope that my statement 
may result in their publication. 

As maximum losses we have figures as high as 22*5 inches, and even 23 
inches, but in each case the areas are small (about 500 acres), and the run-off is 
probably diminished by faults and fissures in the subsoil. These large values are 
always short period values, being the average of three to five years at the most. 

It must not be forgotten that the presence of a limestone stratum, or, more 
especially, of a chalk stratum in a catchment area, alters the usual relation 
between rain-fall and run-off. The stratum is probably fissured, and may afford 
an invisible channel of escape for a large portion of the water that falls on it, 
or may contribute in the form of springs originating in places which, according 
to the surface topography, are not included in the catchment area. The stratum 
(as in the case of bournes such as are found in the limestone and chalk dis¬ 
tricts of Yorkshire, Derbyshire, and Southern England) may act as a reservoir, 
and store up large quantities of water, which are delivered in the form of 
intermittent streams flowing at intervals of years. Since, however, the most 
natural method of securing water in such districts is by means of wells, catch¬ 
ment areas entirely underlain by permeable strata are unlikely to be utilised 
for water supply. Where the catchment area is partially occupied by such 
strata it is wise, unless springs occur, to allow a diminution in the run-off from 
the chalk area of 3 to 5 inches per annum, in addition to the loss indicated by 
ordinary rules. 

Relation between the Rain-fall and Rain-fall Loss for Individual 
Years. _The above discussion permits us to determine z m , the mean rain-fall 


212 


CONTROL OF WATER 


loss over a long period of years for a catchment area the mean rain-fall of 
which during that period is x m in the form : 

British Isles . . . . z m — 14 + 0*06 x m 

Germany . . . . . z m — 16+ o'o6x m 

Eastern United States. . . . z m — i 6 '^+o' 2 ox m 

where the first two cases refer to average catchment areas, while the third 
may be suspected as relating to somewhat more markedly permeable districts, 
but is founded on the most accurate records that I have been able to discover. 

We have now to consider the relation of z, and x, for a given catchment 
area in individual years. The relation appears to take the form : 

z = a + o' 1 6x 

and a, is plainly obtained by putting z = z m , and X — X mj 1 . 6 . \ 

Cl - Z yh O I (jX Yu 

== 14 —o’io x m , for the British Isles. 

16 —o*io.r m , for Germany. 

— i6*5+o , o4^- m , for the Eastern United States. 

This last may be compared with Vermeule’s statement that z = I5'5+o*i6;ir. 
The difference amounts to about 2, or 3 inches for the rain-falls usually occurr¬ 
ing in the Eastern United States, and is quite explicable by the fact that the 
more generally accessible records (such as I have used) are known to refer to 
somewhat unfavourable cases. 

These last relations are very rough, and are put forward in order to 
invite criticism ; and by way of indicating the slight respect they deserve 
it may be stated that: 

{a) All very wet years (usually any years with more than 120 per cent, of 
the mean fall) have been neglected. 

(< b) When examined by the theory of errors, the figure 0*16 becomes 
0*16 ± 0*07 ; and, the figure 14, 14 ± 4*3. 

The only consoling fact is that these figures indicate that the rule has, in 
all probability, a physical basis. 

(c) I would, however, point out that any engineer possessing records will 
easily obtain figures which are more applicable to his own results by graphically 
plotting the and z for each year, as was done in discussing Ingham’s results. 

A table of the values obtained in this manner is given on page 197. 

Penck, (I have been unable to trace the reference) from his studies on the 
question, has arrived at expressions equivalent to : 

z — i2+o'27^ for European catchment areas. 

5- = io-i+o - 20.r for United States catchment areas. 

The values given by the first rule do not differ markedly from mine, and 
any discrepancy is probably due to my neglect of the wetter years, which is 
justifiable for engineering purposes, although out of place in a purely scientific 
investigation. 

The observations utilised to determine Penck’s second equation refer to 
areas possessing climates of both the first and second types, and the divergence 
from my rule, is therefore not surprising. 

As examples of the methods explained above, let us consider : 


BRITISH RUN-OFFS 


213 

(i) A British catchment area of 45 inches mean rain-fall. The mean loss 
over a series of years is 14+0-06x45 = 167 inches. The rule for losses in 
individual years is expressed by : 

z — a+o’i 6 x 

or, 167 = #+0-16x45. Ob a — 9*5, and z — 9'5 + o-i6;r. 

Estimating the rain-fall according to Binnie’s rules, in a long series of years : 

The driest year will have a fall of 30 inches, and a loss of 14-3 inches, or 
a run-off of 15-7 inches. 

The average fall of the two driest successive years will be 33 inches. The 
average loss 14*8 inches, and the average run-off i 8’2 inches. 

The average fall of the three driest consecutive years will be 35 inches. The 
average loss 15*1 inches, and the average run-off 19-9 inches. 

The mean fall will be 45 inches. The mean loss 16-7 inches, and the 
mean run-off 28-3 inches. 

The average fall of the three wettest consecutive years will be 55 inches. 
The average loss 18*3 inches, and the average run-off 36*7 inches. 

For the two wettest consecutive years the figures are: 58 inches, 18*8 
inches, and 39-2 inches respectively. 

For the wettest year, the figures are : 65 inches, 19*7 inches, and 45*3 inches. 

(ii) Similar figures for a rain-fall of 25 inches, are : 

mean loss = i4 + o‘o6#- m = 15-5, loss for an individual year, z— 1 i'5 + o-i6ar, 
and the calculated figures are as follows : 



Rain-fall. 

Loss. 

Run-off. 

Driest year 

*6-5 

(i6'8) 

14-1 

03 ' 2 ) 

2-4 

( 3 ' 6 > 

Driest 2 consecutive years . 

18-3 

( I 9 ’ 4 ) 

1+4 

( I 4 ' 1 ) 

3*9 

( 5 * 3 ) 

Driest 3 consecutive years . 

I 9 T 

(20*0) 

14*6 

(* 3 ’ 9 ) 

4*9 

(6'i) 

Mean of all years 

25-0 

( 2 5 ' 2 ) 

I 5*5 

(16-0) 

9*5 

( 9 * 2 ) 

Wettest 3 consecutive years 

3°*7 

(33*°) 

16-4 

(i6’o) 

i 4*3 

(17-0) 

Wettest 2 consecutive years 

3 2 *5 

(34'°) 

167 

(15-8) 

15-8 

(18-2) 

Wettest year 

3 6 '3 

(3 7 ‘°) 

i 7*3 

(18-2) 

18-8 

(iS-8) 


(Actually observed figures are given in brackets.) 


The records extend over 21 years, and it is believed that these 21 years 
include rather more than a usual proportion of dry years ; thus, while the 
dry year observations probably show the worst that is likely to occur, wetter 
years may possibly be observed. 

As has already been noted, these rules refer to years in which the seasonal 
distribution is normal, and we may expect to find that: 

(i) The run-off for the driest year is underestimated, but the calculated 
figure does not, necessarily, underestimate the minimum yearly run-off. 

(ii) The run-off for the wettest year is overestimated. 

(Hi) The sum of the values for two and three consecutive years will agree 
far more closely with observation than the results of individual years. 

Comparing the two areas, we see that in an extremely dry year the run- 




















2 14 


CONTROL OF WATER 


off of the drier area (when compared with that of the wetter area) is far less 
than the ratio of either the mean or the individual falls would lead us to 
believe ; and in the wetter years the same divergence occurs, although less 
markedly, for all the run-offs. 

As an example that can also be compared with actual observation, take 
an American catchment area of 47 inches mean rain-fall. The relation between 
rain-fall and rain-fall loss being given as z — 15+0*25^. The calculated figures 
are shown below, while the observed values are given in brackets : 



Rain-fall. 

Rain-fall Loss. 

Run-off. 

Driest year 

2 driest consecutive years . 

3 driest consecutive years . 
Mean of 35 years 

3 wettest consecutive years 

2 wettest consecutive years 
Wettest year 

3i*o (3 1 ‘ 2 ) 

34‘3 (35 7 ) 
3 6 '7 ( 3 8 ' 3 ) 
47 ‘o (47 *°) 
5 8 ' 8 ( 5 2 ' 7 ) 
6i *9 ( 59 ' 3 ) 
64*4 (69-3) 

22'8 (21*1) 
2 3’6 (23-2) 
24*2 (23*5) 

26*8 (267) 
297 ( 3 6 ' 6 ) 
3°‘5 (40-4) 

3 1 ‘ 6 (42-4) 

8*2 (10*1) 

107 (127) 

127 (14*8) 

20’2 (20*3) 

2 9 *I (19:4) 
30*9 (18-9) 

35 ' 8 ( 26 ' 9 ) 


The agreement is fair for the dry years, but is abnormally bad for the 
wet ones. On referring to the monthly records, it will be found that while the 
proportion ot summer and winter rain-fall in the dry years is very close to the 
normal, the wet years all have an abnormally large proportion of summer 
rain-fall. It is for this reason that I have selected this adverse example, as 
it seems necessary to illustrate the errors that may be produced by neglecting 
the seasonal distribution. Better results might be obtained by considering all 
years below the average as one group, and those above the average as another, 
and deducing separate relations of the form : 

z = a + bx 

for each group. 

Wet Areas .—For very wet districts (roughly those where the mean rain-fall 
exceeds 70 inches), the above rules are generally considered not to hold good. 
Actual figures are very rare, since such areas are usually small, and give so 
good a yield that scarcity of water is but seldom experienced. 

A study of 45 yearly records of three such catchment areas has led me to 
believe that the law is best represented by the following equation : 

z = a + o' 6 (x —x m ) 

Consequently, the yearly run-off is far more constant than that of drier 
places. 

The basis for this rule is obviously not very broad. In such cases it 
would appear that the total amount of invisible storage (see p. 188) has a 
considerable influence on the yearly run-off; a very large invisible reservoir 
tending to increase4/, and vice versa. This appears to indicate that ground 
surface evaporation from such thoroughly saturated areas is always active, and 
the invisible storage being more or less shielded from surface evaporation, the 
larger the amount of water thus stored, the greater the yearly run-off. I must, 


















MO NTHL Y R UN-OFFS 


2 r 5 

however, point out that the measurement of the rain-fall and run-off from such 
districts is attended by very special difficulties. The rain-fall is heavy and 
patchy, and the stations at which it is observed are usually sparsely distributed 
over the area. The monthly rain-falls being heavy, the special gauges erected 
by the engineers are frequently found to have overflowed. Thus, the rain-fall is 
likely to be underestimated. A large proportion of the run-off passes off in 
floods and freshets, so that accurate estimation is difficult. The results 
obtained at Mercara and at Labugama (see p. 249) are probably the most 
accurate information available and unfortunately refer to Tropical climates. 

Distribution of Run-off during the Year .—The smaller the size of the 
reservoir provided to equalise the run-off over a year, or series of years, the 
more important the question of the monthly or other short period distribution of 
the run-off becomes. In the ordinary British town water supply, the short 
period distribution may be almost entirely disregarded, since the storage 
reservoir is sufficiently large to equalise the supply over the whole year. 
The usual low head power station of the Eastern United States lies at the 
other end of the scale. Here, at the most, the night flow of the river is stored 
up for use next day. In such cases the daily values of the run-off are im¬ 
portant. In general, however, we can assume that a reservoir of sufficient size 
to equalise the flow over a month exists. 

The ruling factor is of course the structure of the catchment area, as 
providing either the visible reservoirs formed by topographical features, 
such as lakes or ponds, or the invisible storage afforded by permeable 
strata. 

An approximate method of obtaining an idea of the influence of this 
storage (especially the geological storage) has already been given and should 
be applied in all cases. It is especially valuable when the district under 
consideration is situated close to a catchment area in respect to which long 
term records of rain-fall and run-off are available. We can then assume the 
difference in the ff s, for the two catchments as calculated for those years over 
which simultaneous records exist, as likely to vary but little in other years, 
and may, (subject to this constant difference), apply the long term records 
to the catchment area which it is proposed to study. Under such circum¬ 
stances, we may believe that the deduced run-offs are more than usually 
accurate. 

The process generally adopted by engineers for the determination of the 
monthly run-offs of a catchment area now requires examination. I give three 
methods. The first is the most general, and all that can really be said is that 
it is simple. The second is not so common, and is even less accurate than 
the first, but is given owing to its frequent employment in the past. The 
third is a logical and scientific method, but is so complicated as to be almost 
inapplicable, except to areas that have been very carefully studied for long 
periods. 

It is to be hoped that, before the final designs are prepared, the engineer 
will possess at least a year’s systematic record of the flow of the streams which 
it is proposed to deal with, and if he is so fortunate as to have statistics for five 
years at his disposal, he may consider himself lucky. 

However, assuming only one year’s record, the engineer will then be able 
to judge by the rain-fall data whether he is dealing with a dry, normal, or wet 
year, and can draw up a monthly table of the following type : 


I 

216 CONTROL OF WATER 



Rain-fall. 

Run-off. 

Loss. 

Percentage of Rain¬ 
fall appearing as 
Run-off. 

January 

2 '55 

2*46 

0*09 

9 6 *5 

February . 

0*76 

I *04 

- 0*28 

136*8 

March 

I*76 

084 

0*92 

477 

April 

1 ‘38 

o *57 

o*8 r 

4 i *3 

May.... 

i *81 

o *45 

1*36 

24*9 

June 

1*30 

0*48 

0*82 

36*9 

July .... 

0*76 

0*23 

OT 3 

3°'3 

August 

1*77 

0*19 

1-53 

io*7 

September 

2*41 

0*23 

2*18 

9*5 

October . 

1*91 

0*24 

I *67 

I 2*6 

November. 

3‘ 2 3 

0*44 

2*79 

13*6 

December 

i*68 

0*52 

1 *16 

3 1 ’ 0 

Total 

21*32 

7*69 

1 3’63 

36*! 


Which is the record for the Thames valley for 1887, and is due to Binnie 
(Report o?i the Flow of the Thames). I regret that I am not permitted to 
publish in detail a more typical British record, although the rain-fall in the 
above example is probably far better determined than is usually the case. The 
above figures are for a very dry year, probably the third driest of the last 
century. The area to which they refer is some 3,855 square miles, with gentle 
slopes, and is almost wholly underlain by permeable strata. The typical 
British reservoir catchment is about 40 square miles, with steep slopes, and is 
generally underlain by impermeable strata. The flow of the Thames is there¬ 
fore (and actual comparison of records confirms the statement) more equable 
throughout the year than is the case in a typical catchment area. 

The figures for the mean of nine years, 1883-1891, are : 

Rain-fall, 27-01. Run-off, 8-49. Loss, 18*52. 

It will be noticed that the dry year loss is less than the average, and this 
may be taken as holding in nearly all cases. Vice versa , the wet year loss is 
larger than the average ; and, as in the case of this particular record, the 
driest year is not necessarily the year of minimum run-off, for in 1884 the 
records were : 

Rain-fall, 22*90. Run-off, 6*56. Loss, 16*34. 

As another example we may take the table on page 217, which forms 
a typical American wet year table, being for the Sudbury River drainage 
of 75 square miles, for the year 1878, the wettest between 1875 and 
1897. 

The mean records for this area for the twenty-eight years are : 

Rain-fall, 45*78. Run-off, 22*22. Loss, 23*56, 


























USUAL METHOD FOR RUN-OFFS 


217 



Rain-fall. 

Run-off. 

Loss. 

Percentage of Rain¬ 
fall appearing as 
Run-off. 

January . 

5' 6 3 

3* 2 3 

2*40 

57*o 

February . 

5*97 

3*97 - 

2 'OO 

66-o 

March 

4*69 

6*26 

- i*57 

i33*o 

April 

579 

2*8l 

2*98 

48*0 

May.... 

0*96 

2 ’49 

- i*53 

260*0 

June. 

3-88 

0*87 

3* 01 

22*0 

July .... 

2*97 

0*23 

2’74 

8*o 

August 

6-94 

0-84 

6*10 

12*0 

September 

1 *29 

0*28 

1 *o 1 

2 2*0 

October . 

6*42 

0*92 

5*5° 

14*0 

November 

7*02 

2 ‘92 

4*10 

42*0 

December. 

6-37 

5' 6 7 

0*70 

89*0 

Total 

5 7 '93 

30*49 

2 7*44 

52-6 


It will be noticed that the loss in this wet year is above the average, and so 
also is the run-off. The negative loss in March, due to melting snow, is 
analogous to the negative loss for the Thames in February, and such large 
Spring negative losses are characteristic of Northern American drainage areas, 
and also occur, although less markedly, and with occasional exceptions, in 
English areas. 

Taking the above as a basis, we must now construct similar tables for 
other years for which we only possess records of the monthly rain-falls. 

Two methods are employed by engineers, and I shall give both, for although 
I am fully convinced that the first is the more accurate, I am well aware that 
many engineers make use of the second. 

I shall term them the Subtractive and the Proportional Methods. 

The Subtractive Method. —This consists in subtracting, (or, when the 
loss is recorded as negative, in adding) the observed monthly loss for the year 
of observation from the observed monthly rain-falls for the other years, and 
considering this result as representing the most likely value of the monthly 
run-off. 

The principal pitfalls occur in dealing with summer months. It is well 
known that in the summer, topographic run-off (as distinct from ground-water 
flow) is almost entirely produced by rain that occurs on days of great rain-fall 
only. Hence, it is quite possible that two summer months of identical total 
rain-fall may give very different run-offs. In the one case, the total rain may 
fall in a short heavy storm, and (especially on an impervious area), a large 
fraction may reach the stream ; while in the other case, the rain may fall as a 
succession of slight showers, of short duration, and may all be absorbed by 
the growing vegetation. 

It is therefore necessary to carefully examine the daily rain-falls of the 
summer months, and to compare their general intensity with those of the year 
























CONTROL OF WATER 


218 


of observation. Such errors are less likely to occur in the winter months, but 
their possibility should be borne in mind. It must also be remembered that 
in climates where a marked feature, such as the melting of the snow, or the 
commencement of the monsoon, occurs, the month does not properly specify 
the season in so far as it affects the run-off. For example, if in the year of 
observation the snow melts in April, it is plain that the April loss should be 
debited to March in years during which the snow melts in that month. 

A study of temperature records will often be of great assistance. It is 
evident that if statistics for three or four years’ run-off can be secured the 
sources of error can be minimised, and, while accurate discharge observations 
are more useful, a study of records of high and low water, or daily gauge 
readings, is not to be despised. 

Proportional Method. —This is, I believe, a relic of certain early, and 
now obsolete, rules for estimating run-off as 60, or some other percentage of 
the rain-fall. 


The method, as now applied, consists in calculating the ratio for 

each month of the year in which the observations were taken, and obtaining the 
run-off in other years by multiplying the rain-fall for each month by this ratio. 

The system does not appear to rest on any very logical basis, and has one 
grave defect, namely, a tendency to overestimate the yield of dry months and 
dry periods. Since the subtractive method tends to underestimate the yields 
of such periods, it is at any rate safer. 

I have taken pains to calculate the monthly ratios for many catchment 
areas over several years, and find that they vary far more than the correspond¬ 
ing losses. It may be that the method is applicable to certain somewhat 
peculiar catchment areas, but, so far as I have been able to ascertain, no 
engineer possessing several years’ records of rain-fall and run-off has been led 
to use it. 

The investigation of the question given in Connection with annual run-off 
statistics shows that if the rain-fall records do not, for any reason, correctly give 
the true fall on the catchment area, the proportional method of estimating the 
run-off acquires a spurious accuracy, which is apparently, and only apparently, 
greater than that of the subtractive method. 

The real deduction to be drawn is that where the rain-fall is accurately 
determined, the subtractive method is preferable. Where it is less correctly 
known, the proportional method has certain advantages, and especially in a 
case where the recorded value of the rain-fall is approximately proportional to, 
and somewhat less than the true value, the latter may prove to be the more 
accurate. 

The methods employed in practice by engineers are very accurately 
indicated by this method of reasoning. In the British Isles, and Germany, 
where the rain-fall is well determined, the subtractive method is usually 
employed. In France, the United States (until recently), and India, the 
proportional method is more common, and in these countries rain-fall observa¬ 
tions are relatively less accurate. 

Third Method taking into Account the Effect of Ground Water Storage on 
Run-off. —The importance of the storage of water in pervious strata and swamps 
has already been considered, and its general effect in partly equalising the 
monthly, and even (although less markedly) the yearly run-offs, is obvious. 



VERMEULE’S EVAPORATIONS 219 

Vermeule (.Report of Geological Survey of New Jersey , 1894) has 

endeavoured to treat the question systematically. While the difficulties are 
apparent, I consider that his methods deserve careful description, and believe 
that the most promising direction for future studies lies along his line of 
investigation. 

Let us consider the calendar year, and let suffix 1, refer to the month of 
January, suffix 2, to February, etc. 

For each month Vermeule specifies a quantity v=ax-{-d where x, is the 
observed rain-fall. Vermeule terms v , the “evaporation,” but it does not appear 
to be proportional to the evaporation from a free water surface, and is 
essentially analogous to what I have termed the “ vegetation and evaporation 
loss” (see p. 186) for the month. I shall hereafter refer to it as Vermeule’s v. 

Tabulating we have as follows : 

For the month of— 

January 
February . 

March 
April 
May 
Tune 

July .... 

August 
September 
October . 

November 
December 

Similarly, Vermeule gives for the: 

Six months, December to May inclusive, V< = 4"20+o-i2Xi 
Six months, June to November inclusive, V/= 1 i'3o+o'20;r/ 
and, for the whole year . . V v = 15-5 +o'\ 6 x y 

Here the V’s are also Vs, i.e. the above three expressions represent rain-fall 
losses which the individual^,U^) etc. do not. 

It is obvious that the three last expressions can only be applied when the 
rain-fall is distributed monthly month according to the proportions generally 
holding good for the climate of the Eastern United States. 

Vermeule also states that these figures can be applied to a climate where 
the mean annual temperature is approximately 497 degrees Fahr., and that, 
for any other mean annual temperature T, they can be adjusted by multiplying 
by a factor o’05T— i'48. 

I have tested the method by means of several well determined records, 
and believe that this statement is probably correct for the Eastern United 
States, but that the correction is not applicable to British and German 
examples. 

Now, tabulate x — v, for each month. This is not the run-off, and Vermeule 
now proceeds to discuss the ground-water factor. 


£>4 = 0-27 + 0-10x4 inches. 
£> 2 — 0’3 0 F o'iox 2 „ 

. £>3 = 0*48 + O’lOXg ,, 

£>4 = 0-87 + 0 *IOX 4 „ 

^5=1*87+0*20^5 „ 

• v 6 =2 ' 5 ° + 0-25x9 „ 

. £> 7 = 3-00 + 0-30*7 ,, 

. £>8=2-62+0-25^5 „ 

. £>9=1-63 + 0-20X9 „ 

• ^10 = o’88 + o*i2X 10 ,, 

• £> n = o-66 + o-iox n ,, 

. £> 12 = 0*42 + o-iox 12 ,, 






2 20 


CONTROL OF WATER 


He divides catchment areas into three classes. (See Sketch No. 52.; 

(i) Highland areas, of bold relief with no drift covering. (That is to say, 
areas which I class as underlain by impermeable strata.) 

(ii) Areas with a covering of drift, but no surface storage. (That is to say, 
areas underlain by permeable strata, and containing no lakes or swamps.) 

(iii) Areas covered with drift, and possessing surface storage. (That is to 
say, areas underlain by permeable strata, and containing lakes and swamps,) 
This last (except in formerly glaciated areas) is an unusual combination ; but 
it also covers such cases as granite areas with small lakes and large accumula¬ 
tions of peat. 

For each of the above Vermeule gives a curve connecting the run-off with 
x—v, and the “storage depletion.” 

I have found these curves difficult to use, and have consequently tabulated 


o 


_ o 


Sketch No. 52.— Curves of Discharge and Depletion, as given by Vermeule (after 
Vermeule), with Approximate Curves for Typical Permeable and Impermeable 
Areas. 

his data in a more useful form, and must therefore be held responsible for 
any errors. 

Vermeule considers the monthly run-off y, as consisting of two portions, 
x—v (taken with reference to its sign), and a contribution (positive, or 
negative) from the ground-water storage. The ground-water storage is 
supposed to have a maximum possible limit; and the magnitude of this 
contribution depends on D, the mean amount which the accumulated water 
storage, in the ground, or as snow, is below this maximum during the month 
under consideration. The term ground water is perhaps slightly inaccurate, 
for it is believed that Vermeule’s figures are somewhat affected by water stored 
up in the form of snow. 

The reasoning is precisely similar to that on page 190, except that v is 
written for ke p . We therefore put 

y=x—v+u 

where u is the ground-water flow, and is analogous to the quantity denoted 
by or —AR, ; , on that page. 





Urea 

of 

Wd h 

Met’ 






' drift 




1Z 








is 

20 

IS 

10 

OS 

0 

25 

10 

A5 

10 

OS 

c 









A 


Drift 

Coverec 

’ (tree 






fto . 

'iwamp. 

> 


1 













— 



Sand) 

r or Dri 

f f Com 

ed fire 

1 Mitl 


_ 




Siyami 

Storai 

>e 








3= 








Total 

Deplet 

on at 

dsrt 0 

r Mon ft 






























































VERMEULE S RUN-OFFS 


221 


—v y . . 

-is the mean 

2 2 


• X — 7 / V 

According to Vermeule,^ is a function of d -+ - where d, is the sum 

2 2 

of all the zz’s, since the period when the quantity of water stored up last, had 
its maximum value. Thus, d, is the depletion of the water storage at the 
beginning of the month, while d— (x—v)-\-y is the depletion at the end of the 

X 

month under consideration, and consequently, D =d - 

depletion during the month. 

Starting with some winter month (December, January, or February for 
choice), we assume the ground storage as full, and write y—x—v, until about 
i st of March (z>., the melting of the snows). 

Thus, for the earlier months of the year, we have : 

yi—x x —v 1 u x =o d x =o 

y 2 =x 2 — v 2 u 2 = o d 2 =°, etc. 

But when, under American conditions, the snows begin to melt, and x—v, 
is less than 2‘o, or 2*5 inches, depletion of the stored water begins, we have : 

tin 


yn — Xn V n T Ui 


dn — O 


d n +i — Un 


D n = 


where, in the cases considered by Vermeule, n, is usually 3. That is to say, 
the month of March. So that at the beginning of the second month after 
depletion commences (April) we have a depletion d n+x = u n ; and y n+ i is 
not equal to x n+x — v n+1 , but has a value corresponding to 

„ , x n + x —v n +\ . y?i+ 1 

-*-'«+1 — di+i 2 - ' 2 ’ 

which is plainly the mean depletion during the month, and there is a further 

depletion u n+ 1 =y n+1 — (x n+x — v n+1 ). So that at the end of the month the total 

depletion is d n+2 = u n +\- i rUn +2 ) and y n+2 the run-off for the (zz + 2)th month is 

that corresponding to : 

D dn\. 2 ~\~ dn+ 2 7 X n + 2 Vn +2 , J^n+ 2 
n +2 ~ —Un+2 ~ r ^ 

Thus the run-offs can be written down. 

As we advance in the year, we finally reach a period (roughly about August 
or September), when the run-offs corresponding to the obtained mean depletion 
become smaller than the quantities x—v. The ground-water reservoir then 
begins to fill up, and in a normal year we arrive at no depletion, or the 
“reservoir” is full up about December. In an abnormally dry year we will 
obviously finish the year with a certain amount of depletion, and, failing heavy 
rains in the early part of the next year, the run-offs of the following summer will 
be materially reduced. 

The process is a very excellent one, and the comparisons made by 
Vermeule with actual observations seem to me most satisfactory, provided 
that the rain-fall is accurately determined. Difficulties do occur, but they are 
not of great importance, and seem rather to indicate that calendar months 
are bad periods to investigate, being too long for the seasons when the de¬ 
pletions are small, and too short for such periods as the end of a dry summer. 

Vermeule has shown y, as a graphic function of D (see Sketch No. 52), which 
necessitates a process of trial and error in every case before y, can be selected. 

y x — v 

The general equation is : D=^ + z 4 -—, where di, is the initial depletion 










222 


CONTROL OF WATER 


v 

of the month considered. Thus, if di = o, x=r82, v— 1-05, we get D=^—0*38 ; 

and from the curve (Class I.) when y— 1*44, D=o - 34, and the initial depletion of 
the next month is given by 2D =y— (x—v)= 1*44—077 =o‘67 inches. 

The information given permits a table to be drawn up as follows : 


D 

y 

D- y - 

2 

O'O 

2'Q 

- ro 

0*05 

i '9 

- CC90 

O’lO 

i*8 

— o‘8o 

O’l I 

17 

-074 

o‘i8 

i*6 

— 0*62 

• I 


so that this transformation permits the tables of y, 


and T)—^=di ——— 

2 2 

as a function of 2 di—x — v, as given on page 224, to be obtained. 

A study of Vermeule’s curves of y, and D, however, is very useful, and we 
can deduce the following general rules for the construction of the curve ofy, as 
a function of D. 

(a) Determine the minimum month’s flow ever recorded in similar catch¬ 
ment areas, and call thisjKn. 

In America y n , is about o’15 inch in small (under 200 square miles), and 
0*20 inch in large catchment areas. 

In England, in catchment areas of 10 or 12 square miles y n , occasionally 
falls as low as o‘io, but o’15 is closer to the average, although 3 or 4 square 
miles of impermeable catchment area often yield no run-off for periods of 
three weeks. 

(b) Determine the maximum depletion of storage ever recorded, and call 
this S. S, is about 9 inches in a permeable area, but may be roughly estimated 
as one-fifth of the maximum oscillation of the ground-water level, and in 
impermeable areas a proportionate deduction must be made, although it 
should be remembered that even granite areas can hold about 2 to 3 inches of 
water in the clay and peat coverings which overlie the granite. 

Then (Sketch No. 52): 

(i) If there are no visible reservoirs, such as lakes or swamps : 

5 

Plot a straight line from y=y n , D = S ; toy = 2y n , D = — ; and continue this 


line by a circular arc, or parabola, up to the point D=o, y 0 = where y m is 

the total run-off of the winter months (six in number) during a series of 
years. 

(ii) If lakes or swamps exist, in the area : 

Let A, represent the whole area of the catchment area, and A u , the fraction 
of the area in which the ground-water level lies lower than the level of the 


water in the lakes or swamps. 


Calculate S„ = S %y„=y. 


Then, from 
















223 


CRITICISM OF VERME DIE’S METHOD 
D=o to D = Sthe curve is a parabola through D = o,y=y 0 , 
and D = S m ,j=j/ u . 

For greater depletions we construct the curve just as if it referred to an 
area for which the maximum depletion is S^i — and the initial point of 
the curve is y—y u . 

Sketch No. 52, shows diagrams thus obtained, and, if necessary, a table of 
y, and D, can be scaled off, and modified into a table of y , and 2 di—{x — v), as 
already explained. 

These curves agree very closely with those given by Vermeule, although 
differences of 10, or 15 per cent, in y, are likely to occur, especially when D, is 
small. The great advantage (which is inherent in Vermeule’s method) is that, 
provided that the curves are constructed with any reasonable adherence to 
probability, positive errors in one month will be largely compensated by 
negative errors in the next, and vice versa. 

We may therefore believe that Vermeule’s method produces really practical 
results provided that S, y n} and y 0 , are determined with some accuracy, and 
the only factor which requires even ordinary accuracy, is y 0 . 

The method is therefore a very excellent one, since it permits the run-off to 
be derived from the rain-fall by a process which takes into account the influence 
which the rain-falls and run-offs of the previous months undoubtedly possess ; 
while other processes usually regard each month’s rain-fall and run-off as 
isolated facts, or, at the best, as subject to influences which are assumed to be 
the same every year during corresponding periods of the year. 

The great difficulty is the determination of the v’s. This is probably best 
effected by careful studies of the observed run-offs, working with a preliminary 
curve ofy’s, and D’s, determined as suggested above. In this manner I find 
that while the mean annual temperature of the Thames valley is about 48*6 
degrees Fahr., the v’s, for this valley are approximately two-thirds of those for 
New Jersey. The ground flow begins in March, in place of April, as in 
America, and if this reduction is applied to other English catchment areas, so 
far as can be judged these catchment areas fall into two classes, for which 
figures are given on page 224. 

It must be distinctly understood that these figures are merely suggestions. 
They are deduced from principles which I certainly believe to be correct, and 
the results obtained by their employment agree better with actual experience 
than those given by any other methods. It is, however, plain that the data at 
present available are insufficient for the production of an accurate solution. 

The following appear to be the chief differences between American and 
European catchment areas, when the relation between y, and D, is considered. 

Firstly, in the typically Insular climates of the British Isles and Western 
Germany, the possible amount of storage is not so great as in the more 
Continental climate of America, because snow neither lies so long, nor 
accumulates in such masses. This difference may be regarded as climatic in 
its causes, and could possibly be allowed for. 

The second difference is due to artificial reasons. Most British and 
German watersheds are provided with a system of catchwater drains in the 
form of field and road ditches, and agricultural tile drains, of a character 
practically unknown in America. 


224 


CONTROL OF WATER 


Vermeule’s tables, arranged according toy, the run-off, are : 

VALUES OF 2 d -( x - v ). 


y 

For American Catchment Areas. 

For British Catchment Areas. 

Class I. 

Class II. 

Class III. 

Impermeable 

Strata. 

Permeable 

Strata. 

2*5 . 

% 

• • • 

- 2*50 

-2*50 


• • • 

2*4 . 

• • • 

- 2*30 

-2*30 


• • • 

2*3 . 

• • • 

- 2*05 

- 2*05 

• • . 

• • • 

2*2 . 

• • • 

- i*8o 

— 1 *76 

• • • 

• • • 

2*1 . 

• • • 

- I "53 

— 1*46 

. . . 

• . • 

2*0 . 

- 2*00 

- 1*27 

- 1*10 

• • • 

• • • 

1*9 . 

-i *79 

-0*97 

- 0*73 

... 

• • • 

i*8 * 

-i *57 

- 0*67 

- 0*27 

. . . 

• • • 

1*7 * 

- i *35 

-o *33 

o *35 

... 

-i *7 

. i*6 * 

- 1 *16 

0*0 

0*90 

• • • 

- i *4 

i *5 * 

- o*88 

0*30 

i*8o 

• • • 

- i*i 

1*4 * 

— 0*60 

0*70 

3*10 

• • • 

-0*7 

i *3 * 

-o *34 

1*10 

6*5 

- i *3 

-o *3 

1*2 * 

- 0*06 

l 'SS 

7*7 

-1*15 

0*05 

1*1* 

0*24 

2*06 

8*4 

- o *77 

o*6o 

1*0* 

0*56 

2*6o 

8-9 

— o *44 

1 *00 

0*9 * 

0*90 

3*34 

9*4 

— 0*10 

1 *70 

0*8 • 

1*25 

4*40 

9*9 

0*24 

2*90 

o *7 * 

1 *66 

7*20 

IO *5 

0*67 

5*60 

o*6 * 

2*14 

9*00 

11 * 1 

1*10 

6*90 

0*5 * 

2*66 

9*80 

12*0 

1*65 

8*30 

0*4 * 

3 * 5 ° 

10*70 

I 2*8 

2*55 

9*30 

0*3 * 

5 * 3 ° 

11 *90 

• * * 

5 ‘ 7 o 

10*30 


The following example of Vermeule’s method refers to a Canadian water¬ 
shed over which the mean temperature is 46 degrees Fahr. Thus, the v’s, for 
this area are 2*30—1*48 = 0-82 of the values of v, calculated from the formula 
when uncorrected for temperature. The rain-fall is the mean of 5 stations, 
which represent the area fairly well, and it is stated that the results agree 
tolerably closely with the actual run-offs (von Schon, Hydro-Electric Practice ). 

Observed rain-falls are stated in Column II., while the v’s, are calculated 
by multiplying the v, for the same month in New Jersey, by 0*82. For example, 
for January 1903, v— (0*27 + 0* 10 x 1*36) x 0*82. 

The filling up of this table (top, p. 225) is fairly obvious. The ground-water 
storage is assumed to remain full until the beginning of March, so that for the 
first three months y = x-v. In March it is assumed that the ground storage 
begins to contribute, and x-v = 0*70. Corresponding to this, for Class 
I • y 1 44 > so that 11, is o 74 ) producing a depletion of 0*74 at the beginning 
of April. During April, 2d-(x-v) = 1*48-0*10 = 1*38, and the corresponding 
run-off is 0*77. Thus each month is successively worked out. 



























MO NTHL Y R UN-OFFS 


225 


Month. 

Rain-fall x . 

Vermeule’s v . 

Difference x — v . 

Run-off y . 

Contribution from the: 

Stored Water u . 

Depletion at begin¬ 

ning of Month di . 

& 

1 

H, 

1 

Ss 

O 

<U 

> 

December 1902 . 

2’l8 

0-52 

VO 

'P 

M 

r66 

0*0 

0.0 

O’O 

January 1902 

i’ 3 6 

°’33 

1*03 

1-03 

O’O 

O’O 

O’O 

February 1903 

i’8o 

o *39 

1*41 

,•41 

O’O 

0.0 

O’O 

March 1903. 

1*19 

0-49 

070 

i *44 

074 

O’O 

— 070 

April 1903 . 

0^89 

079 

0*10 

077 

0*67 

074 

+178 

May 1903 

274 

1*98 

076 

0’62 

- CC14 

i* 4 i 

2’o6 

June 1903 . 

2-85 

2*63 

0-15 

0-56 

o’4i 

1 ’27 

2*39 

July 1903 . 

2-68 

3 ' 12 

- 0-44 

0-38 

0*82 

1’69 

3 * 9 6 

August 1903 

2 *87 

2 *74 

0*13 

0*33 

I ’20 

2-51 

4-89 

September 1903 . 

3‘54 

1 ’92 

I’62 

o *39 

- I * 2 3 

271 

3 * 8 ° 

October 1903 

3 ‘ 9 2 

i - ii 

2’8l 

1*13 

- 1-48 

1-48 

■> °' l 5 

November 1903 . 

0^96 

0’62 

0-34 

0*89 

O’O 

Full 

O’O 

December 1903 . 

4^28 

0*69 

3'59 

2’90 

O’O 

Full 

0*0 


Month. 

Eastern United States. 

British Isles. 

January 

X-, 

y 1 — 0*40 -f ~ 

X, 

^=0-50 + — 

February . 

x„ 

v, = 0'90+ — 

Xn 

4 / 2 = 070 -b — 

O 

March 

Xo 

y 8 = 1 *6o + - 

Xo 

3 's = o' 5 °+ y 

April .... 

x^ 

^ 4 =i ‘° 5 + 7 

X. 

4/4=0-15 + ^ 

May .... 

^6 = o - 75 + y 

>5 = 0*20+^ 

June .... 

■Xg 

^6 = 0 ‘ 3 °+ y 

x« 

>« = 0-12+7 

July .... 

x 7 

9 't = °' i 5 + 7^ 

.Xk 

y 7 = o’20 + — 

20 

August 

y 8 = o-i° + ^ 

Xo 

7 S “°-i 5 + y 

September. 

y 9 = o-io+-g 

Xq 

y q = o*2o h— 1 
^ J 40 

October 

X IQ 

Jio = °' I 5 + y 

jo 

+io = °'>5 + I0 

November . 

' 11 3-5 

X 11 

-I'll =:°'30 + —- 

December . 

+12 = °’ 4 ° + y 

X 

3 'i 2 = °' 3 ° + y 


i5 




















































2 26 


CONTROL OF WATER 


Special Monthly Formulce .—These formulas are open to the objection 
which has been already stated, namely, that the month does not really specify 
the same season in each year. Further, such formulae cannot take into account 
the special circumstances obtaining in previous months. Subject to these 
remarks, we obtain the lower table on page 225. 

These figures are only approximations, and it must be remarked that 
the American results for the months November to March, inclusive, and the 
British results for November to February, show distinct traces of a term 
in x 2 . 

This whole discussion will have been written to very little purpose, unless 
the reader is by now well aware that at the end of each hot season, and even 
more markedly at the end of a long period of small rain-fall ( e.g . the summer 
of the last year of a period of three dry years), the run-off is almost exclusively 
dependent on the stored water, and is consequently not so much a meteorological 
phenomenon as a geological one. 

Determination of Reservoir Capacity.— -The results obtained by the 
preceding methods are extremely inaccurate. When applied to existing records, 
by utilising observations over 5, or even 10 years, to predict the remainder of the 
series, errors of even 200 per cent, in the values of the flows for individual months 
are by no means unknown. The results for individual years, however, are better, 
and I believe that under favourable circumstances an error as large as 15 per cent, 
should but rarely occur, provided that the rain-falls of individual months (and in 
the case of heavy storms of rain, of individual days) are carefully considered. 

It is plain that the process is at best approximate, and is only sufficiently 
accurate for practical purposes, where a reservoir is constructed of a size 
sufficient to equalise the flow over a long period. When such a reservoir exists, 
errors in the determination of the flows of individual months are of minor 
importance, because overestimates at one period will probably be balanced by 
underestimates at another, that is supposing that care is taken to avoid unduly 
favourable assumptions. 

In climates of the type now under discussion, the general practice is to 
provide a reservoir of a capacity sufficient to equalise the flow over “ the 3 
driest consecutive years,” by which we understand those 3 years in succession 
of which the total run-off is less than that of any period of 3 years that is likely 
to occur during say 50 or 60 years. 

A solution of the problem can only be obtained by long experience, and the 
history of the question in Great Britain suggests that it is not yet completely 
solved. 

Hawksley (representing let us say the best available knowledge for the years 
1830-1860), gives the following : 

The mean annual rain-fall over a long term of years being x m , the mean 


annual rain-fall of the 3 driest successive years of this period is x 8I) = 


5-Y?i 


', and 


the mean annual run-off of these three years is y 3D ~ 


5 Xm • 1 

—15 inches 


expressed 


as inches depth over the catchment area. Then, the capacity of the equalising 
reservoir for 3 dry years, i.e. the reservoir permitting constant delivery at 
the daily rate corresponding to a delivery of the volume represented by 

v 3D , per annum, is represented by days’ supply. That is to sav 

v x 3 u 1 ’ 



EQUALISING EE SEE VOLE 227 

the reservoir capacity converted into inches depth over the catchment 
area is : 

- TOOQ inches = 274—= inches. 

365 ^3D 

{Note .—One inch depth over one square mile = 2,323,000 cube feet, say 
~3 million cube feet, and if this volume be delivered at a constant rate 
in a year the supply is 39,750 imperial gallons, or 47,700 U.S. gallons per 
day.) 

The general history of British waterworks during this period renders it 
probable that this capacity was insufficient. It is but rarely that we do not find 
on record that shortage of water occurred once in a generation, as indicated 
either by the curtailment of the hours of delivery to the houses, or by the 
installation of temporary additional supplies. 

The rule, however, allowed for a supply which satisfied the popular ideas of 
that generation. About the year 1870, the introduction of the practice of 
constant supply, combined with the fear of possible pollution, became general. 
Consequently, it was found necessary to enlarge, or supplement existing 
reservoirs. Rofe has proposed the following formula : 

Capacity = days’ supply = — °^~Cr = i*37T3d 0 - 67 inches 

is y 3 d 365 s!y$ d 

as representing these results, and also as sufficient to ensure delivery at the 
rate of9%), inches per annum during the driest probable three years. 

The rule (except in unusual circumstances) affords an adequate capacity for 
such a supply. 

In England, catchment areas of the necessary size, and reasonably free 
from pollution, affording the required volume, are becoming somewhat difficult 
to procure. Further, engineers no longer remain satisfied with securing the 
yield of the three driest years. Present circumstances, therefore, economically 
justify a larger expenditure of money, in order to obtain a greater yield. 

Consequently, we have a third rule, which appears to be very well 
represented by : 

Capacity =17 to r8jj/ 3 D 0 - 67 , 

# 

and which may be considered as the result of experience during the last 
droughts (1893-5, and 1905-7). 

We may classify and tabulate as follows : 

(i) Hawksley’s rule, applicable to cases where catchment areas are easily 

secured, and a temporary shortage of supply once in 30 years may be 
regarded as permissible. 

(ii) Rofe’s rule, where shortages cannot be permitted. 

(iii) An extension of Rofe’s rule, which allows of a somewhat greater (10 to 

12 per cent.) supply being delivered, but which is only economical 
when any enlargement of the catchment area is difficult to obtain. 


I tabulate the figures, under the assumption that yzv=x 3l >—14 inches. 






228 


CONTROL OF WATER 


Xm 

•*" 3 D 

y 3 d 

Hawksley’s Rule. 

Rofe’s Rule. 

New Rule. 

Number of Days’ 
Supply. 

Capacity in 

Inches. 

Capacity 

Q 

m 

12 

0 ) 

• H 

U 

be 

cs 

1-1 

<v 

> 

< 

Number of Days’ 

Supply. 

Capacity in 

Inches. 

Capacity 

Average yield y 3D 

Capacity 

in 

Inches. 

Capacity 

Mean yield 

70 

56 

42 

134 

I 5-4 

0*37 

144 

16*6 

°‘39 

2 1 to 2 2 

0*40 

65 

52 

38 

I 39 

14*4 

0*38 

149 

J 5’5 

0*41 

19 to 20 

°*39 

60 

48 

34 

144 

13*3 

0*39 

T 54 

i 4*3 

0*42 

18 to 19 

0*40 

55 

44 

30 

151 

12'4 

0*41 

161 

13*2 

0*44 

17 to 18 

°‘43 

5 ° 

40 

26 

158 

I I *2 

o '43 

169 

12*0 

0*46 

15 to 16 

o *45 

45 

3 6 

22 

167 

IO*I 

0*46 

179 

io*8 

0*49 

14 to 15 

°*47 

40 

32 

18 

177 

87 

0*48 

191 

9 *4 

0*52 

12 to 13 

0*50 

35 

28 

14 

189 

7*2 

0*52 

207 

8*o 

0*56 

10 to II 

0*52 

3 ° 

24 

10 

204 

5*6 

0*56 

232 

6*4 

0*64 

8 to 9 

o *57 

2 5 

20 

6 

224 

37 . 

0*61 

275 

4‘5 

o 75 

6 to 7 

0*65 

20 

16 

2 

250 

i *4 

0*69 

397 

2*2 

1*09 

3*5 

0*70 


The average year’s run-off in the last column is calculated from 

ym=Xm— 15 inches. 

It is believed that the above ratios may be accurately applied even in 
cases where the mean rain-fall loss differs from 15 inches; since, as a rule, 
where the rain-fall loss is abnormally low, the run-off is more than usually 
variable from month to month, and vice versa. 

A similar process of successive increase in reservoir capacity has taken 
place in Germany, and the Eastern United States. Intze’s earlier designs were 
for the utilisation of good catchment areas, of unusually large yield, with mean 
rain-falls from 35 to 45 inches, and losses of 12 to 14 inches. The available 
records were for 10 or 12 years, at the most, and the capacities, on the average, 
were approximately those given by Rofe’s rule. The later designs had 
frequently to be adapted to less favourable circumstances, and capacities 
similar to those given by the third rule occur. I am not, however, disposed 
to consider this as entirely due to Intze’s greater foresight, or more complete 
information, but believe that the present state of design in Germany is similar 
to that in England about 1885, and that future experience (combined with a 
greater development of water storage), will lead to an increase in the present 
capacities. 

A German stream is notably more variable than a British one, under 
similar circumstances ; and I consider that the difference of 10 per cent, 
between Hawksley’s rule, and Intze’s earlier designs, and between Rofe’s rule, 
and later German designs, is due to this fact, and that further experience will 
lead to the adoption of reservoirs of about 10 per cent, greater capacity than 
those shown by the new English rule. 

Catchment areas of the Eastern United States apparently bear the same 
relation to those of Germany, that those of Germany do to those of Great 
Britain, and storages 20 per cent, greater than those indicated by the British 































MASS CURVE 229 

1 ules appear to be advisable, allowance being made for the fact that natural 
storage in lakes is more common in the North-Eastern States, than in either 
Germany or Great Britain. 

Mass Curve. —The only accurate method, where the necessary records 
exist, is to construct a mass curve according to the plan laid down by Rippl 
( P.I.C.E ., vol. 71, p. 279). This is a diagram showing the total run-off 
horn a fixed date to any other date as ordinate, with the period elapsed as 
abscissa. The necessary data are therefore the measured run-offs, usually month 
by month, and these are best expressed as inches over the catchment area. 

A convenient scale for plotting is 1 inch = 10 inches of run-off, and 6 months ; 
but much depends upon the absolute magnitude of the average annual run-off. 

Having plotted the mass curve, we can find the storage required to permit 
any rate of draught up to the maximum possible, as follows : 

Lay off on the diagram straight lines at slopes corresponding on the scale 
of the diagram to the various rates of draught which it is proposed to study. 
Rule parallel lines from the mass curve at the various humps A, B, C, and note 
where these, drawn in a positive direction in time, again cut the mass curve at 
AE, BD, and CF (see Sketch No. 53). 

The vertical intercepts between these lines, and the mass curve, represent 
the total volume of the reservoir which has been emptied of water under such 
circumstances. The horizontal distances between A, and E, B, and D, C, 
and F, indicate the periods during which no water escapes from the reservoir, 
which is evidently full at A, and again full at E, etc. 

This having been done, a study of the diagram will show what year (or 
period of years) covers the time when the reservoir is most depleted, which is 
consequently the most critical period. 

This critical period should now be re-plotted on an enlarged scale, and 
correction should be made for evaporation if necessary ; either assuming a 
water surface of constant area, or, better still, calculating from the volume of 
the proposed reservoir site, and the results of the preliminary mass curve, the 
water surface during each month, and correcting for the evaporation from this 
variable water surface. In either case, it will probably be necessary to bear 
in mind that the original run-off records are already subject to a certain 
amount of water surface evaporation, due to the exposed surface of the 
existing reservoir. 

Then, the storage capacities required to supply any given draught are easily 
obtained by repeating the original process. Or, if refinement is considered 
advisable, the result of a variable draught, such as is called for in the supply 
of water to a town, may be studied, by substituting a curved draught line, 
plotted like a mass curve, for the straight lines AE, etc. 

The results of the process are most interesting. Freeman’s Report on 
the Water Supply of New York shows clearly how important a chance down¬ 
pour (or rather, its accompanying run-off) may become, when an attempt is 
made to develop the utmost possibilities of a catchment area by large storage. 

Let us now consider the general characteristics of a mass curve. In every 
year there is a season when the run-off reaches its maximum, and these 
seasons succeed each other at intervals of approximately 12 months. Thus, 
we find a series of more or less prominent humps on the mass curve, following 
each other at intervals of nearly 12 months. 

Let us connect up B, C, D, E, &c., the tops of these humps, by a series of 


23 o CONTROL OF WATER 

straight lines, BC, CD, and DE (See Sketch No. 54). Then, the various 
intercepts such as /F', gG\ and hW, between these lines, and the mass curve, 



Sketch No. 53.—Shows a mass curve plotted for the Croton (New York) 
records (see Freeman ut supra) during the droughty period 1879-84. 

The upper curve C K L is that actually observed, the lower curve C G N shows 
what might have occurred had the heavy rains of September 1882 not replenished the 
reservoirs. It will be seen that assuming a supply of 18 inches per annum as shown 
by the line O M ; there will be a depletion of 97 inches (approximately 217 days supply) 
about January 1881, and that failing the rains of September 1882 a somewhat larger 
depletion (approximately 240 days supply) would occur about January 1883. A supply of 
17 inches per annum, as shown by the line O N, can however be obtained with safety 
if a reservoir of 10 inches capacity (allowing 10 per cent, for water below draw-off level) 
be provided. 

The lines A E, B D represent supplies of 16 inches per annum, and this supply can 
plainly be obtained with certainty since the reservoir is refilled each year under the 
actual circumstances, though once in a century it is probable that the reservoir will not 
overflow for two years in succession. 






















YEARLY MASS CURVES 


231 



Sketch No. 54 is founded on the records of the Redmires (Sheffield) catchment area, 
as given by Marsh ( P.I.C.E ., vol. 181, p. i). The curves plotted are : 

(i) Monthly mass curve for the year of minimum run-off (1887). 

(ii) Yearly mass curve for the five years’ period 1886-90. 

(iii) Monthly mass curve (shown in two pieces) for the droughty period May 1st, 
1904, to January 31st, 1906. 

The first curve shows that the maximum depletion, if the year’s run-off of 15 ‘50 
inches be drawn off equably, occurs about October 1st, 1887, and that the equalising 
reservoir should have a capacity of 4*25 inches, as shown by the intercept A A' 
(27*4 per cent, of the year’s yield). 

Similar monthly mass curves are then set off about the yearly mass curve, or 
polygon O a /3 y S e obtained from Marsh’s records of the run-offs of the calendar years 
1886-90 inclusive. On this assumption, which is plainly a very unfavourable one, 
we obtain a mass curve with humps B, C, D, E, at the dates January 31st, 1886, 
January 31st, 1887. Joining up the humps January 31st, 1887, and January 31st, 
1890, we obtain the line B, E, representing an equalised supply at a rate of 22*94 inches 
per year, which, owing to the assumption already indicated, is slightly in excess of 
2273 inches, the mean yield of the three calendar years 1887-1889. If the monthly 
variation of the run-off be neglected, the depletions are plainly represented by intercepts 
such as Ff G g, H/i. Allowing also for the monthly variations we obtain the depletions 
FF', GG', HII'. The capacity of the equalising reservoir therefore, for these three 
years, is FF', the largest of these ; and is approximately 8*6 inches. 

The period plotted does not include the three driest years in the record, which 
were 1904-06, and which produced a mean yearly run-off of 21*20 inches. The 
example, however, forcibly illustrates the theoretical difficulties introduced by tabulating 






























































































232 


CONTROL OF WATER 


the run-offs by calendar years, although, since records of the monthly run-offs are always 
available, the difficulty does not occur in actual practice. 

The curve KLMN, shows a very droughty period, where for 21 months the run-off 
averaged 1 *55 inch monthly (i8'6o inches yearly). The line KN, shows the effect of a 
drought at this rate, producing a depletion OCT, of 4*77 inches, about October 31st, 1904, 
and PP', 4’6 o inches, about October 31st, 1905. The lines LM, and QR, on the other 
hand, show how the year 1905, although yielding 20 inches, required only 3*31 inches 
reservoir capacity (RP / ) to equalise its yield, in place of the 5*48 inches that a year of 
equal total yield but with a monthly distribution similar to that of 1887 would require. 


represent the storage required to deliver, during each period, a constant supply 
equal to the mean yield of the (approximately) one year interval. Now, with 
very rare exceptions it will be found that for mass curves similar to those 
obtained from climates such as are common to the North Eastern United 
States, the British Isles, and Germany, this “equalising storage” for any such 
period is between 30 and 45 per cent, of the total yield of that period, 
approximately a year. The lower value is appropriate to British conditions, 
and the higher to those prevailing in the Eastern United States. 

Let us now examine the simplified mass curve formed by the series of 
straight lines, which is that which would be obtained by considering, as the 
unit of time, the periods from one yearly hump to the next in succession, 
in place of one month as previously. The storage capacity of the equalising 
reservoir required for any yield less than the mean annual run-off can be 
determined from this simplified mass curve by the usual construction, and 
it is evident from the diagram that : 

The storage capacity for the original monthly, or (for that matter) daily 
mass curve say, FF', is equal to the storage capacity for the simplified, or 
yearly mass curve, say, F/"plus f¥\ the storage capacity necessary to equalise 
the yield of the year in which the reservoir is drawm down to its lowest level 
(see Sketch No. 54). This, abnormal circumstances apart, is invariably the 
year during which the run-off is a minimum. 

Now, we can, with very fair approximation, plot the simplified, or yearly 
mass curve, from the rain-fall records, by the rules already given. 

Thus, we arrive at a graphical construction for the required approximate 
storage capacity as follows (Sketch No. 55): 

Plot a yearly mass curve, where for definiteness the total run-off of each 
calendar year is set off on the line representing the 31st December, or, better 
still, of each water year on the line representing the end of that water year. 
P rom this find the storage capacity for the given yield (including evaporation 
and percolation losses), and note in what year the maximum depletion occurs. 

Then, the total storage capacity required is : 

Storage capacity obtained as above, plus 30 to 45 per cent, of the gross 
yield of the year during which the maximum depletion occurs. 

This rule appears somewhat rough at first sight when compared with the 
more accurate results obtained from the monthly mass curve, but it is in reality 
more correct than it seems, for two reasons. The only uncertain factor com¬ 
pared with the result of the method of monthly mass curves is the second term, 
the 30 to 45 per cent. Now, the maximum depletion of the reservoir almost 
invariably occurs during a very dry year ; and the monthly distribution of the 
run-off during very dry years differs inter se , far less than the monthly dis- 









EQUALISING RESERVOIR FOR DRIEST YEAR 233 

tribution during years selected at random differ mter se, so that the figure 
30 to 45 per cent, is far more constant than might at first sight be expected. 
We can also make our approximation a little more definite by carefully 



Sketch No. 55. —Yearly Mass Curve, Yearly Equalising Reservoir, for Redmires, 
1898-1906, with Mass Curve and Equalising Reservoir for the worst Case recorded 
by Deacon (after Deacon), and for Thames in 1887. 


considering the rain-fall for the two or three years during which the above 
construction shows maximum depletion as most probable. I am of the opinion 
that a consideration of the monthly rain-falls is too uncertain to be of practical 

















































































234 


CONTROL OF WATER 


value, unless it so happens that we possess a good rain-fall and run-off record 
for a catchment area of very similar characteristics. 

The following work is of utility, and is advantageous as fixing the position 
of the humps more accurately than a mere examination of the average of years. 
Assume the year, for Temperate climates, as divided into : 

(a) The period of active growth. 

(b) The replenishing period, during which vegetation is inert, but the 

ground is being saturated with water. 

(c) The storage period, during which vegetation is inert, and the ground 

is more or less saturated with water. 

Now, during (a) the rain-fall loss is fairly easily calculated as follows : 

The consumption of water by vegetation, is given by Risler as : 

Meadow grass from o'122 to 0*287 inch daily 


Oats 


0*140 

jj 

0*193 

jj 

Lucern . 

jj 

° -I 34 

5 } 

0*267 

j j 

Clover . 

)) 

0*140 

JJ 

0*200 

»j 

Indian corn . 

>> 

0*1 10 

5 ) 

o*i 57 

jj 

Vines . 

)> 

°*°35 

JJ 

0*031 

jj 

Potatoes 

j) 

0*038 

JJ 

°’°55 

jj 

Wheat . 

>> 

0*106 

JJ 

O'l 10 

jj 

Rye 

)> 

0*091 



jj 

Oak trees 

jj 

0*038 

JJ 

0*035 

jj 

Firs 


0*020 

JJ 

0*043 

jj 


From this, and from an estimate of the area covered by each species of 
vegetation, we can infer the requirements during period ( a ). 

These, in a dry year, will usually be very close to, if not greater than, the 
rain-fall during period (a). Consequently, excluding possible intense falls on 
individual days, caused by thunder-storms, the run-off due to rain-fall in period 
(a), of a very dry year, is quite small, or nil, or possibly even an apparently 
negative quantity. 

The actual run-off during this growing period is derived from ground- 
water storage, and it will be found that the value is very nearly constant at 
about i£ inch, over the catchment area, when the rain-fall is equal to the 
crop requirements, plus evaporation from any free water surfaces that may 
exist. In a very dry year, such as we are now considering, part of this 
1 i inch may be absorbed in supplying the requirements of vegetation. 

Thus, on the average, we may say that in Europe during the period April 
or May (according to latitude and climate) to August or September, the 
following figures represent the bare minima of rain-fall that will suffice to 
supply the requirements of vegetation (Rafter, Report on Genesee Storage ). 


Tilled land 

. Average, 

10*3 

inches 

Meadows 

• j j 

16*0 

99 

Woodland and forest 

• jj 

3*7 

99 

Miscellaneous . 

• jj 

5-8 

99 






CONSUMPTION BY VEGETATION 


2 35 


If the rain-fall is equal to these values a total run-off of about inch will 
probably occur, but the ground will become so dry that at least inch of rain 
will later be absorbed by the dry soil after the drought ends, before any increase 
in the stream flow can be observed. If the rain-fall is less than these values, the 
vegetation will wilt and suffer from drought, and while the streams may still 
yield i| inch total run-off (especially if the permeable beds are covered by a 
thick coating of soil so that the ground water is not easily reached by the roots 
of the vegetation) yet all the deficiency in rain-fall and the ih inch must be 
made up before the stream-flow increases. 

It will therefore be evident that it is inadvisable to consider that the total 
run-off of the growing period exceeds inch unless the rain-fall markedly 
exceeds the values given above. In view of the facts regarding the replenish¬ 
ment of soil moisture it is plain that safety can be secured (if evaporation 
calculations are neglected) by considering the ii inch of run-off as occurring 
during the last month of the growing period. 


25 


20 


15 


10 



So 

de 

0\ 

s rn 

n 18. 



N 




/-as. oac< 

1 


OvCi 

is h 

'ire/ 

flhc, 

'orq 

ini 

902 


At 


1 




Si 

i#1 



V.S 

fqu 

T% 

jflSI, 

’=21 

'lot 

ven 

f/ar 

oir 

i Runoff 


/ 

e 

fUd! 

R8t 

•sine 

r ol 

Res 

ilea 

ern 
rs h 

’un8i 

9701 

V 

1 

/Jr 

7 l 

\ 


1 








1 




80.000 

f 

§ 






A 



• 

1 

s 

> 

/ 







/ 

* 

* 

s 

* 


l 

N 

/s 



68,000 

3 





\ 

V 

vf 


/ 

/ 

/ 

4 







✓ 

V 

V* 

s 

s 





40.000 



J 

< 

id 

f' 


/ 

/ 

/ 

/ 





$ 




\/ 

• - 

~58 

Jdl/] 

'-27 

'ing 

X o> 

Res 
' ge< 

eru 

irs 

ir 

tun, 

rtf 

e 0.000 

Vj 

l 


\ 

/ 


1 / 
/ / 
1/ 

/ 








1 

K 

$ 

ffe 

& 

7)S(. 

4 

'hei 

3 

d . 
1 

fesi 

3 

r/6 

4 

tf/, 

M. 

■) It 

4 

% 

. A 


"1 

1 


3 

\ 

% 

4 


4 


4 


Sketch No. 56.—Mass Curve and Equalising Reservoirs for Saale, in 1874, 
Remschied in 1890 (German), Ovens (Victoria), in 1906. 


During the period ( b ) the ground water has to be replenished. The 
actual loss mainly depends on the character of the strata, whether permeable, 
or impermeable, and it may be remarked that when in period {a) the run-off is 
indicated as an apparently negative quantity, this deficiency must be made up 

. , _ ' , ' . run-off r , 

before any run-off is assumed. The actual percentage of — . after the 

i| inch has been made up, varies according as the rain falls in bursts, 
or in steady drizzles. In the first case, a high figure may be assumed. In 
the second, a very low one, on the average say 10, to 20 per cent. In actual 
practice, the daily rain-fall records of exceedingly dry years during the first 
month or so of this period should be studied. 

In period (c) we can assume that 60, to 70 per cent, of the rain-fall appears 
as run-off, plus a certain soak out or contribution from the ground storage, 
if the rain-fall of period (b) has been heavy. 

Towards the end of period (b) this soak out may also occur, but its quantity 


































































236 CONTROL OF WATER 

is uncertain. If the calculated rain-fall loss in the two periods (a) and (b) greatly 
exceeds the assumedly known mean annual rain-fall loss, it may be necessary 
to consider this excessive amount as replaced by a gradual soak out during 
period (c). I believe that this is the only help that ground storage can usually 
be relied upon to afford towards the end of a very dry period. 

The assumptions are obviously unfavourable, especially in that their nett 
effect during periods (b), and (e), is to cause the run-off to lag behind the 
rain-fall, and during this delay the consumption draught continues to deplete 
the reservoir. In cases where the margin of safety is small, it will be necessary 
to consider the daily rain-falls carefully, since, in such instances, an intense 
downpour is frequently the salvation of a water supply. Nevertheless, it 
should be remembered that after a dry summer the depleted ground storage 
has, sooner or later, to be made up, and the best we can hope is that the 
reservoirs being low, they may obtain replenishment from the ground water 
somewhat more readily than is usually the case. 

We thus obtain figures for the run-off as distributed over the three periods, 
and can plot them as occurring at the beginning of the final month of each 
period, without any great error. Thus, we get a very fair idea of the positions 
which the humps assume during the critical period of depletion, and also 
learn whether the storage necessary to equalise the yield over the driest 
year materially differs from 30 to 45 per cent, of the total yield of that 
year. 

If the available records are plotted either in monthly or yearly mass curves, 
certain general principles become apparent. 

(i) Firstly, apart from the evidence of an unusually dry series of rain-fall 
years, as indicating a probable sequence of years of small run-off, it appears that 
fully 40 years’ records are necessary before we can be certain of having, even 
approximately, experienced the maximum depletion of a very large reservoir. 

(ii) In Temperate climates, at any rate, it seems that if we attempt to 
develop a catchment area by storage, so as to yield considerably more than 
the average of three dry years, the effect of a chance flood, such as may be (and in 
the case of the Croton Reservoirs, actually was) produced by a series of summer 
thunder-storms, is so great that it is inadvisable to equalise the yield over 
perhaps more than five years. This, it should be remembered, will mean that 
no water will escape from the reservoir for periods of nearly five years on 
end. 

(iii) It also appears that these developments lead to reservoirs of so large a 
capacity that, unless the topography is unusually favourable, the exposed water 
surface forms so high a percentage of the catchment area as to cause the 
effects of evaporation to be unduly marked. 

An attempt has lately been made by Messrs. Gore and Brown {The Central , 
October, 1910), to arrive at a scientifically correct method of calculating the 
capacities of reservoirs. The method adopted is as follows : 

The rain-fall record for a long period is treated by the methods of frequency 
curves developed by Pearson, and the probable value of the rain-fall for 
the driest year of a century is calculated. Similarly, the probable values of 
the average rain-fall of the two consecutive, three consecutive, etc., driest 
years of a century are calculated. 

The method is obviously a refinement of Binnie’s studies upon the 
variability of rain-fall (see p. 176). 


PROBABILITY METHOD . 


237 


The figures arrived at for a century, from a 72 years’ British record, are : 
Driest years’ fall=0*69 of mean annual rain-fall. 


Average of 2 consecutive driest 

years’ 

fall— 074 

of mean annual 

rain 

>> 

J 


33 

= 077 

33 

33 


4 

33 

33 

=o*8i 

33 

33 

5 ) 

5 

33 

33 

= o‘85 

33 

33 

33 

10 

33 

33 

=0*90 

33 

33 


The annual rain-fall loss is assumed as constant, and the equalising 
reservoir for the driest year (see p. 232) is taken as 30 per cent, of that year’s 
run-ofif, as calculated on the assumption of a constant rain-fall loss of 15 inches 
per year. This figure of 30 per cent, is obtained from the worst recorded 
English years’ flow, as given by Deacon ( Ency. Brit., article on “ Water 
Supply”). (See Sketch No. 55). 

The method is applied in the following manner : 

x m —66'$ inches 2’™= 15 inches, so that _y nl = 51*5 inches 
and the minimum y, is about 30*9 inches. 

The equalising reservoir for that year is about 9'3 inches capacity. The 
reservoir capacities required for any other supply are then determined by the 
mass curve method already explained. The results agree very well with Rofe’s 
rule when the three dry years’ supply is considered, and the equalising reservoir 
necessary to give a yield at the rate oiy m , over the whole century has a capacity 
of 103 inches, say 730 days’ supply. 

The circumstances assumed are favourable. For instance, Pole (“ Lectures 
on Water Supply”) found 930 days’ supply for a case where x m , was apparently 
45 inches, and y m , was 14 inches. Freeman’s mass curve for the Croton 
Reservoir indicates that approximately 1040 days’ supply is required. 

The method is logical, and can be applied to any circumstances when the 
requisite information is obtainable. 


Locality. 

Area. 

Number 

of 

Years. 

Xm 

2»t 

Remarks. 

Reference to 
Original 
Authority. 

Torquay, 

961 

2 3 

4o - 8 

i6"i 

Very accurate. 

Ingham, 

Devon 

acres 





Ra in-fall 



Min. 

2 y 5 

I 3 ‘ I 

Driest year 

and Evap- 






also. 

oration in 



3D 

34'3 

I 5*2 


Devotishire. 

Thames 

3855 

18 

26*4 

i8 '3 

Very accurate. 

P. /. C. E., 

Valley 

square 





v 01. 167, 


miles 





p. 190. 



9 

2 7*0 

l 8*5 

Do. 

Binnie, Re- 



Min. 

2 2‘8 

17*5 


port on 



iD 

21*3 

1 3 '6 


FI ow of 







Thames. 


[ Table continued 


















238 CONTROL OF WATER 

Table continued ] 





Number 



* *- v q * 

Reference to 

Locality. 


Area. 

of 

Xm 


[Remarks, g 

Original 




Years. 



Authority. 

Woodburn, 


3405 

14 

3 8 *4 

13*7 


Leslie, Ti'ans. 

Ireland 

acres 

Min. 

28*8 

I4‘2 

Driest year 

of Roy. Soc. 




3D 

32-8 

13*7 

also. 

of Scotland. 
1870-71. 

Wandle 

• 

• • • 

14 

• • • 

21*5 

Tributaries 

B. Latham, 
Q.J. Me-- 






of Thames. 

Graveney 

• 

• • • 

14 

• • • 

19*7 

Accurate. 

teorologica l 
Soc., 1892. 

Entwhistle 


3 ’ 2 

24 

5 T *5 

170 

It is suggest- 

Swindlehurst, 



square 




ed that the 

Trans. As- 



miles 




gauges 

soc. of 

Heaton 


• • • 

24 

39 * 8 

127 

show less 

Water- 

Belmont 


2 ‘8 

24 

57 *o 

i6'9 

than the 

Works' 



square 




true rain- 

Engs., vol. 



miles 




fall. 

8, p. 12. 

Rivington 


• • • 

5 

43*9 

io*4 

These are 

Binnie, Lee- 

Longendale 


• • • 

12 

5 2 ’4 

9*5 

abnormal, 

tures 0 n 







but Mr. 

Water 







B i n n i e’s 

Supply. 







authority 
is high. 



r 

35 1 

3 

25-8 

20*1 

Three dry 

Hutton, 

Exmouth, H 


acres 




years. 

Engineer. 

Devon 


290 

3 

26'I 

177 

Do. 

July 16, 

Warrington 

l 

acres 





I 9°9 


• • • 

1 

2 7'5 

i9 - o 

Very dry year. 

P. I. C. E., 




1 

2 5-5 

i8’o 

Do. 

vol. 52, p. 34 

Whittledean 


• • • 

r 

i 7*7 

n *4 

Do. 

Do. 

Sheffield 


5 °°o 

3 

35 *o 

15*01 

Dry years, 

P. I. C. E., 



acres 




very accur- 

vol. 167, 







ate. 

p. 212. 

Do. 


• • • 

1 

... 

i 5 *o 5 

Do. 

The rain-fall 



• • • 

1 

36-5 

T 5*5 

A c c u rate, 

is not given 







possible 

in original 







error 0*3 

reference, 







inch. 

but is ab- 



• • • 

1 

34*9 

16*o 


stracted 



Larger 

1 

3 I ‘ 7 (?) 

15-6 


from Sy- 



area 





mon's Brit. 
Rain - fall, 

Rotherham 


• • • 

2 

2 i *3 

18*6 

Dry years. 

I 9 ° 5 - 

Do. 

Doncaster 


• • • 

3 

25*8 

22 *3 

Do. 

Do. 


[ Table co7itinued 






















RAIN-FALL LOSSES 


2 39 


Table continued T] 


. 1 

Locality. 

Area. 

Number 

of 

Years. 

Xm r 

2 m 

Remarks. 

Reference to 
Original 
Authority. 

Northampton 

• • • 

I 

• • • 

I7*0 

First year 
after con¬ 
struction. 

• • • 

Boston, 

Lines. 

1920 

acres 

2 

16*6 

iy 6 

Two dry 
years. 

Rodda, Notes 
on Water 
Supply. 

Leicester 

10,760 

acres 

3 

217 

i 5'5 

Three dry 
years. 

Trans, of 
W a t e r- 
Works’ 
Engs., vol. 

7, p. 191. 

Unspecified 

6000 

acres 

17 

Min. 

3D 

61 *o 
41*9 
56*8 

14*0 

io‘6 

20*4 

Driest also. 

• • • 

• • • 

Do. 

572000 

acres 

5 

20*4 

12 *8 

• • • 

Unwin, Hy¬ 
dra u lies, 

’P- 2 49 

Hallington, 
Northum - 
berland 



3 8 ’ 9 

27*6 

Loss from 

1 9 t2 to 
iyid Max - 
recorded in 
England 

P. I. C. E., 
vol. 52,Vp. 
34 


Catchment Areas situated in Climates of the Second Type— The 
second type of climate (i.e. a well defined wet season succeeded by a well 
defined dry season, during which the catchment area becomes thoroughly dry) 
occurs over nearly the whole of India. 

The best records exist in the Reports of the Bombay Public Works 
(Irrigation) Department, and refer to the large storage reservoirs which are 
used for irrigation in the Deccan. Some records also exist of reservoirs for 
town water supply and irrigation in Rajputana, and the Central Provinces. 
The information has been collected by Strange {Indian Storage Reservoirs ), 
and the table on page 241 gives his ideas on the subject. 

It will be noticed that if the wet season rain-fall exceeds 48 inches, the 
increase in run-off produced by 2 inches extra rain-fall is greater than 2 inches. 
This seems somewhat peculiar, but is not necessarily impossible, especially if 
the catchment area is permeable. The difficulty does not occur in average, or 
bad catchment areas. It will be plain that it is hardly safe to reckon on any 
run-off if the wet season rain-fall is less than 10 or 12 inches, and that the dry 
Season rain-fall has no appreciable effect on the 1 un-off. 

The method adopted is plainly an assumption tha.ty—px, where/, increases 


















24 o CONTROL OF WATER 

UNITED STATES CATCHMENT AREAS IN CLIMATES OF FIRST TYPE. 


Locality. 

Area in 
Square 
Miles. 

Number of 
Years. 

Xm 


Remarks. 

Sudbury 

75 ’ 2 ° 

2 3 

45 ‘ 8 

23*6 

All these (except the 

Z — 20'0 + 0*08^^ 


Min. iD 

32*8 

21*6 

Croton) and many 



2D 

34 ' 1 

21*4 

others are tabul- 

’ t • 


3 d 

38*8 

22*2 

ated in the Report 

Cochituate 

190*0 

35 

47*0 

26*7 

on the Erie Canal 



Min. iD 

3 1 ’2 

21*1 

of 1908. The dif- 

I + o'2\X 


2D 

35 ‘8 

23*2 

ferences in areas 



3 D 

38-3 

2 3*5 

make the facts very 

Mystic Lake 

27*70 

20 

43 ' 8 

24*0 

useful as showing 



Min. iD 

3 1 ’ 2 

21*9 

how small influ- 

14-3 + 0*23* 


2D 

35 ’ 2 

23*0 

ence this factor 



3D 

37 ‘ 2 

21*3 

has on the yearly 

Passaic 

822*0 

17 

47*1 

21*6 

means. The gen- 

2 = 1 c*8 4- 0*12.# 


Min. iD 

35 ‘ 6 

20*4 

erally higher values 



3D 

3 8 ‘9 

20*8 

for 2 , than English 

Tohickon 

102*20 

14 

5 0 * 1 

2 1*4 

or German areas 

Z — IO ’2 0*2 2X 


3 d 

3 8 ’4 

24*2 

of approximately 






the same mean 






temperature, are 






explicable by the 






fact that the sum- 






mer temperatures 






are much higher 






and the winter 






much lower. 

Croton 

33 8 ‘° 

32 

48*1 

25*1 

Freeman’s Repoi't 



Min. iD 

36*9 

2 4'3 

on Water Supply 

z = 20*5 4- o'ix 


2D 

42-3 

21*3 

of New York. 



3D 

42*3 

20 'O 



as x, increases. The rule does not agree with the results obtained in climates 
which belong to the first type. I have therefore endeavoured to find whether 
any formula of the type : 

y—x—a — bx 

can be discovered. The results are not encouraging, and there is no doubt 
that for the present the proportional method must be adopted for preliminary 
work. This fact is not surprising, for it must be remembered that the records 
of rain-fall are not as accurate as could be desired, as the rain-gauge stations 
are sparsely distributed, and are usually lacking at the very places where the 
rain-fall is greatest. It may indeed be said that most of the records are 
those of valley stations, and that most of the run-off is provided by the 
rain-fall on the neighbouring hills. Thus, a priori, the proportional method is 




































RAIN-FALL LOSSES : 

EUROPEAN CATCHMENT AREAS IN CLIMATES OF FIRST TYPE. 


Locality. 

Area. 

No. of 
Years. 

X)n 

z m 

Remarks. 

Reference. 

S. Norway . 


2 5 

3 8 ’ 4 

io ‘6 


Tech. Uge- 

Germany— 

. 





blad , 1907 

M e m e 1 

46,050 

8 

26"I 

15-8 

Very accurate. 

Ztschr.D.I. V., 

Delta 

acres 

! 





13th July 







1909. 

Murgtal . 

• • • 

!5 

6 ri 

24-9 

Very wet. 

Die Wasserk. 


— — 





Anlage in 







Murgtal. 



i 5 

72-8 

3°’9 

Stream fre- 







q u e n 11 y 


Freiberg 

3 0 ’ 10 

21 

3 r 3 

I 9*5 

dries. 


Res. 

sq. miles 







See also Keller’s results, 

page 208. 


Italy— 







Delta of 

io,5°o 

10 

28*5 

18-1 

Accurate. 

P.I.C.E.,v ol. 

Po 

acres 





47 > P- 147 


125,000 

1 

24'0 

i8'o 

Dry year. 



acres 

1 

41 - o 

25-8 

Wet year. 


France— 

Sq. miles 






Mousson . 

i6 3'5 

• • • 

29*0 

17-4 

For these references and 

Var 





their computation in 

(Vosges) 

167 


2 9'5 

177 

English measure I am 

Meuse 

607 


3 i -5 

i 7'3 

indebted to the “ Report 

Somme 

2140 


2 5 ‘ 2 

I2'4 

on Barge Canal,” referred 

Arde 

2510 


2 7‘5 

I 5‘4 

to on p. 

240. An ex- 

Escaut 

2 545 


23-6 

I 3 ‘° 

animation of the original 

Moselle . 

2600 


2 9'5 

20-3 

authorities 

led me to 

Meuse 

2896 


28*3 

i 6*2 

reject three of the in- 

Do. 

8480 


4 2 '5 

217 

stances as 

being doubt- 

Vilaine 

3475 


2 7'5 

13-2 

ful. 


Charente . 

3866 


33*4 

217 



Saone 

11 5 5 1 

4 

32-6 

127 



Seine 

27460 


24*1 

T 7‘ T 



Garonne . 

32820 


3°'4 

14'6 



Gironde . 

35 °°° 


32-3 

l6'2 



Rhone 

38100 


37’4 

T 5 ' 8 



Do. 

... 


3 6 '3 

i 3*5 



Loire 

44500 


27-2 

16*1 



Durance . 

• • • 

17 

32*1 

IO’I 

Relation is 2 = 

= 10*2 - O’O^JX, 






so rain-fall is probably 






underestimated. 

Montaubry 

• • • 

15 

33 *o 

2 3'5 

s = 13-8 — o*24.t, therefore 






rainfall underestimated. 






The stream dried 11 times 






in the 15 years. 


16 

































242 


CONTROL OF WATER 


o 

<o 


5 ? 




o 


o 

fVi 



'O 








Q> 

<\l 


Sketch No. 57—Typical Relations between Total Monsoon Rain-fall, and Total Run-off, in India. 



































SECOND TYPE OF CLIMATE 


243 


STRANGE’S TABLE SHOWING THE PERCENTAGE OF RUN-OFF TO 
MONSOON RAIN-FALL, AND DEPTH OF RUN-OFF DUE TO RAIN¬ 
FALL IN INCHES, FOR A GOOD CATCHMENT AREA. (See Sketch 57.) 

hor an average Catchment Area, take three-quarters of these figures. 

For a bad Catchment Area, take half these figures. 


Total 
Monsoon 
Rain-fall in 
Inches. 

Percentage 
of Run-off to 
Rain-fall. 

Depth of 
Run-oft' due 
to Rain-fall 
in Inches. 

Total 
Monsoon 
Rain-fall in 
Inches. 

Percentage 
of Run-off to 
Rain-fall. 

Depth of 
Run-off due 
to Rain-fall 
in Inches. 

1 

0*1 

0*001 

26 

21*8 

5* 6 7 

2 

0*2 

0*004 

27 

22*9 

6*18 

3 

°*4 

0*012 

28 

24*0 

6*72 

4 

07 

0*028 

29 

25*1 

7*28 

5 

1*0 

0*050 

3 ° 

26*3 

7*89 

6 

I ‘5 

0*090 

3 1 

27*4 

8*49 

7 

2*1 

0*147 

32 

28*5 

9*12 

8 

2*8 

0*224 

33 

29*6 

9*77 

9 

3*5 

0 * 3 I 5 

34 

3°'8 

10*47 

10 

4*3 

0*430 

35 

3 i *9 

11*17 

11 

S* 2 

0*572 

3 6 

33 *° 

ii*88 

12 

6*2 

0*744 

37 

34 *i 

12*62 

1 3 

7*2 

0*936 

38 

35*3 

i 3 * 4 i 

14 

8*3 

1*162 

39 

3 6 *4 

14*20 

15 

9*4 

1*410 

40 

37*5 

15*00 

16 

io *5 

1 *68o 

42 

39*8 

16*72 

17 

11 *6 

i *972 

44 

42*0 

18*48 

18 

12*8 

2*304 

46 

44*3 

20*38 

r 9 

i 3*9 

2*641 

48 

46*5 

22*32 

20 

i 5 *° 

3*000 

5 ° 

48*8 

24*40 

21 

16*1 

3 ‘ 38 i 

52 

5 1 * 0 

26*52 

22 

i 7*3 

3*806 

54 

53*3 

28*78 

23 

18*4 

4*232 

56 

55*5 

31*08 

24 

19*5 

4*68 

58 

57'8 

33 ’ 5 2 

25 

20*6 

5* I 5 

60 

6o*o 

36'00 


likely to be the best suited for practical purposes, so long as the present distri¬ 
bution of the rain-gauge stations continues. 

The best method of treating such observations as are usually available is 
that adopted by Binnie ( P.I.C.E ., vol. 39, p. 1). The records considered are 
those of Nagpur (Central Provinces, India). The year has two well marked 
divisions, namely, the wet, or monsoon season (June to October), and 
the dry season (November to May). The rain-fall records are as shown in 
table on next page (see ut supra , and P.I.C.E ., vol. no, p. 259). 

The following facts are fairly plain, and are characteristic of all small 
catchment areas in climates such are now considered. 

(a) Except in extremely abnormal years, which need not be taken into 
















244 


CONTROL OF WATER 


OT 'HiV/ J;! 

OT Ti .. I \ 

Year. 

• M| *•> ? > ' ' , 1 ■ * . 

Rain-fall during the 

i'.'i :f r ;: /J 7 . *. 

Monsoon. 

. / f J.! ' '< 

Dry Season. 

\ ■ 1 : 1 ' . '. i . ■ 

-1854-1855 

48^0 

2*06 

1855-1856 

24*04 

2*03 

1856-1857 

44*33 

2 *77 

*857-1858 

33*46 

3*32 

1 S58— 1 859 

3 r8 7 

4*21 

1859-1860 

29*48 

1*32 

1860-1861; 

44 * 5 ° 

5*00 

1861-18621 

40*89 

i*i 5 

1862-1863 

43* 2 9 

3 * 6 i 

1863-1864 

37*46 

4*73 

1864-1865 

28*96 

6*87 

1865-1866 

38-16 

2*40 

1866-1867 

41 *01 

4*18 

1867-1868 

53*72 

6*26 

1868-1869 

19*28 

o*88 

1869-1870, 

3 2 ’ 11 

4*09 

1870-1871 

37*34 

! 

2*29 

1871-1872 

44* 8 5 

1 *27 

1872-1873 

39*82 

2*70 

i ^ 1 . ■ i ► 

Average of 19 Years . 37*52 

I 'i 

*, ) : 

3*21 


account in practice, the wet season rain-fall alone is effective in producing a 
run-off. 

( b ) The condition of the catchment area in respect to dryness of surface 
is certainly the same at the beginning of each successive wet season, and 
this statement can probably be made with equal accuracy concerning the 
ground water, except in very permeable catchment areas after abnormally 
wet years. 

Thus, a given fall of rain measured from the beginning of each wet season 
will produce an approximately constant run-off. Any variations which occur 
are caused only by the manner in which the rain falls (as is partially indicated 
in columns 2 to 4, top of p. 247), and are quite independent of the fall during the 
preceding wet season. 

Binnie, when preparing his final designs, possessed rain-fall records to 1873, 
and the observations on rain-fall and run-off shown in table on page 245. 

At first sight the observations only afford two figures, that is to sav : 

* 


In 1869 a rain-fall of 2979 inches produced a run-off of 7-87 inches 
n l8 7 2 » 4365 „ „ 17-46 


< ; / 1 ; i 


' ' i 


A little consideration will show that each of the entries in Columns No. 4 
and 5 can be Considered as giving the run-off that would be produced by a wet 


























BINNIE’S METHOD 


245 


Year and Month. 

I 1 

i 

Rain-fall. 

Run-off. 

Total Rain¬ 
fall since 
Commence¬ 
ment of 
Wet Season. 

Total 

Run-off 

since 

Ratio : 

Total Run-off 

--- 

—I 

• 

same 

Date. 

Total Rain 

Year 1869 — 




« 

n 4 ' 

.*1 

June 17th to 
July 31st . 

12*76 

1*25 

12*76 

• 

1*25 

o*o98 ? 

August . 

9 *61 

3*36 

22*37 

4 *61 

0*20 

September 

7*41 

3*26 

29*79 

7*87 

0*268 

Year 1872 — 

June 

677 

°’ 3 2 

677 

0*32 

v - ** 

6*047 

July 

12*70 

2*88 

19*47 

3*20 

0*16 

August . 

11*82 

6 *59 

3 i * 2 9 

9*79 

0*31 

September 

7*99 

5*95 

39*28 

15*74 

0*40 

A break in the 
. , rains now 


r « * 




occurred 

d c *.. k i. ’ *. 

, n > ' "*; 

« 

t • . ; * > - , 


£ Ji ' 

October . ' . 

•4*37 

r 1^72 

43^5 

17*46' 

A 0*40 

Ct 

ir 

ft 

• ;; ' 

r (» 



season rain-fall of the same total magnitude as the rain-fall that had occurred 
up to the end of the month considered. *,;• 

Thus, up to the end of July 1872, 19*47 inches of rain produced 3*20 inches of 
run-off, and the observation may be considered as indicating that, since the whole 
wet season fall of r868 was 19*28 inches, the run-off of that year was probably 
about 3*17 inches. Thus, theoretically at any rate, from observations taken over, 
these two years we can assign the probable values of the run-off produced by 
any rain-fall which is less than 43*65 inches. In actual practice this statement 
is subject to qualification. The question is best investigated by considering, 
what happens at the end of the wet season. As a matter of observation, the 
stream flow rapidly decreases in all such catchment areas, and the river draining 
this Nagpur catchment area (which is 6*6 square miles in area, and consists of 
steep trap rocks, which are but slightly covered with soil) is generally dry in 

4 or 5 hours at the most after the last rainstorm. A study of Binnie’s records 

of the reservoir levels shows that the reservoir surface rarely rises appreciably 
after 24 hours has elapsed since the last rain-fall. Thus, in this case the 
assumption is justified. .> 

The question is best settled in any particular case by observations of the 
duration of stream flow. Thus, if the stream is usually found not to run dry for 

5 or 6 days, it would probably be advisable either to correct the partial records 
obtained as above by allowing for the probable volume of the stored-up water 
which will later appear as stream flow (as discussed on p. 188), or to treat, 
by this method, only those total rain-falls at the end of which the stream ran 
dry before the next fall commenced. 

As an example, I give the following record of rain-fall and run-off from a 
steep catchment area of 18 square miles, approximately 4 square miles of which 
were underlain by permeable strata ; 


























246 


CONTROL OF WATER 


Date. 

Total 

Rain-fall to 
Date. 

Total 
Run-off to 
Date. 

Remarks. 

June 

l6 . 

O 

• 

0 

Rains began 


30 . 

3*13 

O 


July 

7 • 

4-18 

0*20 


J> 

i 5 • 

5*92 

0*78 


)> 

16 . 

6*82 

I ’20 


5J 

25 . 

9-84 

1 * 3 6 


J5 

28 . 

9-84 

1-42 

Stream runs dry 

J5 

3 1 • 

10-15 

1*46 

Stream begins to run 

August 9 . 

ii *44 

1-58 


5J 

11. 

: 5 ’ 3 2 

1-78 


5 J 

19 . 

x 5 ’ 3 2 

2*18 

Stream runs dry 


Here it is plain that only the following deductions can correctly be made : 

A rain-fall of 9-84 inches produced a run-off of 1-42 inches 
if I5'32 ff ff 2*i8 „ 

In fact, Binnie’s method is best suited for steep, and impermeable catchment 
areas ; and may lead to entirely erroneous results if blindly applied to large, 
flat, and permeable areas, where the ground-flow contribution forms a material 
portion of the run-off*. 

Where properly applied to suitable areas, the method is a powerful one. 
Thus, Binnie predicted that the average monsoon fall of 37'52 inches might be 
expected to yield I4'23 inches of run-off, and that the average monsoon fall of 
the three driest consecutive years would be about 30 inches, and that one such 
year would have a run-off* of 8*4 inches. The fall and run-off* of the driest year 
were similarly predicted at i9’28 inches and 3 inches. Now, the actual results 
of observations extending over 18 years (as given by Penny) indicate that 23^3 
inches of rain-fall produce an average run-off* of 5*30 inches, and that the 
driest years have a run-off* of 3-6 to 4 inches. Thus, the errors in prediction 
are almost entirely due to incorrect assumptions concerning the rain-fall 
variability (see p. 248). 

run off 

Sketch No. 57 shows Binnie’s results as plotted with the percentages of - . 

as ordinates, and the rain-falls as abscissae, and it will be plain that the 
observations coincide very closely with Strange’s curve for a good catchment 
area. 

The principles are now obvious. We can regard each storm during the 
rains as a unit, if the stream draining the area runs dry after it ceases, and 
before the next storm occurs. Thus, if we analyse the results, we can usually 
arrive at a table of the type shown at top of page 247 (given by Strange). 

This table, if properly applied to records of daily rain-falls, will produce 
results which are less subject to error than those given by Strange’s formulae 
for annual run-off, and such results are often found to agree extremely well 
with observation in small, steep, and impermeable areas. 






















EFFECT OF PERMEABLE STRATA 


24 


Rain-fall in 

24 Hours in Inches. 

Ratio Run-off to Rain-fall. 

State of Catchment Area previous to the Rain-fall. 

1 

4 

Dry. 

Nil 

Damp. 

Nil 

Wet. 

0*12 

1 

0 

Nil 

0*10 

0*14 

1 

°'°5 

0*14 

0*20 

2 

0*10 

0*25 

°’34 

3 

0*20 

0*40 

o '55 

4 

0*30 - 0*40 

0*50 - o*6o 

0 

CO 

0 

1 

0 

b 


In permeable and semi-permeable areas (especially if large) the problem is 
somewhat more difficult. 

Owing to the fact that the river does not rapidly run dry, a year’s observa¬ 
tions will rarely provide more than two points on a curve of the type used by 
Binnie (see Sketch No. 57). The following table, which represents the results of 
observations on a flat catchment area of about 100 square miles in Bengal, may 
be considered as giving the best available information on this somewhat 
obscure subject: 


Month. 

! 

Ratio Monthly Run-off to Monthly Rain-fall. 

Ordinary Year. 

Wet Year. 

June 

°‘°5 

0*10 

July 

0*10 

0*20 

August . 

0*25 

0*5° 

September 

0*40 

0*5° 

October. 

0*40 

0*50 


The figures are vague (although not more so than the difficulties of the 
subject warrant), but the difference between the columns fairly accurately 
represents the influence of the damper surfaces, combined with an increased 
storage of ground water. 

In practice, however, such areas are not usually developed for purposes of 
water storage, so that the question is not very acute. Valuable information can 
be obtained by observing the ground-water level, and my own practice has been 
to estimate the water stored up in the invisible reservoir at various dates, and 
to tabulate as follows : 


Date. 


Total 

Rain-fall. 


Total Visible 
Run-off. 


Total Increment in 
Water Storage since 
Beginning of Rains. 


Probable Total Run¬ 
off if Rains were to 
cease on this Date. 


The figure in Column 4 is calculated from the observed rise in ground-water 
level by the formula given on page 188, and that in Column 5, is the sum of the 


































CONTROL OF WATER 


248 

terms in Columns 3 and 4. The assumption is obvious. We neglect any 
possible future depletion of the ground water by underground leakage, or by 
evaporation produced by vegetation. 

The likelihood of loss by leakage can be estimated by a survey of the 
permeable strata. The second form of loss probably occurs, but may be 
considered to be balanced by the fact that we have neglected the water which 
is absorbed in producing a partial saturation of the upper layers of permeable 
soil above the ground-water level. This evaporation is probably only large in 
those localities where the subsoil-water level comes within 3 or 4 feet of the 
natural surface ; but the nature of the vegetation has a great influence upon its 
amount. 

Variability of the Wet Season Rain-falls. —Nearly all climates of 
this type fall into the exceptional class discussed on page 180, where the possible 
annual variability in rain-fall is larger than is generally the case. Thus, in a 
thirty years’ record the minimum wet season rain-fall is frequently as low as 
o'33 of the mean, and ratios of 0*20 or o'25 are not unknown. Similar 
abnormalities occur when the average of the two or three driest successive years is 
discussed. The matter is now well understood both in India and in California, 
but must be borne in mind whenever climates of this type are dealt with in newly 
settled countries. In some of the earlier Indian projects a short period rain-fall 
record for the locality considered was compared with a long period record for 
Calcutta, and the variability ratios for Calcutta were believed to apply. This is 
now known to be erroneous. A similar error is likely to be made in other 
countries, unless pointed out; as long period records in a newly developed 
country are generally confined to the coastal districts, where the variability ratios 
are usually normal in type. 

Capacity of Reservoirs. —The determination of the capacity of the equalis¬ 
ing reservoir under such circumstances is a simple matter. In view of the periodic 
oscillations of the time at which the wet season begins and ends, we must 
generally assume that no reservoir will suffice, even for one year, unless it 
holds a supply sufficient for 365 days at the end of the wet season. It is 
always possible that in one year the stream flow of the wet season may end 
say in August, and that in the next year the stream flow may not begin 
until August. A study of the yearly run-offs will enable us to determine 
whether we can rely upon the reservoir being refilled in the driest year, and 
if not, a capacity approximately equal to a supply extending over two years, 
or 730 days, is obviously required. As a matter of practice, a study of the 
capacities of Indian and Californian reservoirs for town water supplies, or for 
permanent irrigation (i.e. such crops as fruit trees, or lucern, where the crop 
cultivated is perennial), shows that the rules adopted are very much as 
follows. 

Where calculation indicates that the run-off of the driest years will probably 
fill the reservoir, a capacity of 650 to 730 days’ supply is provided. 

If the driest year will not fill the reservoir, a capacity equivalent to about 
1000 or 1100 days is provided. Cases exist where a capacity of 1400 and 
1500 days’ supply is found to be necessary. 

For irrigation of such crops as wheat, and cotton, a smaller margin of 
safety is usually provided; and some Indian and Algerian reservoirs are 
designed on the assumption that once in 10 or 15 years no irrigation can be 
effected. The matter is evidently a question of finance, and in view of the 


THIRD TYPE OF CLIMATE 


249 


fact that in moist climates crops are frequently damaged by excessive rains, 
the irrigators can hardly be considered to be very adversely situated. 

Values of the Rainfall Loss .—In the typical climate of this class the relation 
between x and z is not of much practical importance. The following records 
are of first class accuracy, but refer to Southern Indian climates where two 
wet seasons occur each year. It is probable that during most years the 
catchment areas become dry between the monsoons, but during the wetter 
years this certainly does not occur. 


■ 7. f: i 


Locality. 

--*--- 

Area. 

X 

1 

y 

z 

Authority. 

Mercara, 

Acres 

48 

11918 

44 ‘ 3 X 

74*87 

*- , , w r s 

P.I. C.E. , vol. 113, 

Southern India, 
one year 

- 

Labugama, 

2 3 8 5 

162*81 

84*98 

7 7 ’ 8 3 

p. 312. No run¬ 
off in December 
to February in¬ 
clusive 

Ceylon 

• • • 

I2 7'55 

76*66 

50*89 

Driest year since 

Years 1905-7 in- 

• • • 

1 5 5 *79 

114*60 

41*19 

1897 

Reports of P.W.D., 

elusive. 

r 

Of' 



Ceylon, for years 
concerned 


Climates of the Third Type. —Here the run-off of each separate fall 
of rain is an independent unit ; since, except in abnormal cases, the area is 
always dry, so that the first column of Strange’s second table (see p. 247) 
may be considered as applicable. For example, Collins ( P.I.C.E. , vol. 165, 
p. 271) assumes that near Johannesburg in the Transvaal: 

> . , i ( % ’ » • * • ** r\ 

Falls of less than 1 inch in a day produce no run-off. 

Falls of between 1 and 2 inches per day produce a run-off equal to 
0*20 of the rain-fall. 

Falls exceeding 2 inches per day produce a run-off equal to 0*40 of 
the rain-fall. 

The assumption is stated to be favourable, and a yearly run-off equal to 
0*07 of the yearly rain-fall cannot be relied upon. The determination of the 
reservoir capacity is effected by applying these, or similar figures, to the 
records of daily rain-falls over long periods. 

In certain instances, where the catchment area is large, the river will be 
found to have a perennial, or approximately perennial flow. In such cases 
gauge records usually exist, and may be employed to estimate the yearly or 
monthly run-offs. The studies of daily rain-falls may then be applied to 
investigate whether the river is ever likely to run dry. It must, however, be 
remembered that the “rain-fall” over a large catchment area of this type is 
usually only an ideal figure, as those falls of rain which produce any run-off 
are probably only local, torrential downpours. 




























CONTROL OF WATER 


250 

The uncertainties are admirably illustrated by the following record of the 
yearly run-offs of the Sweetwater (California) catchment area. 

Since even the deepest natural bodies of water existing in such climates 
are known to dry up by ordinary evaporation during intense droughts (say 
three or four times in a century), a permanent water supply, such as can be 
obtained in moister climates, must probably be set aside as an unattainable 
ideal. 

In cases where it is necessary to provide a permanent water supply in such 
climates the problem is usually solved in one of the three following ways : 

(a) Frequently by deep wells, which, in many cases, develop the under* 
ground flow of a well-marked subterranean water channel. This is the normal 
method of supplying cities and oases in desert climates. Any discussion of 
the methods of discovering such supplies is futile. Where they exist, a desert 
city or oasis will be found. The publications of the Egyptian Survey Depart¬ 
ment, and of the United States Geological Survey on Desert Water Supplies 
may be consulted. Beadnell (An Egyptian Oasis: Kharga) describes a case 
where the supply is semi-artesian, and sufficiently copious to form a basis 
for large scale agricultural operations. 

(b) The water is stored in high lands adjacent to the desert, and is delivered 
by long conduits. The city of Los Angelos, Cal., although hardly a desert 
city, is supplied in this manner, since the population is now too large to be 
fed by storage or underflow developments of the adjacent country which has 
a climate of the second type. 

(c) Selected areas of rocky ground are rendered impermeable, and the 
whole rain-fall is collected in deep tanks. The typical example is Aden, and 
for military reasons Gibraltar is also thus supplied, (see p. 256). 

Records of the Sweetwater (California) Catchment Area. —The following 
particulars are taken from Schuyler (Reservoirs, p. 233). The catchment 
area is 186 square miles, and the elevation above sea level varies from 
220 feet (at the dam) to 5500 feet in the mountains bounding the catchment 
area. The mean elevation is about 2200 feet. The rain-fall is that which 
is recorded at the dam, and certainly does not represent the mean rain-fall 
over the whole catchment area. While the recorded rain-fall may bear some 
relation to the mean rain-fall over the whole area, it is believed that the 
run-off of similar Californian catchment areas is mainly produced by the 
far heavier local rain-fall which occurs in the higher portions of the catch¬ 
ments. The circumstances may therefore be regarded as analogous to those 
of the Melbourne catchment area (see p. 201), but the difference in rain-fall 
produced by changes in elevation is probably far greater. 

The reservoir originally had a capacity of 18,053 acre-feet (1 acre-foot 
equals 43,560 cubic feet), say 1^ times the mean annual run-off. In 1896 it 
was enlarged to 22,566 acre-feet. The reservoir was completely dry by 1899. 
Tube wells were therefore sunk in the reservoir bed, and infiltration galleries 
excavated in the river bed below the dam. By pumping from these sources 
sufficient water was obtained for domestic purposes, and in addition a “ depth 
of water equal to 0^28 feet ” was applied to the citrus trees which were usually 
irrigated from the reservoir. This amount enabled the trees to be kept alive 
from May to the 23rd November 1899. Similar pumping became necessary 
in 1900. The history is typical of that of many reservoirs in arid countries, 
and it is hard to see what more could be done, as the reservoir loses 15 per 


DESERT SUPPLIES 


251 

cent, of its capacity each year by evaporation. The real lesson is that 
investigations in search of ground-water supplies should be made in all similar 
cases, and that they should not be deferred until the reservoir shows signs of 
failure. 


Year. 

Total Run-off. 

Yearly Rain-fall 
at the Dam 
in Inches. 

In Acre-Feet. 

In Cusecs per 
Square Mile. 

1887-1888 . 

7,048 

00524 

Not given 

1888-1889 

2 5^53 

°* i8 75 

1 3 ‘5 3 

1889-1890 

20,532 

°* I 5 2 5 

16*52 

1890-1891 

2 i, 5 6 5 

0*1602 

12*65 

1891-1892 

6,198 

0*0460 

9*88 

1892-1893 

16,261 

0" 1210 

11 *62 

1893-1894 . 

1.338 

0*0099 

6*20 

1894-1895 . 

73.412 

o ‘5452 

16*19 

1895-1896 

1.321 

0*0098 

7*29 

1896-1897 

6,892 

0*0512 

10*97 

1897-1898 

4*3 

0*00003 

7*05 

1898-1899 

246 

0*0018 

5*°5 

1899-1900 

0 

0*0 

5*54 

1900-1901 

828 

0*0061 

7 *o 5 

1901-1902 

0 

0*0 

4*86 

1902—1903 

0 

0*0 

572 

i 9 ° 3 - i 9°4 . 

0 

0*0 

6*39 

1904-1905 . 

13,760 

0*1022 

1 5 *55 

i 9 ° 5 -i 9°6 

35 , 000 

0*2600 

^•s 2 

1906-1907 

30,000 

0*2228 

12*88 

Average 

12,983 

0*0964 

9 ' 5 2 


Victorian Records of Rainfall and Run-off .—The following values of the 
rain-fall and run-off of various catchment areas in the State of Victoria 
(Australia) are abstracted from Stuart Murray’s publication (River Gaugings 
of the State of Victoria , Melbourne, 1905). The results are extremely inter¬ 
esting for the following reasons : 

(a) The State of Victoria, north of the Dividing Range represents precisely 
that class of condition where knowledge of the character now discussed 
proves most valuable. The rain-fall is sufficient to support a population which 
desires a good water supply, but the run-off is not so abundant as to permit 
the designing engineer to guess at random and be none the worse. The supply 
must be obtained from catchment areas of relatively small size, and snow-fed 
rivers are absent. 

(h) As usual, in such cases, the rain-fall records are probably less accurate 
than the run-off records, which are quite as accurate as any records referring to 
rivers of the same size. 

On the other hand, the climate of the State does not fall into any one of the 




















25* CONTROL OF WATER 


























VICTORIAN RUNOFFS 


253 


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CONTROL OF WATER 


254 

three typical classes. There is no sharp division into wet and dry seasons, as in 
Northern India ; nor is any portion of the State a desert, since wheat is grown 
without irrigation all over the land, but it is believed that every river in the 
State, even the largest, ceases to flow once in a century, if not more frequently. 
The climate is probably best described as belonging to the second class, but 
the catchment areas are frequently not thoroughly dry for three or four years in 
succession. Further details are given in connection with the individual areas 
(see pp. 252-3). 

The original paper gives the rain-fall and run-off by months. 

An abstract of yearly rain-falls and run-offs, including several rivers of 
somewhat similar characteristics in the Western United States, is given by 
Fuertes ( P.I.C.E ., vol. 162, p. 148). It is believed that the rain-fall records 
are less accurate than those tabulated by Stuart Murray. The run-off records 
are also probably slightly less accurate in some cases, but I do not possess 
the detailed information that is at my disposal for the Victorian records. 

Secondary Catchment Areas.—A site is frequently found where a reservoir 
can be economically constructed of a capacity greater than that required for 
the catchment area which would naturally feed the reservoir. In such cases, 
works are sometimes formed in order to divert the flow from other catchment 
areas into the enlarged reservoir. So also, when the yield of a catchment area 
has been overestimated, it is frequently necessary to supplement it by 
diversion from other catchment areas. 

Such works usually consist of a diverting dam, or weir, across the natural 
drainage channel, with a connecting channel to carry the water collected across 
the natural line of water parting into the main catchment area. 

The design of a diversion dam, or weir, is not a difficult matter. The 
capacity of the diversion channel needs careful consideration, since the 
circumstances calling for the inclusion of a secondary catchment area require 
the collection of as much water as is consistent with economy. The construc¬ 
tion of the diversion channel will probably prove costly, owing to the deep 
excavation entailed by crossing the line of natural water parting. 

A sufficient number of examples does not exist to enable any useful rules to 
be drawn from general experience. The Vyrnwy watershed includes two 
secondary catchment areas, as follows : 

The Cownwy, of 3092 acres, with a diversion channel of 120 million 
gallons daily capacity. 

The Marchnant, of 1650 acres, with a tunnel of 88 million gallons daily. 

These two combined areas are said to yield about 10 million gallons daily. 
Since the yield of the remaining 18,000 acres is about 55 million gallons daily, 
it would appear that the diverted areas only contribute about 70 per cent, of 
the normal yield per acre. The rain-fall over the catchment area is irregular, 
and no very satisfactory deductions can be drawn. The run-off observations 
are known to have been systematically carried out for more than 20 years. 
We may consequently say that in this particular case of a catchment area of 
high, but somewhat irregular yield, a diversion channel with a capacity of 
approximately twenty times the average daily yield of three dry years proved 
economical. 

Usually, it may be assumed that before the diversion channel need be finally 
designed, the engineer will have run-off records of approximately four or five 


SECONDARY CATCHMENT AREAS 


2 55 


years to study. These, combined with a consideration of the capacity of the 
reservoir (usually only a small one), formed by the diversion dam, will enable 
him to draw up tables showing the total volume of water diverted when the 
channels are of various assumed capacities. These, together with the 
estimates of constructional expense, enable a selection to be made of that 
channel which yields the greatest volume of water in proportion to its cost. 
Such a channel may be assumed to be too large, since what we require is a 
somewhat smaller channel yielding the greatest volume of water during the 
critical period of depletion (i.e. usually the period of three successive dry years). 
It would generally appear that a channel of about 80 per cent, of the above 
capacity best suits the circumstances. 

There is another aspect of the matter, which is not only a useful guide for 
preliminary estimates, but must be considered in the final designs. The 
channel should not be liable to silt up, and a study of the bed of the natural 
stream will usually enable us to make a very fair estimate of the flow which is 
not frequently exceeded. This may be roughly estimated as the discharge 
corresponding to the “bank stage” of the natural channel. If the diversion 
channel is proportioned so as to carry this discharge with approximately the 
same velocity as that occurring in the natural channel, we may feel secure 
against any considerable deposit of silt or stones. If, however, this capacity 
of channel is much exceeded, a somewhat higher mean velocity is necessary. 
Failing this, the larger channel may rapidly adjust itself to a discharge 
capacity which is exactly that which the stream can keep free from deposits. 
In that case, somewhat costly yearly cleanings will become unavoidable. The 
area of the natural channel, and the quantity of silt carried by the stream 
should therefore be carefully studied. If silt is an important factor, it will be 
found advisable to design the diversion channel of a capacity not greater than 
that indicated by the discharge of the natural stream when running bank full. 
Under such conditions, in a British catchment area, we may generally reckon 
on securing about three-quarters to five-sixths of the total run-off in a dry year. 
It would therefore appear that the Vyrnwy diversion channels have been 
proportioned with a somewhat smaller capacity than even this rule indicates, 
unless the dry year yields of the Vyrnwy catchment area are proportionately 
higher than is usually the case. 

Coghlan ( P.I.C.E ., vol. 75, p. 187), discusses the question of channels for 
draining secondary catchment areas in New South Wales, and gives a formula 
which indicates that a channel with a capacity equal to the mean discharge of 
a stream, will actually carry off a fraction equal to : 



of the total discharge ; 


where x, is the rain-fall, and y, the run-off in inches per annum. He also 
states that if the capacity is equal to : 


75 per cent, the mean discharge, 0.835 of the above quantity is secured. 
50 „ „ °‘ 6 34 

25 


1 2i 


7 i 

5 


55 

33 

33 


3 ) 

33 

33 

33 

33 


0*380 


0*253 
0*160 
0*1 18 


33 

33 

33 

33 

33 


33 

33 

33 

33 

33 


CONTROL OF WATER 


256 

Carrying the results to three figures is obviously excessively exact, but the 
formula is founded on six years’ experience of two hilly catchment areas. 

Coghlan’s actual figures show that in the worst year the fraction delivered is 
.18 to 20 per cent., when the capacity is equal to the mean yield. This fraction 
decreases far less rapidly than his table indicates. The mean figures are : 




Capacity of Channel. 


Mean of both Results for 

Mean 

Run-off. 

^ ditto. 

1 ditto. 

| ditto. 

ditto. 

Worst year 

18*8 

i4'o 

10-3 

77 

4*5 

Best year . 

627 

37*3 

21-3 

11*6 

. \ \ 

5 ’° 


The figures being the percentages of the total run-off actually delivered 
during that year, and the best year’s yield being in the one case four, and in 
the other 6*5 times that of the worst year. 

The above figures refer to a catchment area in New South Wales, but a 
study of the run-off records does not indicate that the flood and low water 
periods are more marked than is usually the case in mountainous catchment 
areas. 

If applied to a level area containing a large amount of permeable strata, the 
channels might possibly be diminished in size. They should certainly be in¬ 
creased in climates of the second class, where the whole run-off occurs during a 
short period of the year only. It may be suggested that if the main daily yield 
is then calculated not over 365 days, but over the average duration of the wet 
season, the results will not err greatly. 

In dry climates (especially those belonging to the third class), systematic 
drainage of the catchment area will greatly increase the run-off. The usual 
methods consists of contour drains, about 6x4 inches traced by a plough which 
throws the sod on to the lower side of the drain. 

In actual work in the northern parts of Victoria (with = 35, to 40, and 
z = 25, to 30 inches) I have noticed that such a section, although producing a 
noticeable increase in run-off, is too small. Better results are obtained if the 
drains can carry about two cusecs per 100 acres, even in well grassed areas 
of 300 to 400 acres. 

The principle may be extended. The rock areas used for collecting water 
at Aden and Gibraltar illustrate its extreme development, where, after carefully 
cementing all cracks, and draining all hollows, a yield equal to 90 or 95 per 
cent, of the rain-fall is secured. 

Collection of Water from other Sources than Stream Flow.— It 
is not proposed to discuss the methods of discovering springs and underground 
flows of water. The only scientific methods are geological, and, unfortunately, 
the experience acquired in, say, the British Isles can only be utilised in other 
countries by a skilled geologist. For, while geologists consider strata as per¬ 
meable, or impermeable, the geological classification of strata pays no regard 
to this characteristic. Hence, an enumeration of British water-yielding strata 
would be worse than useless if applied to Indian conditions. 

The question of the determination of the volume of water flowing in an alluvial 
bed has already been considered (see p. 205). Sketch No. 58 shows an under- 


















SPRINGS 


257 


ground dam for the collection of the “underflow” in a gravel bed. It may be 
remarked that the results of such methods are generally disappointing, but it is 
believed that the preliminary estimates were usually vague and unscientific. 
So far as I can judge from three personal experiences, an engineer’s connection 
with such schemes will usually be confined to preliminary investigations, and 
the compilation of a report showing that the scheme is not economically profitable. 

Sketch No. 59 shows a design for the collection of water from a spring. 



Sketch No. 60 shows two typical German designs for the collection of water 
by catchment galleries : (a) from a permeable stratum underlain by an imper¬ 
meable stratum, and ( 6 ) from a deep bed of sand or gravel. 

In the above cases geological surveys should be undertaken to ascertain the 
area that supplies the spring or underground flow. Such developments, if 
carefully studied, are usually successful, and are very widely adopted for town 
water supplies in Germany and Austria. Further details are given under Wells. 

The dune sand water supplies of the Hague, Leyden, and other Dutch 

17 



















































258 


CONTROL OF WATER 


cities, may also be referred to. In these cases (see Engineering , 1889, p. 249), 
the rain water absorbed by the dune sands is collected either by open trenches, 
or by agricultural drain pipes. The local conditions need careful study, as the 
fresh water floats on a body of salt water derived from the adjacent sea. In 
some cases the collection is effected by tube wells. 

The principles concerning the collection of all underground water supplies, 
except springs, are best illustrated by a careful consideration of the problem of 
a well sunk in a large bed of sand or gravel. 

Wells in Uniformly Permeable Strata. —A bed of pure sand 
may be taken as the typical example of a uniformly permeable stratum. A 
substance of this character is equally permeable by water in all directions, 
and definite channels, or passages, do not exist. Thus, the quantity of 



water yielded by a well sunk in such strata does not depend upon its 
position. 

In fissured rock (eg. granite) the water is found in distinct and clearly 
marked channels, and the yield of a well depends almost entirely on whether 
or not one or more of these veins are met with. 

The properties of a water yielding stratum may vary between these two 
extremes of granite (where the fissures alone yield water), and pure sand, 
where a defined fissure cannot exist. For example, the chalk which yields so 
much water in the country round London has properties almost midway 
between granite and sand. A well sunk in chalk will always give some water, 
owing to regular percolation similar to that occurring in sand ; but, in many 
cases, the cutting of a fissure, either by the well, or by an adit, greatly 
increases the yield. 

The yield of a well in uniformly permeable strata is determined by two 
factors : 

(a) The permeability of the stratum, which depends on the size of the 
interstices between the individual grains. 


































WELLS 


259 


(b) The natural slope of the ground water surface. This, of course, 
depends partly on the permeability of the stratum ; but, putting this aside, 
the greater the natural slope, the greater is the available supply of water. 

,Temporary Yield of a Well .—Consider the capacity of the well from the 



Sketch No. 60.—Cross-sections of Collecting Gallery in Sand or Gravel, 

and in Fissured Rock. 


point of view of a machine for sucking water from the subsoil; and, for the 
moment, neglect the question whether the subsoil can permanently supply the 
water which the well can draw. 

The flow of water through the pores of the subsoil is evidently capillary. 
We therefore have : 

Velocity of flow = Kx slope of subsoil water surface, 
































26 o 


CONTROL OF WATER 


and the quantity of water delivered is equal to the velocity of the flow multi¬ 
plied by the permeable area through which flow occurs. 

The velocity of flow above defined is consequently that of a solid column 
of water, and the actual velocity of the water in the pores of the soil is from 
three to four times as great, since the void space in such substances as wet 
sand is about 33 to 25 per cent, of the total volume. 

The area through which the flow occurs is bounded at the top by the 
ground water surface, and in theoretical investigations we assume that the 
permeable stratum is underlain by an impermeable layer {i.e. the “ sand ” 
is underlain by a bed of “clay”). We also assume that the well is sunk 
through the sand to this clay, or that the collecting gallery rests on the bed 
of clay. 

The velocity of flow is usually very small, and it is advisable to express the 
yield of the well, Q, in cubic feet per 24 hours. The values of K, hereafter 
referred to, are therefore expressed in these units. If it is desired to express 
the velocity in feet per second, or Q, the yield of the well, in cusecs, the appro¬ 
priate value is: 


K s = 


K for 24 hours as unit 


86,400 

In symbols, we have, if: 

y, be the height of the subsoil water above the level where flow ceases, 
{i.e. in the theory, above the impermeable stratum) at any point distant x, 
from the centre of the well, and if v, be the corresponding velocity of flow 
(Sketch No. 61, Fig. III.): 


Then, v = K x slope of subsoil water surface = K 

dy 


dy 

dx 


and Q = jy x area of permeable so\\ = 2nxyK~, gives the quantity of water 
reaching the well per 24 hours. 

Hazen’s experiments permit us to determine K, in terms of the effective 
size of the particles of sand or gravel (see p. 25). In practice, however, K, is 
best determined from experiments on trial wells. 

The last equation shows that if s, be the slope of the ground water surface 
at a distance x feet, from a well which is yielding Q, cube feet of water per 
24 hours, then : 


K = 


or, 27 tK ydy — 


Qdx 


27 rxys 

Integrating the equation, we have : 

Q log e x = nK {y 2 + C ) 

Thus, if we observe^, at two points : y = H, at a distance R, and y = h, at a 
distance r. 

R 


Q loge — = 7tK O' 2 -**), whence K = 


Qlo 


ge 


r ~ " tt(H 2 -/* 2 ) 

or, substituting for n, and using logarithms to the base 10, we have : 

R 


Q log 


K = 


1-36 (H 2 -/* 2 ) 
Either of these equations serves to determine K. 








PERCOLATION VELOCITIES 


261 



! 




































262 


CONTROL OF WA TER 


It must be noticed that in deducing these formulas and those given later 
on for a catchment gallery, it has been implicitly assumed that the surface of 
the ground water was horizontal before pumping was started. Thus, in 
practice, it is necessary to take the observations of slope or height along a 
line of test wells originally sunk along a contour line in the ground watei 
surface, or to correct for the slope by putting s , for the average change in the 
slope all round the circle of radius x, and H, and /1 , for the average depths at 
distances R, and r , from the centre of the well. (See Sketches Nos. 61 and 62.) 

(i) Using the first equation. Let Q = 47,000 cubic feet = 294,000 imperial 

gallons per day. Let when x = 300, and y = 40 feet. Then, 

K = 47 )°°° * = 504, corresponding to an effective size of o'qo mm. or 

o'2o X 300 X 40 

o‘oi6 inch (that is to say, clean and rather coarse sand). 

(ii) Taking the second equation. Let H = 40, when R= 1000 feet. Let A = 36 
at the well, i.e. when r— 3 feet, for a well 6 feet in diameter, and Q = 14,000 
cubic feet per day. 

Then, K— I 4^o°o l°gg _ 333 _gr corresponding to a very fine sand of 
3-14(1600-1296) 31 

about 0*006 inch effective size. 

The formulas for a long catchment gallery resting on an impermeable 
layer are not so useful for the experimental determination of K ; but are 
necessary, since this form of collector is frequently used in lieu of wells in 
actual practice. They are : 

Q = K bys 

K£(H 2 -// 2 ) 


and, 


Q = 


2 (L— x) 

* - t 

where Q, is the yield of a gallery b, feet long, and s, is the ground water slope 
at a point where the depth of ground water above the impermeable stratum 
is y ; and H, and A, are similar depths at distances L, and x, measured 
perpendicular to the length of the gallery. These formulae are for the usual 
case where water enters the gallery from one side only. If ground water 
seeps in from both sides (which occurs only very rarely when pumping is 
continuous), Q, must be doubled. 

As indicated in the second example, the second form of the equation is most 
easily applied ; and, in practice, the usual method of obtaining K, is as follows : 

Observe the difference between the water level in the well before pumping 
commences, and the level of the impermeable stratum. Let this be H. 

Similarly, let h, be the difference between the water level in the well when 
Q, cube feet per 24 hours, are being pumped from it and the top of the 
impermeable stratum. 

Then, if r, be the radius of the well, and R, the distance from the well 
at which the ground water level stands at a height H, above the impermeable 
stratum during pumping, we find that: 

Q lo g 7 

K = i T 36(H 2 -// 2 ) 

As a rule, it is usual to assume that R = 1000 feet. In actual practice, 
however, the distance from the well at which long-continued pumping does not 







SUBSOIL WATER 



4 
3 


Contours during Pumping 


j 


o 


Contours before Pumping 

Sketch No. 62.—Contour Lines, as actually observed in a Case similar to 

Sketch No. 61. 






















264 


CONTROL OF WATER 


alter the slope of the subsoil water surface is a very important factor, and should 
be ascertained by observation. In future this distance will be denoted by Rj. 

A systematic determination of K, and Ri, is best effected by pumping from 
a trial well, and observing the drop of the subsoil water levels in a series of 
small test bores sunk at distances of say 200, 400, or 800 feet from the well. 
As a rule, the water level in these test bores becomes steady after pumping 
for 48 hours, and the value of K, thus ascertained, may be used to calculate 
whether any further test bores are required. 

Since a preliminary and fairly accurate value of K, can be obtained by 
sizing tests (see pp. 269 and 350) of the soil, fresh bores are not usually required. 

Examining the various factors upon which Q, depends, we have as follows : 

K, and R 1} are physical quantities depending on the permeability of the soil. 

H — h, is the pumping head of the well, and is fixed by economic considera¬ 
tions, or by the “ blowing ” of the well. 

H+//, depends on the depth at which the impermeable stratum is found. 

Thus, the only factor which can be greatly varied is r, the radius of the well. 

When H 2 — /z 2 , R 1} and 
obtain the following table : 


. 1 

K, are constant, Q, varies as- 

log— 1 


and we 


Ri 

r 

r R i 

Q 

E°ge r 

K(H a -A a ) 

2000 

7*60 

0*132 

IOOO 

6*91 

0*145 

667 

6-50 

0*154 

5 °° 

6’2 I 

0*161 

250 

5*52 

o‘i8i 

100 

4‘6i 

o'217 

5° 

3’9 T 

0-256 


As an actual example, assuming that Ri = 1000 feet, and taking the yield 
of a well of 1 foot diameter, as unity, we find that: 


A well of 2 feet diameter 

55 3 55 

33 4 33 

33 8 „ 

33 20 ,, 

33 40 33 


will yield no units. 
„ 1*17 33 

3, 1’2I „ 

„ r 37 „ 

33 * 64 ,, 

33 1 ‘94 33 


so that the possible yield of a well increases far more slowly than its size. 

The whole question has been carefully considered by Forcheimer {Ztschr. 
oesterreicher Ing. Vereins , 1898, p. 629, and 1905, p. 587), and the general 
accuracy of the above equations appears to be fairly well established, so that 
observational differences may be regarded as explained by variations in perme¬ 
ability, which my own experiments show may often amount to 10, or even 
20 per cent, of K, even over short distances. 

The above equations refer to a well through the walling of which water 
percolates as easily as through the subsoil. This, in fairly coarse sand, can 

















TEMPORARY YIELD OF WELLS 265 


be secured without difficulty ; but in fine sand, or where surface pollution is 
feared, impermeable well linings must be adopted. Forcheimer (ut supra) 
gives the following equations : 

(a) The supply is derived from a river at a distance a, from the well, and 
the well lining is permeable : 

7 rK(H 2 -/* 2 ) 

.(Accurate) 


Q = 


, 2 a 

l°ge - 


(^) The well is only permeable for a height /, less than /i, and no water 
enters by the bottom of the well. Divide the above values of Q by : 

—.(Approximate only) 

v t ' 2// — t 

(c) As (£), but the bottom of the well is also permeable. Divide the above 
values of Q, by : 


V-bri/ 


/-f— 


h 

2 h — t 


(Approximate only) 


As an example of their application to a series of wells, let us assume that 
we have three wells as already investigated, yielding q 2 , and q 3 , and that 
the last two are distant from the first x 12 , and x ls feet. Then, the value of 
H 2 — h? for the first is : 


H : 




The practical value of this equation is somewhat doubtful, but it serves to 
show that wells do not materially interfere with each other’s yield, provided 

that they are spaced about — feet apart, and that many small wells are 

3 


preferable to a few large ones. 

They also permit us to predict the possible yield of large permanent wells 
from observations of the yield of small tube wells. 

Practical experience, however, teaches us that other factors limit the amount 
of water that can be drawn from a well. 

The first condition is that the amount drawn from the well should not be 
so great as to cause grains of sand to be carried into the well. This condition 
becomes more and more pressing, the smaller the size of the grains of sand ; 
and in beds of fine sand the safe yield of the well is reached long before the 
theoretical yields above given are attained. 

Thiem gives the following table : 


Diameter of Grains in 
Inches. 

Water Velocity, in Feet 
per Second, which causes 
the Grains to rise. 

o‘o to O’OI 

o’o to 0*10 

O'OI ,, 0*02 

0*12 „ 0*22 

0'02 ,, 0*04 

0*25 „ 0*33 

0*04 ,, 0*08 

o *37 „ °’ 5 6 

0*08 „ 0-12 

o’6o ,, 2*60 
















266 


CONTROL OF WATER 


My own experience on wells up to 20 feet diameter in fine sands of 001 
inch in diameter, and under, say K = 100, causes me to regard any yield over 
o'o$r to o'o6r cubic feet per second, as liable to produce failure, the sand being 
removed from under the well curb, and the well rapidly sinking, and becoming 
filled with sand. These observations were, however, taken on roughly con¬ 
structed Indian wells, where the well lining itself did not permit water to pass, 
and the whole yield entered under the well curb, thus producing a very intense 
flow around the circumference of the bottom of the well. It is therefore probable 
that in a well with sides sufficiently permeable to admit water, but capable of re¬ 
taining the smallest grains of sand, yields equivalent to those given by Thiem’s 
values, calculated over the whole permeable area of the well, might be attained. 

So also, in one case, the well bottom being covered with a properly graded 
reversed filter, I was able to obtain yields equivalent to (o'i5xarea of well 
bottom in square feet) cusecs, without any sign of failure. 

It will be evident that such large yields from wells in fine sand, say K = 80 
to 100, are only obtainable with high values of H —h, or exceedingly deep 
wells, in which H +h, is large. For example, take R x = 1000 feet, and 
r — 3 feet, and assume that the yield is 2*82 cusecs, or that 
Q = 2’82 x 3600 x 24 cubic feet per day. When K = 100, we get : 


H 2 —A 2 = 5184 


or, if H — h = 20 feet, H -\-h = 259 feet, or a well 6 feet in diameter must be 
sunk some 130 feet below the subsoil water level. 

Taking what is the more usual Indian practice, for town water supply 
wells, i.e .: 

H — /z = 6 feet, H +h = 90 feet 

we get : 


314x540 ^ 
V 6*5 


26,162 cube feet per day, or about o‘3 cusec. 


Tested by the rule given above, the yield is about twice the safe yield when 
r — 3 feet; and, as a matter of fact, such wells rarely, if ever, give a regular 
yield of much above o’i cusec. 

Permanent Yield. — This introduces us to the second limitation of wells. 
The above well, regarded as a machine, is capable of taking 0*3 cusec out of the 
ground, if provided with a proper reversed filter ; or, at a smaller depression, 
(say H — h = 3'5 feet) will yield about o'i6 cusec with safety, it is actually 
considered to be successful if it yields o’i cusec. The explanation is obvious, 
—the ground water is not replenished sufficiently rapidly. 

The maximum possible replenishment of ground water can be roughly 
calculated as follows. The natural slope of the ground water surface in such 
districts is about and this alone replenishes the ground water when the 
pumping is long continued. The area supplying the well, measured normal 
to the natural flow, is roughly 2R X x 50, say 100,000 square feet, and the velocity 
of flow is i^th of a foot per day. Thus, a continuous yield of 10,000 cube feet 
per day ( = o‘ii cusec approx.) is all that can be expected from day and 
night pumping, although the same total volume could be obtained with safety 
in about 16 hours. 

The preliminary studies for a well are therefore as follows : 

(i) Discover the natural slope of the ground water. 

(ii) By pumping from a trial well estimate R 1} and K, and also the safe 
yield from the point of view of sand “ blowing ” into the well. 



PERMANENT YIELD OF WELLS 267 

Hence, we can calculate the rate at which ground water will be supplied to 
the well, and thence its permanent yield. Then we can determine the value 
ot r, such that the permanent yield is nearly equal to the safe yield, and so 
can ascertain the cheapest well (which will generally be the smallest possible). 

In cases where no impermeable stratum exists, the problem (if regarded 
exclusively as a mathematical one) is somewhat more difficult. In Indian 
practice, as deep a well is sunk as is commercially practicable, which (under 
Indian conditions) corresponds to a depth of about 50 feet below subsoil 
water level. 

In the studies conducted at Amritsar when preparing a project for irrigation 
from wells, the sand bed was at least 300 feet deep ; except in one case, 
where a small patch of clay existed about 30 feet below the well curb. The 
values of K, obtained from observations of the yields of the wells when H, 
and h , were measured from the well curb level, were about 30 per cent, greater 
than those obtained from small scale experiments on percolation through the 
sand, or by sizing the sand with sieves (both these methods gave very concordant 
results). 

It may therefore be inferred that the subsoil water was in motion down to 

a depth below the well curb approximately equal to —. The sand was very 

fine, K, as ascertained from small scale tests, varying from 80 to 125, and, 
as ascertained from the well yields, from 100 to 170. 

In practical work, the obvious procedure is to sink the test well to the 
depth to which the permanent wells are proposed to be sunk, and to calculate 
the yield of the permanent wells from the experimental value of K, as as¬ 
certained by using the equation on p. 262 when H, and h. are measured from 
the well curb. 

As a rule, Indian wells are too large for the quantity of water which they 
can permanently yield, if 24 hours’ pumping is contemplated. The wells are 
proportioned so as to be safe against blowing when yielding the quantity which 
is initially observed ; and, as already stated, this quantity is frequently twice or 
three times as great as the quantity which the natural slope of the ground 
water surface supplies to replenish the ground water near the well. 

In consequence, “large and permanent falls in the subsoil water level” are 
produced, and the partial failure in the supply is frequently attributed to a 
succession of dry years. So far as my experience goes, dry years have but 
little influence, and the actual facts are that the line ot« wells is yielding more 
than the natural replenishment of the ground water can supply. 

According to the equations already given, if: 

L, be the total length in feet, of a line of wells measured normal to the 
direction of the natural ground water flow, and if S, be the natural slope of the 
ground water surface before the wells are installed, the total permanent yield 
cannot possibly exceed : 

Q = KS(L + 2R 1 )H cube feet per 24 hours 

where H, is the depth of the well curb below the natural ground water level, if 
K, be ascertained from a trial well ; or H = 1-25 to 1*30 depth of well curb 
below the natural ground water level, if K, be ascertained from small scale 
experiments. This value is the maximum possible permanent yield, and the 
spacing of the wells and their size should be so selected as to permit this daily 


268 CONTROL OF WATER \ 

yield to be obtained in 8, 12, or 16 hours, or whatever other period is selected 
for pumping. 

The one exception to this rule is where a permanent stream, or lake, exists 
close to the wells, and the equation : 

_ ttKCH 2 -/* 2 ) 

^ , 2<Z 

loge- 

r 

is applicable both for temporary and permanent yields. 

The possibilities of pollution are obvious, but otherwise the case is very 
favourable, and should be selected wherever practicable. The actual estimation 
of the probable yield of an extensive scheme for ground water pumping, is 
difficult. Rain is the source of the ground water, but the catchment area is 
ill defined. 

The field wells of a large and highly cultivated area in the Sialkote district 
of the Punjab are capable of supplying at least 6 to 7 inches depth of water 
yearly, over the whole area, and the only apparent source is a rain-fall of about 
20 inches per annum. But, since the water is used for local irrigation, some 
portion may have been used twice over, and percolation from neighbouring hill 
torrents may occur. So also, chalk wells in England appear to give yields 
corresponding to 6, or 8 inches depth ; but, after a series of dry years signs of 
exhaustion, vanishing in wetter years, are noticeable. 

The only safe method, therefore, is to actually ascertain the ground water 
contours over a large area, say 3, or 4 square miles, and to estimate the velocity 
of flow, either as discussed on page 205, or by the surface slope. The effect of 
dry years can then be disregarded, unless the draught from the wells is very 
nearly equal to the calculated supply ; since, a general fall of say 4, to 6 feet 
over the whole area, will amply tide over even a long term of dry years. 

The usual installation, in such cases, consists of a line of wells perpendicular 
to the ascertained direction of ground water flow. The individual yields (after 
allowing for interference), can be calculated by equations of the form given for 
a system of three wells ; but, in actual practice, the gross yield is very close to 
that of a catchment gallery of a length equal to L + 2R l3 where L, is the length 
of the line of wells. 

For calculations of the permanent yield, it would appear safe to take the 
velocity as given by the natural slope of the ground water, and an area equal 
to (L + 2R 1 )xH 1 , where H 1? is either the depth of the impermeable stratum 
below subsoil water level, or 1*25 x depth of well curb below the same level, 
whichever is least. It will also be wise to allow for possible extensions of the 
line. 

If the general equations are considered, it will be evident that the major 
portion of the pumping head H —h, is lost in the soil close to the well. Thus, 
if the finer grains could be removed from this portion of the soil so as to increase 
K, near the well, the pumping head for the same yield would be diminished, 
and failure by blowing would be less likely to occur. The principle has been 
applied in several ways. The well is surrounded by a reversed filter, of graded 
material, or the bottom of the well is covered with a similar reversed filter. 
The most practical method appears to be that produced by “ well plugs.” 
These are orifices covered with fine meshed gauze, formed in the sides of the 
well. When the well is first set to work, steam under pressure is turned through 



WELL PLUGS 


269 

these orifices, and is allowed to escape outside the well. The finer particles of 
the soil close to the orifices are thus blown away, and a reversed filter is 
obtained. In practice, the finer particles are sooner or later carried towards 
the gauze by the flow of water, and clogging occurs. The steam blowing 
process is then repeated. The method is practical, and should be adopted in 
all cases where failure by sand blowing is apprehended, or where the calcu¬ 
lated permanent yield can only be obtained under a large pumping head. 

The system described above is that most usually adopted, but it is useless 
in fine sands. The only system that is really useful under such conditions 
consists of a circular removable gauze cylinder, fixed on a frame inside the 
well, which is in communication with a plug screwed into the well lining. The 
apparatus chokes more rapidly in fine sand than the usual well plug does in 
coarse sand, but it is arranged so as to be systematically and frequently blown 
free by pressure water taken from the main pumps. 

The values of K, corresponding to the effective sizes indicated by the 
following sieves, are given below : 


Number of Meshes per 
Linear Inch. 

K in Feet per Day. 

Effective size in Mm. 

6 

50000 

3'9 

8 

32000 

• • • 

10 

135 °° 

2*04 

12 

10500 

1 '5 2 

16 

580° 

I*IO 

20 

3000 

0^96 

24 

2500 

• • • 

3 ° 

1650 

070 

40 

700 

o ‘46 

5 ° 

5 °° 

°‘39 

55 

43 ° 

... 

60 

333 

0*32 

70 

190 

0‘24 

80 

160 

0‘2 2 

90 

130 

0'20 

100 

io 5 

o'i8 

120 

80 

°‘ I 5 S 

140 

60 

o*i 35 

i 5 ° 

55 

• • • 

200 

40 

• • • 


The velocity through the pores of the sand may be taken as about 
3K slope, but the factor may vary from 37 to 2*2, or even a little less. 

Mota Wells —The principles involved in this type of well are illustrated in 
Sketch No. 63. The well is sunk in sand down to the surface of a lenticular mass 
of clay, or other hard material lying in the sand. The upper surface of this mass 
of clay must be below the subsoil water level, and the clay bed must be limited 
in extent, so that the two beds of sand above and below it are, hydraulically 









270 


CONTROL OF WATER 


considered, identical. The clay bed is then pierced by a pipe which is not 
extended below the lower surface of the bed. On pumping from the well all 
leakages into the well from the upper bed are carefully stopped. If the process 
is successful a small void space is formed below the clay by removing the sand, 
and thereafter clear water enters through the pipe under a head equal to H h, 
the difference in the levels between the water inside and outside the well, less 
any frictional resistance to flow in the sand round the edge of the clay bed. In 
practice the last term is negligible. The process evidently amounts to the 
prevention of blowing of the sand, and thus the well can be worked under a far 
greater head than would otherwise be permissible. 

The method is well known to Indian villagers, and roughly speaking a mota 
well (Urdoo, mota = c lay) is considered to yield three times the quantity usually 
obtained from a non-mota well of the same dimensions. Also such wells are 
found to fail less rapidly when (due say to deficiency in rain) the subsoil water 


;j 0 ( 



Sand 

Sketch No. 63.— Mota Well. 

level falls below its usual height. The circumstances are obviously somewhat 
peculiar, and the discovery of the clay beds is a difficult matter. 

So far as I am aware, the greatest recorded yield of such a well is approxim¬ 
ately 1-5 cusec. This I obtained at Amritsar. As a rule, however, yields exceed¬ 
ing 0*5 cusec are rare, and the average of some forty carefully constructed wells 
was o'3 cusec. 

The liability to failure by fracture of the clay bed under excessive pumpino- 
is obvious, but distribution of the pressure by steel beams inserted in the clay 
and built into the well will frequently prevent this. 

My own recommendation was to sink all wells down to the clay bed, if such 
exist at a reasonable depth, and then put in the pipe with a valve ; but I do 
not advocate working the well exclusively as a mota well unless forced to do 
so owing to deficiency in supply. 

The method forms a very useful standby, and wherever clay beds are met 
with the possibility of its adoption should be investigated. 


























ARTESIAN WELZS 


271 


Artesian Wells.— Sketch No. 64 shows the ordinary basin theory of an 
artesian well. The conditions are founded on theory only, and probably but 
rarely occur. It may also be said that if the permeable stratum was actually full 
of water which was quite at rest until a well was bored, this water would (through 
age-long contact with the minerals of the stratum), be so charged with salts as 
to prove useless for human or agricultural consumption. This was actually the 
case with the non-artesian waters pumped from the Severn tunnel during the 
first three or four years after its construction. 

Sketch No. 65 shows what is probably the true explanation of all, or nearly 
all, artesian wells. The water in the permeable stratum is in slow motion towards 


!ion - A rtesian Ron-Artesian 




Permeable beds 



Impermeable beds 


Sketch No. 64.—Theoretical Artesian Basin. 

some distant (frequently submarine) outlet. The friction head resisting this 
motion being greater than that opposing the movement through the boie pipe 
of the well, the water rises, and either issues under its own pressure, or can be 
pumped from the well. 

The artesian waters of Western Australia and the Atlantic coastal plain of 
the Eastern United States are certainly of this character, as aie probably those 

of Queensland and New South Wales also. 

If observations are taken of the yield of an artesian well, and the piessuie 
of the issuing water ; or, in the cases where the water does not rise to ground 
level, the depression of the water surface, it will be found that in either case the 
























































































































































272 


CONTROL OF WATER 


supply is almost directly proportional to the decrease in pressure, or depression 
below the level of the water when at rest. 

This fact permits us to infer that the water issuing from an artesian well is 
supplied by percolation through the permeable stratum. Consequently, any 
idea that large cavities filled with water under pressure exist in the subsoil, and 
are tapped by the bore, must be abandoned ; since, if such existed, the supply 
would be proportional to the square root of the decrease in pressure. 

The vertical thickness of the permeable stratum can be estimated by observ¬ 
ing the temperature of the water issuing from the bore. The rate at which the 
temperature in deep bores increases is known to be fairly uniform, and corre¬ 
sponds to an increase of about i degree Fahr. per 50 to 60 feet depth. But, 



since hot water is lighter than cold water, the temperature of the issuing water 
will be very nearly equal to that of the warmest water in the permeable stratum. 
Thus, while the depth of the well is approximately equal to the depth of the 
top of the permeable stratum, the temperature of the issuing water corresponds 
more closely to the temperature prevailing at the bottom of the stratum. 

For example, the Queensland artesian waters are usually (see Williams, 
P.I.C.E., vol. 159, p. 319) some 32 degrees Fahr. (at shallow depths), to 
47 degrees Fahr. (at greater depths), hotter than is explained by the depth of 
the bore. The vertical thickness of the permeable strata may therefore be 
taken as averaging from 1760 ( = 55x32) to 2585 feet, ( = 55x47); the usual 
temperature gradient in borings being about 1 degree Fahr. per 55 feet increase 
in depth. 


























ARTESIAN WELLS 


273 


The yield of an artesian well cannot in any way be predicted. The average 
of 805 Queensland bores in 1901 is given as 444,000 imperial gallons per day, 
(say 532,000 U.S. gal., or o‘8i cusec), but some go as high as 11 cusecs, while 
dry bores are not infrequent. 

So also, it is at present impossible to estimate the ultimate yield of an 
artesian basin. No doubt, if a survey of the outcrop of the permeable stratum- 
were made, we could estimate the supply by percolation as a fraction of the 
rain-fall on the outcrop area ; but this does not take into account such matters 
as extra supplies due to leakage from rivers, or water-bearing surface deposits 
which cross the outcrop, or losses due to portions of the outcrop being covered 
with clay, or other impermeable cappings. 

As an example of the difficulties found in such problems, David (Artesian 
Water in N. S. Wates), estimates that the nett area of the New South Wales 
outcrops is about 44 square miles, and on this assumption, he finds that the 
minimum total yield of artesian water is about 76 cusecs. Allowing for leakage 
from water-bearing gravels which cross these outcrops, he finds a possible yield 
at the rate of 3800 cusecs ; and finally, by considering leakage from the Darling 
River, yields up to 44,000 cusecs, are obtained. The last two figures are probably 
excessive, while the first is some 10 per cent, below the actual yield at the date 
of Professor David’s paper. 

It may, however, be stated that there are indications that the artesian wells 
in Algeria, as a whole, are now discharging less than in 1900. The artesian 
water level under the City of London has (subject to slight fluctuations due to 
unusually wet or dry years) also been falling at a rate varying from 18 inches 
to 3 feet per annum, for at least ten years past. 

I am inclined to believe that the deficiencies in supply which occasionally 
occur in artesian wells are due either to faults in the casing of the well; or, 
where the supply is permanently and markedly less than that given by neigh¬ 
bouring wells sunk to the same stratum, that local variations in the perme¬ 
ability of the stratum are probably the cause. 

The quality of the water yielded by artesian wells is usually good. Organic 
pollution (except where the casing is leaky) may be disregarded. As already 
stated, the water may be mineralised, yet cases where the amount of salts con¬ 
tained is so excessive as to render the water useless are rare. 

Deep artesian wells must be regarded as sources of water for human con¬ 
sumption only, being far too costly to yield an adequate financial return when 
the water is employed for irrigation purposes. Shallow artesian wells are 
occasionally used to irrigate valuable crops, but the conditions giving rise to 
such wells (say less than 100 feet deep) are rare, and the area enjoying such 
favourable circumstances is generally small (see p. 250). 

As typical figures likely to occur in calculations regarding artesian wells, 
let us consider the map given by Williams (ut supra). 

The lines of equal pressure in the artesian bores of Western Queensland 
are, on the average, spaced about 30 miles apart, per 100 feet fall in 

pressure. 

Taking the unfavourable assumption that the effective size of the grains 
of the permeable bed is equivalent to a 70 mesh sieve (i.e. fine sand), we 
find a velocity coefficient of 189 at ordinary temperature, or, approximately 
400 at a temperature of 122 degrees Fahr., which is roughly that of the 

artesian water. 

18 


274 


CONTROL OF WATER 


The velocity of flow (in a solid column with an area equal to that of the 
cross-section of the bed), is therefore : 

400x100. , . , , 

160000"" * eet P er da y = 3 mc “ es P er day, 


and taking the thickness of the bed as 2000 feet, we find that each 1000 feet 

2000 X IOOO 

horizontal width of bed carries -—-, or 50,000 cube feet per day. 

The length over which flow occurs is about 700 miles, or the total available 
quantity is probably between 150 and 200 million cube feet daily. The yield 
of the existing wells appears to be about 70 million cube feet per day. 

If we endeavour to apply similar calculations to the yield of individual wells, 
it will be plain that either very great differences in pressure must exist close 
to the bore tube, in order to force the water through the stratum ; or, that all 
the finer grains of sand are swept out by the first rush of water, and that the 
flow in the last ico to 200 feet near the bottom of the bore tube is through 
well defined channels, rather than of a capillary nature. The remarkable 
variability of the yield of individual artesian wells is consequently not 
surprising, and wells yielding quantities such as 3, or 4 cusecs, are only likely 
to occur when the strata are coarse-grained, taking the form of beds of large 
gravel, or greatly fissured rock. 

The principles of geology can, however, be applied to indicate certain 
general laws concerning artesian wells. 

The permeable stratum represents the remains of ancient marine or 
alluvial deposits, and, even if the ancient coast line has been entirely removed, 
the materials found near the edges of the existing stratum are probably the 
remains of beds which were laid down near the shores, and the centre of the 
existing stratum represents beds laid down in deeper water. Thus, the beds 
at the edges may be composed of all materials ranging from large boulders to 
fine clay (laid down by an ancient river) ; but, as a general rule, they will be 
far coarser and more variable than the central beds, which will almost 
certainly prove to be entirely composed of fine sand (clay beds in the centre 
may be considered as unlikely to occur, since the stratum as a whole is 
assumed to be permeable). 

Applying these principles to predict the yield of wells, we see that : 

Dry wells (representing local clay beds), and wells yielding very large 
quantities of water (representing local beds of coarse gravel) will generally be 
found to occur near the edges of the artesian basin. 

Near the centre of the basin, dry wells, or very large yields, are unlikely to 
occur ; but, on the average, the yield of wells will be less than the average 
yield of wells sunk near the edges. 

In view of the great cost of an artesian bore, the fact that artesian wells 
are usually deep (i.e. sunk near the centre of the basin) is not surprising. 
An investment of ^3000 or ^4000 (which is fairly certain to yield some 
water) is more readily undertaken than one of ^300 or ^400, which may 
either yield no water, or a far greater quantity than is required. 

Similarly, the services of an expert geologist are in reality most necessary 
when shallow wells are proposed. 




CHAPTER VI.— (Section B) 


FLOODS 


Floods. —Relation between the intensity of rain-fall and the time during which the rain¬ 
fall continues—Observations required—Bruyn - Kops’ values—Connection between 
intensity of a flood and the absolute size of the area whi^h. produces it—Critical 
period—Relation between intensity and time—General rules. 

Flood Discharge of a Stream or Catchment Area. —General principles—Special 
rules—Estimation of critical period—Ratio of run-off to rain-fall—Shorter formulae— 
Examples. 

Flood Discharge in a Reservoir. —Gould’s table—Examples. 

Design of Waste Weirs. —Old and new values of coefficients of discharge. 


The Relation between the Intensity of Rainfall and the Time during which 
the Rainfall coiitinnes. —Before any logical treatment of the questions concern¬ 
ing flood discharge, and the drainage of small areas can be undertaken, it is 
necessary to consider the relation between the possible intensity of a rain-storm 
and the time between the beginning and end of the storm. 

Consider any interval of /, minutes, during a fall of rain (where no 
assumption that the rain begins or ends simultaneously with the period t, is 

ll 

ma.de). During these t, minutes let K—j- inches of rain be collected in a 


rain-gauge at the point considered. Then I, is called the hourly intensity of 
the rain-fall during the period of t, minutes, and R, is the total rain-fall 
during the same period. 

The present section is devoted to a consideration of R, and I, as functions 
of /. The values of R, and I, can only be obtained by a systematic study of a 
long period record of an automatic recording rain-gauge. It will be obvious 
that R, and I, are extremely variable, but when a long period record is 
studied, it is possible to lay down certain values of R, or I, which will not be 
exceeded more than say once in io years, twice in io years, etc., down to once 
a year, twice a year, etc. 

In this sense, and in this sense only,. can we consider R, or I, as 
functions of t. 


Thus, de Bruyn-Kops {Trans. Am. Soc. of C.E. , vol. 60, p. 248), from 
studies of a 17-year record at Savannah (Georgia) (see Sketch No. 66, Fig: II.) 
where the mean annual rain-fall is about 50 inches, found that : 


Maxima records of the 17 years. 

' ■'. } ;‘!l* • 

• ^ s * , ‘ 1 • • ' 

Occur once every two years 

Occur once a year 


I = 


. ' I = 


191 inches 


/+30 per hour 
163 


I = 


t+27 

141_ 
t + 27 




275 






276 


CONTROL OF WATER 


Occur twice a year 
Occur 3 times a year . 


I 

I 


104 

t+22 

86 

/+19 


inches 
per hour 


>> 


Occur 4 times a year.I = » 

63 

Occur 5 times a year. 1 = ” 

The examples are typical, as may be verified by a study of meteorological 
journals, and the fact that I, increases as /, decreases is the really important 
part of the investigation. 

The importance of the investigation must now be elucidated, before pro¬ 
ceeding further. 

Consider an asphalted area (i.e. a practically water-tight area), A, acres in 
extent, and of such a configuration that the rain-water falling at the boundaries 



Sketch No. 66. —Relations between Time and Total Rain-fall, in Inches, in England, 
according to Mill; and at Savannah (Ga.), according to de Bruyn-Kops. 


of the area arrives at the drain grating 5 minutes after it reaches the ground. 
Then, according to de Bruyn-Kops’ curves, the drain must be capable of 
disposing of the water at a rate corresponding to a discharge of 

A - 9 - = 5’ 47 A 

35 5 


cusecs. Otherwise, once at least in 17 years, rain water would (temporarily at 
any rate) accumulate on the area, and flooding might occur. If, however, an 
equal area, but of different configuration, such that the rain water falling on the 
boundaries took 30 minutes to arrive at the drain, be considered, the capacity 

of the drain need only be A-^ = 3‘I9A cusecs. (Note .—1 inch of rain per hour 

running ofif in 1 hour = roi cusec per acre=i cusec per acre, approximately). 
The practical objections to the theory are : 

The time /, of arrival at the drain, depends on the quantity of water already 
on the area, the size of the channels, etc. 

In the case actually considered, if the drain connected with the first area 
could only discharge 3*I9A cusecs, the flooding at the end of the first 5 minutes 

would amount to an average depth of ——- = 0*19 inch over the whole 

X 2 
































CRITICAL PERIOD 277 

area, and would be reduced to nothing 25 minutes later, which is not a very 
important matter. 

d he practical principle, however, that the maximum discharge per acre, or 
per square mile, of any area, whether permeable or impermeable, increases as 
the time decreases is undoubtedly true, and the method of considering the 
intensity of rain-fall as a function of the time is the most logical process of 
arriving at the rate of increase. 

Let us therefore assume that /, is not necessarily the time water falling as 
rain takes to arrive at the entry to the drain, or the locality where the flood is 
measured, but that /, in some way depends on this time, and let us call l, as 
thus approximately defined, the critical period. 

If f be the fraction of the rain-fall that is actually discharged (i.e. f—v 00, 
for a water-tight area, such as an asphalt, slate, or cement surface, and f 
decreases down to say o‘io, for a sandy surface) then the average discharge 
from an area of A, acres during the time is : 

Q = L/A cusecs 

or, Q = I/_/M X640 cusecs, if M, be the area in square miles. 

If we select I<, from the maximum recorded curve, it is plain that Q, will 
represent the maximum flood during the period of the record, while if I<, is 
selected from the curve of rain-fall intensity which occurs twice a year, a dis¬ 
charge equal to, or exceeding, Q, cusecs may be expected twice every year. 

In practice, /, is usually estimated by calculating the velocity of the water 
in the stream, or discharge channels, when these are carrying half- or three- 
quarters of the quantity represented by Q, and, as a rule, the information being 
deficient, /, is merely estimated by some such rule as : 

_ Maximum dimension of the area in feet 
200 to 300 

corresponding to a mean water velocity of 3, to 5 feet per second. 

Returning to the relation between I, and /, the following information is 
available : 

Symons (.British Rain-fall , 1892) gives, for Great Britain in general : 


/, in Minutes. 

10 

20 

30 

40 

5 ° 

60 

90 

120 

t-, . fR, inches 

requen | ^ inches per hour 

TT , (R. inches . 

nusua 1 i nc h e s per hour 

070 

r8o 

°’55 

3 * 3 o 

0*42 

1*26 

0*90 

270 

0*52 
1‘04 
1 '22 

2 ’44 

°‘59 

0*89 

1-44 

2*16 

o - 6c: 
078 
1 ’64 
r 9 7 

072 

072 

1*82 

1*82 

0*82 

o ‘55 

2*10 

1*40 

0-85 

°’43 

2*20 

I ’IO 


Mill (British Rainfall , 1908), using further information, states (Sketch No. 
66, Fig. I.) • 


l , in Minutes. 

IO 

20 

30 

40 

5 ° 

60 

Too numerous fR, inches . 

to discuss \ I, inches per hour 

-p. , ,, fR,inches . 

Remarkable . -( I;inchesperhour 

* (R, inches . . 

Very rare • j If inches per hour 

0'20 

i’8o 

0-65 

3 ’ 9 ° 

I ‘OO 

6*oo 

°’53 

i *59 

1 ’06 
ri8 
1758 
474 

070 

1 ‘40 

1 '35 
270 

2 ’00 

4*00 

0‘82 

1-23 

1 ’54 

271 

276 

3’39 

0*92 

1*10 

1*67 

2*00 

2-42 

2*90 

1 '00 

1*00 

1 '75 

i 75 

2 ’ 5 ° 

2*50 












































CONTROL OF WATER 


278 

Thirty-three cases of falls exceeding the “ Very rare ” curve are on record 
in the 49 years of observations discussed by Mill. The absolute maxima are : 


' = • -5 r 5 

3 ° 

45 

60 minutes 

R= . . 1*25 1*46 

2*90 

3 ’ 4 2 (?) 

3*63 inches 

For longer periods, we find : 

i|- hours 2 hours 

3 hours 

5 hours 

9 hours 

R= 375 4'8o 

6-70 

6*5° 

4-90 inches 


A comparison of the two sets of figures indicates that the short period (5 to 
30 minutes) records are likely to be increased, as autographic rain-fall recorders 
become more common. 

The very rare curve is fairly represented by . T — 


and the remarkable curve by 
and the too numerous curve by 


I = 
I = 
I = 


/4-30 per hour. 
168 

^+ 3 ° 

84 

/+30 






Lloyd Davies’ observations at Birmingham, which 
extend over four years {P.I.C.E., vol. 174, p. 48), T= 
accord very fairly with. 


In Berlin the following is stated to occur once a year I — 
Talbot gives for the Eastern United States : 

Maximum authentic. 


- 6 3 
^+ 3 ° 

36 

/+10 
420 




if 


r).j 


Probable maximum 


At Baltimore the maxima are 

• f / ') , ' 

For ordinary falls in the Eastern United States 


: < 


Talbot gives. 

Dorr gives. 

Kuichling gives .... 
And other records agree fairly well with 


I = 

I = 

I = 

I = 

I = 
I = 
I = 


/+ 3 ° 

360 
t +30 

270 

^+ 3 ° 

105 
/+15 
i$o 
^+ 3 ° 
120 
/+20 
180 




>> 


55 








/+ 3 ° 




The above figures are typical of the general conditions prevailing in Temper¬ 
ate climates, and while individual observations may be better represented by 
such curves as : 

38*64 


1 = 


f 0-687 


and I = 

V t. 


. Sherman’s maxima, 
Gregory’s “ winter storms,” 


and so forth, the curve I = 


*+ 3 ° 


is never very far wrong. 















INTENSITY OF FAIN-FALL 


279 


For the 1 ropics, the only systematic information is obtained from records 
extending over 4 years, at Manilla (Philippines), as follows : 


Ordinary, I = 

/+30 


Maxima, I = 


290 

/+30 


inches per hour. 


1 he following deductions rest mainly on records obtained in Temperate 
zones, but are believed not to be contradicted by the unsystematic, and as 
yet uncollated, information existing in the records of the Indian Meteorologist’s 
Office. 

In the first place, if the ordinary curve obtained from records of 3, or 4 years 
be represented by : 


I = 


A 

/+30 


inches per hour 


then the maximum curve obtained by long observation, and the isolated records 
made by engineers and other observers, will probably not be very far removed 
from : 


/+30 / + 30 


inches per hour 


where both curves refer to an area over which the climate does not vary 
markedly. 

The value of the constant A, is not very far removed from 25 times 
the maximum fall of 1 day that occurs in a 20 years’ record for one locality, 
not (carefully note) of the maximum day’s rain-fall on record in such offices as 
those of the United States Weather Service, or of the Indian meteorologist. 
This indicates that, in a long period of time, the quantity of rain that occurs in 
1 day once in 15 or 20 years may be expected to occur in about hours. 

It is believed that these rules will permit an engineer to predict the values 
of l t , required for estimating maxima flood discharges (i.e, h = the maximum 
intensity recorded over a long period), and the drainage capacity necessary 
to prevent detrimental flooding {i.e. I< = the intensity which occurs once in 
4 years, say). 

These rules probably hold up to : 

t— 200 to 250 minutes, or 3 to 4 hours. 


For areas in which the critical period is greater than 3, or 4 hours, no 
general law can be given. I have usually been accustomed to collect the 
records of a large number of stations (say 50) adjacent to the locality 
considered, and assume that : 

Re = ^ = the maximum day’s rain-fall occurring in the records 

for all values of t, up to 1440 minutes or 24 hours. This is probably an under¬ 
estimation of the true state of affairs. 

While the maxima intensities for short periods are probably produced by 
thunder-storms of small area, the maxima intensities for such periods as 
6, 12, or 24 hours, usually occur during long-continued winter (speaking of 
Temperate climates) downpours covering a large area. The fact that floodings 
of streets and railway cuttings usually occur in the summer, while floods 
covering 10 square miles or more usually occur in the winter or spring, is well 






280 


CONTROL OF WATER 


known to engineers. Thus, it is probable that the maxima flood discharges 
are best estimated by putting : 

Re = -—b = maximum day’s record, obtained from say 50 stations, and 
60 

observations extending over 20 years, for t =600 to 1200 minutes. 

Rj == -~—\t = maximum 2 consecutive days’ record, as above defined, 

60 

for t= 1200 to 2400 minutes. 

The value of the run-off factor f, also needs consideration. The values 
given on page 282, are fair means. They are probably somewhat high for 
areas of which the critical period is 1 hour, or less ; and may be low for areas 
with critical periods of 24, to 48 hours. The rules given for I<, probably pro¬ 
vide for this. 

Flood Discharge of a Stream, or Catchment Area.—The maximum discharge 
of a stream is one of its most important hydraulic properties, since the requisite 
provision for weirs, spillways, bridges, etc., entirely depends upon this discharge. 

Also, while an erroneous estimate of the low-water discharge may possibly 
lead to inconvenience, an underestimate of flood discharge may lead to 
disaster and loss of life. 

The maximum discharge of a stream depends on : 

(i) The duration and intensity of rain-fall, and area over which it occurs. 
Also whether the storm producing the rain-fall moves with, or against the 
general direction of the stream. 

(ii) The storage, both natural (including absorbent strata) and artificial, in 
the catchment area. 

(iii) The size of the catchment area, relative to the area covered by storms 
producing intense precipitation. 

(iv) The general topography of the catchment area, such as its slope, and 
shape, character of surface, whether forested, cultivated, or impervious. 

It should be particularly noted that the combination of steep slopes of 
tributaries, with a flat slope of the main stream, is very favourable to intense 
floods. 

Since large floods rarely occur more frequently than once in 40 years, 
actual observation is plainly impossible. The water levels of former high 
floods are often remembered, and, if reliable, the discharge which should be 
provided for may be estimated from them. 

It must be borne in mind that local report is often absolutely untrustworthy, 
and invariably needs checking by connecting up the various spots pointed out 
by actual levelling. Also, assuming that the cross-section and surface slope 
for the record flood have been accurately determined, even by reliable 
observers, the selection of the correct discharge formula is frequently a difficult 
matter, and in some cases (possibly owing to the flow being turbulent, or the 
bed in motion) an application of any usual formula to well-ascertained flood 
levels and cross-sections leads to absolutely absurd results. 

For example, take the case shown in Sketch No. 20, which is by no means 
an unusual one. It will be found that a rise of the river from level AB, to 
level CD, gives, upon calculation, a decreased discharge, owing to the reduc¬ 
tion in hydraulic mean radius, due to the extra wetted perimeter BC, DA. 

The more correct method of separately estimating the discharge in the 
flood channel and flats, is fairly obvious, but such a fact does not tend to 


FLOOD DISCHARGES 


281 


increase our confidence in these calculations, and it is by no means an 
insignificant fact that the two records of the most intense floods known to me, 
which are anything more than rough estimates, were both arrived at by this 
method. For example, in the flood at Devil’s Creek, Iowa, 1300 cusecs per 
square mile occurred, (see Floods in United States in 1905), and in the 
Oberlausitz (Saxony) records of 1015, and 1160 cusecs per square mile are 
reported in the Deutsche Bauzeitung for 1888, p. 264. 

It is not intended to impugn the general accuracy of these records, since 
well observed floods occurring in certain Japanese rivers are known to have 
attained a magnitude of similar order (760, 885, 980, etc., cusecs per square 
mile), and it is believed that these are not absolute maxima, since higher 
flood levels are on record, but the figures referred to above are probably 
subject to at least 20 per cent, of error. 

As a check, therefore, on such methods, and for application in cases where 
no reliable flood observations can be secured, it is useful to possess simple 
formulae for flood discharges. 

For preliminary discussions, the most practical type is : 

Q = C x (area) n 

where Q, is the total maximum discharge in cusecs. 

Here, as a rule, we may say that C, represents the combined effect of the 
intensity of rain-fall, and the character of the surface of the catchment area ; 
while ?z, which is less than unity, seems to depend more on the slope both of 
the stream and its catchment area, than on the other factors. 

As example we may contrast Fanning’s formula for New England : 

Q = 2ooM 0 - 83 

where M is the catchment area in square miles ; with Cooley’s formula for the 
Upper Mississippi valley, where the slopes are flatter, and the rain-fall less : 

Q = i8oM 0 - 67 

while, for Australia, Kernot, by plotting cases of disasters to bridges and 
culverts, found that: 

Q = 4 ooM 0 - 75 approximately 

in a country of very intense rain-falls, but by no means steep slopes. 

Also Dickens’ formula for Bengal : 

Q = 825 M 0 ' 75 

where the slopes are not steep. 

For the British Isles, owing to the large number of old bridges, such 
formulas are not so necessary ; but it may be stated that the floods on imper¬ 
vious catchment areas in the Pennines very closely follow the formula : 

Q = 5ooM 0 - 83 

while for absorbent flat areas the records fall as low as : 

Q = iooM 0 - 67 

All these empirical formulae are merely approximations, and, unless of very 
limited applicability, are usually approximations tending to overestimate the 
flood discharge. They form, however, a first step towards the rational method 
of determining a flood discharge, which I now proceed to give. 

Using the rough estimate obtained as above, it is fairly easy to calculate, 


282 


CONTROL OF WATER 


with approximate accuracy, the time which rain-water falling at the extreme 
limits of the catchment area would take to reach the point where the flood 
discharge is required, when the stream and other channels are carrying about 
half the maximum discharge as above ascertained. 

We define this time as the “ critical period ” for the catchment area under 
consideration. 

Now, from the local rain-fall intensity curves we can estimate the 
maximum intensity of rain-fall possible in this critical period, and, hence, the 
whole volume of water falling on the catchment area during the period. From 
a knowledge of the character of the catchment area we can estimate what 
fraction of this volume will flow off during the period. We thus get : 

If I, be the intensity in inches per hour, or cusecs per acre, of the rain 
during the critical period of /, minutes and M, the area in square miles of the 
catchment area : 

Then F== 640x60 IM/, is the total number of cubic feet that fall on the 
catchment area, during the period of /, minutes ; and if f be the fraction that 
flows away during a period of / minutes : 

The flood discharge is : 

Q = 640/IM cusecs 

where plainly f depends on the character of the surface of the catchment 
area being: 

0*25 to 0*35 for flat country, sandy soil, or cultivated land. 
o'35 to o‘45 for meadows, and gentle slopes. 
o - 45 to o’55 for wooded hills, and compact, or stony ground. 
o‘55 to 0*65 for mountainous, or rocky ground, or non-absorbent (eg. 
frozen soil), surfaces. 

The values of I, have already been discussed, and it is plain that in such 
cases we must use the “Very rare’’curve, and must allow some margin even 
on this. 

In this method the estimation of /, the critical period, requires a certain 
amount of judgment, and it is quite possible in some cases, by omitting the 
contribution of an isolated and far distant portion of the catchment area, to 
obtain a far smaller value for /, and therefore a greater value for I, which may 
produce an absolutely greater flood, in spite of the fact that the flow from a 
portion of the catchment area has been neglected. 

Such conditions are usually hinted at when the intensity of flood obtained 
by this method, as applied to the whole catchment area, is markedly less than 
that given by a locally approximate formula, or than that deduced by a com¬ 
parison with previous observations. 

So also, especially in small areas, where the critical period is a few hours 
only, and the maximum rain-fall intensity is usually produced by thunderstorms ; 
the course of the river in relation to the prevailing direction of rainstorm motion 
must be considered. Thus, if (as is generally the case in England) the rain¬ 
storms move from south-west to north-east, a river which flows from north-east 
to south-west (i.e. against the direction of rainstorm motion) may be expected 
to have less intense floods than an otherwise identical river which flows in the 
reverse direction, and is consequently liable to floods produced by the simul¬ 
taneous arrival of the flood wave from the upper tributaries, and the run-off from 


APPROXIMA TE FLOOD FORMULAE 


283 


the lower portion of the valley produced by a rainstorm which has travelled 
down the river at approximately the same rate as the flood wave. The motion 
of the rainstorm, in fact, has decreased the critical period. 

Thus, while the general principles are universally applicable, each catchment 
area must be treated independently. 

In town, or agricultural drainage systems, however, general formulae are 
frequently required, and since all the minor catchment areas are of nearly 
similar geometrical form, it is evident that t (and therefore also I), are to a 
certain degree functions of the mean slope, and the linear dimensions of the 
area. Hence, the following collection of formulae is put forward for use in 
connection with artificial drainage only. 

Putting A, for the drainage area in acres, and S, for its mean slope in feet 
per 1000 feet, we have as follows : 

Hawksley’s rule, for London . Q = 07A 



Modified Hawksley’s rule, used 
in New York 

Burkli-Ziegler’s rule . 


M‘Math’s rule 


New York tables 


Parmley’s rule 


Gregory’s rule 
Adams’ rule 


«-/</! 


with f — 07 to o'9 

I = 1 to 3 inches per hour 

• Q 

with f= o’l to o’8 
I = 1 to 275 

6 / C 1'62 

• Q=/I v^ 

/1 = 1-05 to 1*62 

• • * •! t * 

with / = o to 1 
1=4 

S 0 ' 186 for impervious 


1:: 

JO 


2-8A 


Q=/IA 


A 0 ' 

7 


areas 


SI 

AI 


when I = 1 

837 

See Gregory’s paper, Trans. Am. Soc. of C.E., vol. 58, p. 458. 

It is doubtful whether all the authors employ the symbols f and I with 
precisely the same meaning with which I have defined them, and in many 
cases the results are applied to town areas where / is probably equal to 07 
to 0-95. It will, however, be plain that some formula of the type : 

q _ C^O ‘75 to 0 86 g 016 to 0 25 

usually be arrived at where C depends on the value of f and on the 


can 





CONTROL OF WATER 


284 


absolute magnitude of the rain-fall, while the indices of A and S, mostly depend 
on the form of the rain-fall intensity curve when expressed as a function of t. 

It is, however, believed that the extended and rational method should be 
applied to all important cases, and that the deduction of a compressed formula 
of the type now suggested is only legitimate after a certain amount of experi¬ 
ence has been accumulated. The one important fact is that the flood discharge 


per unit area, i.e. 


or for a small area, is more intense than that of a larger 


A 


M 


area of the same mean slope. 

As an example of the erroneous deductions regarding flood discharges, that 
may be obtained through relying too exclusively on the results deduced from a 
survey of the old structures existing on a stream, the preliminary studies of the 
Kali Nadi Aqueduct ( P.I.C.E ., vol. 95, p. 287) are interesting. 

In this case, a road bridge, over one hundred years old, crossed the stream 
a little below the proposed site. Flood marks above and below the bridge were 
quite plain, and taking the head thus indicated (1*5 foot), allowing for a velocity 
of approach of i‘ 48 feet per second, and a coefficient of discharge of o'6o 
through the arches, a flood discharge of 8436 cusecs was obtained. 

The engineers concerned evidently did not place complete reliance on this 
result, and provided for more than twice the quantity. It will be recognised 
that the calculation is adequate, and even if a coefficient of 0*90 is taken (my 
own experience leads me to believe that o*6o may possibly be a trifle low, but 
no drawings of the bridge are given) the value is only 12,600 cusecs. 

As a matter of observation, however, the year after the aqueduct was con¬ 
structed, a flood of at least 37,000 cusecs occurred, and it was found that the 
flood breached the approaches to the bridge, but did not damage the structure. 
The approaches of the aqueduct not affording a similar safety valve, it was 
badly damaged, a heading up of 3^5 feet occurring. 

Next year an even larger flood occurred, and after the water had headed up 
9*8 feet the aqueduct arches blew up, but the old bridge was merely submerged. 
The flood was estimated at 132,475 cusecs, i.e. about 11 times greater than the 
original bridge observations would indicate, even when treated in the most 
inflated manner. 

As a test of the rational method of estimation we may take the following 
figures : 3,025 square miles of flat and sandy catchment area, and a rain-fall of 
I7'6 inches on the 16th July 1885, followed by 3 inches on the 17th. The 
critical period may be estimated as 48 hours, and the run-off factor as o’2o. 

21 

We thus get a run-off rate of say ^gXo-2o=o’o9 inch per hour, or, at the rate 


of 58 cusecs per square mile, or say 176,000 cusecs ; and the aqueduct as now 
designed appears capable of passing about 200,000 cusecs, and has stood 
since 1887. 

Equalising Effect produced by a Reservoir.—The above discussion permits 
the volume of water that reaches a reservoir to be estimated with more or less 
accuracy. It is not, however, necessary that the waste weir should be able to 
pass off the flood as rapidly as it arrives at the reservoir, since the rise of the 
top water level of the reservoir which must occur before the waste weir begins 
to discharge at its maximum capacity, temporarily stores up a certain volume 
of water. Thus, the discharge over the waste weir continues for a longer 
period than the flood, and is consequently not so intense. 


FLOOD STORAGE IN RESERVOIRS 


285 


The question can be mathematically investigated as follows : 

Let B, denote the area of the water surface of the reservoir in square feet, 
at a height of H feet, above the spillway crest. 

Then, in any time It, a volume Qdt, flows into the reservoir of which B^fH, is 
stored up in the reservoir, and CLH l - 5 dt, flows away over a spillway L, feet in 
length under a head H. 


Then : 


dt_ dH 
B Q —CLH 1 - 5 


Now, this is integrable if B, and Q, are taken as constants, and putting : 


Q 


CLHrt 1 - 5 and r=~ 

ria 


where H a , is evidently the head over the weir when the discharge is Q, cusecs 
we get: 


T = 


2B 


3(C 2 L 2 Q)S 


[ 




V 1 -f- V r-\- y 


- V; 


' 3 { 


tan -1 —=(2 + 

V3 


*>-!)] 


= K <\>{r) 

2B 

Where K is written for-.. Gould ( E?ig. News , December 5th, 

3(C 2 L 2 Q)* 


1901) has tabulated cf)(r ) as a function of r (see p. 289). 

This equation gives the time during which the reservoir rises from H = o, to 
H = rH a , and in any practical case there is a certain factor of safety, since B, 
increases as H, increases. 

It is also possible, in cases where our knowledge of Q, the flood discharge 
into the reservoir, and C, the coefficient of discharge of the spillway, are 
sufficiently accurate, to obtain a very close approximation to the manner in 
which the water surface of the reservoir actually rises, by considering B, Q, 
(and C, if necessary) as constants only during a small variation in H, say 
o'5 foot. We can thus for the first half foot calculate K, H a , and r, and find T 1} 
the time during which H, rises from o to o’5 foot. 


Thus, T, = K{ 0 (g 5 )-#>)}. 


Now, with the new B, (and the new value of C, if advisable) calculate the 
new K, say K&, and if a new Q, or C, are used, the new H a , say H&, and 

corresponding to H=o*5 foot and r 2 = 77- corresponding to H = ro foot. 

Hj) 

We thus get 

T 2 —T 1 = I t>{<Kr a )-<Kr 1 )} 


as the time during which H, rises from o - 5 to ro foot, and the process may be 
continued as necessary 

As a simple example, consider a Pennine water-shed of say 6 square miles, 
with a critical period of 200 minutes. I, is, for “ very rare” intensity, 1-05 inch 
per hour. Take ri5 inch per hour, and take f as o'6o. We get a very intense 
flood at the rate of 442 cusecs per square mile. 







286 


CONTROL OF WATER 

The general formula gives : 

goS — 37 2 cusecs per square mile ; 

so that the discharge is certainly not underestimated. 

Now, assume that B = 3 per cent, of the catchment area (say 5‘2 million 
superficial feet), and that L=i2o feet as Hawksley’s rule would give. While 
C = 3 , for safety. (3 = 2652 cusecs. 

Thus 36oH a 1>5 = 2652 : or H a 1,5 ?= 7 ' 37 . H 0 =379 feet. 


K= -— — IQ, 4 OQ,OQQ - - = 4815 seconds, approximately. 

3(9 x 14,400 X 2652) 3 


Thus, assuming that there is no change in B, or Q, we find that the surface 
of the reservoir rises from H=o, to H = 3 feet, or r, changes from o to 079 in 
48i5Xi’862 seconds. Thus ^ = 8960 seconds, or just under 3 hours 30 
minutes. 

Let us assume that before the storm burst a flow of 600 cusecs was already 
running out over the spillway. We have : 

360 H 1 1 - 5 = 6oo Hi 1 - 5 =1*67 H L = 1*41 foot 


and 74 = 0*37. Therefore, <^(r 1 ) = 0*614, and, for a rise to 3 feet, i.e. 74 = 079, 
<K r 2) =I *862, and: 

T 2 — ^ = 4815 (1*862—o*614) = 6010seconds, ora little over 1 hour 40 minutes. 
Again, take an area of 1 square mile, with a critical period of 140 minutes. 
We find that: 

Q = 6ox 1*4x640 = 538 cusecs 

. .. • r, ... ■ ., > •' 

and, with L = 2o feet we find that H a h5 = 9*oo H„ = 4*33 feet 

Taking B, again as 3 per cent., i.e. 20 acres, or 820,000 square feet 




1,640,000 
3(9x400x 538)^ 


- i 

L . ■ • - » ' ‘ *-■ 

= 4370 seconds 




Now, if H = 3 feet; r=o*69, $(>") = 1 ’ 44 > T = 63oo secs. = i hour 45 min. 
and if H=4 feet; r=o*92, (f>(r) = 2*923, T= 13,830 secs. = 3 hours 50 min. 


and the general deduction can be made, from these examples, that for such run¬ 
offs as can occur under the assumptions above stated, Hawksley’s rule for the 
length of spillways, that is to say : 

20 feet per square mile 

. . ... 

is amply safe with reservoirs of 3 per cent, water surface. 

Let us now consider a reservoir of which the area : 

at H=o . . . . is 17,500,000 square feet 

at H = 5 feet . . . .is 20,000,000 „ 

at H =6*5 feet . . . , is 20,500,000 „ 


and L = 7o feet. We assume that Q = 8,700 cusecs. C = 3. 

Taking B, for the first portion of the rise as 17,500,000 we get 

35,000,000 


I< = 


= 16,000 seconds 


3(9 x 4900 x 8700) 

H a = 10*98 feet. 




210 






WASTE WEIRS 287 

Thus, the rise to H = 2-20 feet, or r = 0*2 ; <p( 0*2) = 0*314 is accomplished 
in 16,000x0*314 seconds = 5024 seconds, or 1 hour 24 minutes. 

For the rise from H = 2*20 feet, up to H = 5 feet. Take B = 18,700,000. 
K 2 = 17,090. r x — 0*20, r 2 = 0*46 ; </>(r 4 ) = 0*314, (jf>(r 2 ) = 0*802 

Therefore, T 2 —T 4 = 17,090 (0*802—0*314) = 17,090x0.488 
= 8350 seconds = 2 hours 20 minutes. 

Next, for the rise from 5 feet to 6*5 feet. Take B = 20,250,000. 

K 3 = 18,500. r 2 = 0*45, r 3 = 0*59; <£(r 3 ) = 1*113. 

T 3 — T 2 = 18,500(1*113—0*802) = 18,500x0*311 
= 5760 seconds = 1 hour 36 minutes. 

And for the rise from 6*5 feet to 7*25 feet we can take B = 20,500,000 square feet. 

K 4 = 18,750. r s = 0*59, r 4 = o*66 ; 0 (r 4 ) =1*338. 

T 4 -T 3 = 18,750(1*338-1*113)= 10,750x0*225 

= 4217 seconds=i hour 10 minutes. 

Now, just previous to the Johnstown (Pa.) dam catastrophe, a rise of 9 inches 
in one hour was observed, when the height above the spillway was about 7 feet 
The areas and discharge used above are the nearest round figures to those 
given in the Report of the Commission of the American Society of Civil 
Engineers on the subject {Trans. Am. Soc. of C.E. , vol. 24, p. 447), and on 
referring to this report it will be found that the process leads to results 
corresponding with observation. Thus, the rise to 7 feet above the spillway 
took place in about 8 hours, while the calculation gives the period as about 
6^ hours, and it is doubtful whether the flood discharge attained a value of 
8700 cusecs throughout the whole period. 

The catchment area was 48*6 square miles, and the assumed figure of 8700 
cusecs, or 179 cusecs per square mile, is probably far better ascertained than 
most of the recorded values of intense floods. The formula Q = 2ooM 0,83 gives 
154 cusecs per square mile, so that the recorded discharge is about 16 per cent, 
greater than that given by the formula which applies to catchment areas 
which are on the average somewhat flatter than that now considered. The 
critical period is probably about 10 hours, and I, from Talbot’s curve of 
“maximum authentic rain-falls” is about 0*67 inch per hour. If we assume 
that f— 0*40, we get a discharge of 171 cusecs per square mile. The assump¬ 
tions are legitimate, and it may be observed that while the general formulae 
might lead to an unduly small length of waste weir, the more logical method 
yields a result that would certainly have secured a waste weir of adequate 
dimensions. 

Design of Waste Weirs.—T he theoretical design of a waste weir is 
simple, but accurate knowledge of the coefficients of discharge over the weir 
(especially if partially drowned), and of the relation between the velocity and 
surface slope in the escape channel, is very deficient. 

The difficulties are principally due to the fact that the head over the weir 
is often considerably greater than is usual in accurate experiments. The flow 
in the escape channel is always turbulent (due to the agitation produced by 
the weir), and is frequently varied (as in the case of a weir which is oblique 
to the escape channel). The deficiency is more apparent than real ; since, 
although the coefficients are mainly selected by the general consensus of 
engineering opinion, these coefficients have also been employed in the calcula- 


283 


CONTROL OF WATER 


tion of the volumes discharged by the floods observed ; and, consequently, 
any error equally affects our fundamental assumptions as to the volume that 
the weir has to discharge. 

For this reason I generally employ the coefficients usual among engineers, 
and regard the newer values (which have lately been obtained by direct ex¬ 
periment) as refinements that do not necessarily require to be introduced 
into practical calculations. These newer values should, nevertheless, be 
employed in working up fresh observations, and are therefore put on record 
in the appropriate places. 

Let Q, be the number of cusecs which it is proposed to discharge over a 
weir L, feet in length. 

If the weir be of the free overfall type (Sketch No. 67, Fig. 1), we have : 

Q = CiLD 1 - 5 

for the discharge produced by a depth D, over the weir sill. If the flow in the 
escape channel be steady, we also have : 

Q = 7/A = CA \! rs 

where A, is the area of the wetted section of the channel, 
r, is the hydraulic mean radius 

j, its slope, which may be taken as equal to the designed bed slope of 
the channel. 

The usual design is a flat-topped weir, and if the crest be less than 3 feet 
broad, the value : 

Q = 3'o9LD 1,5 

has been very frequently adopted. While for broader crested weirs : 

Q = 2-64LD 1 - 5 

The experiments of the United States Deep Waterways Board at Cornell 



( Wet? Expei ivients, p. 89) indicate that Cj, is in reality variable, and putting 

H = D + — : , we get: 

* Q = CjLH 1 -* 

and the values of C x are tabulated on page 130. 





































GO ULUS FUNCTION 


289 

The usual assumptions therefore appear to be safe, and the value C x = 3 09^ 
is probably a very good mean for the narrower topped weirs when D, does 
not greatly exceed 3 feet, as is usual in British practice. 

When the weir is drowned, and is of the form shown in Sketch No. 67, 
Figs. 2 and 3, the formula are : 

Q = CjLVD^Da + fDj) 
and, Q = CA I rs = CA \f d x s approximately 

where, in the second figure, d 1 — D 2 +.r, and in the third figure d x = D 2 . 

The Cj, coefficients are less well determined. For flat-topped weirs, or no 
weir as in Sketch No. 67, Fig. 3, Strange takes the C l5 coefficient as follows : 

Di + Dg in Feet 34 5 6 7 8 9 10 11 12 13 and over 

Ci . . . 3-20 3-31 3-41 3-52 3*63 374 3-84 3-95 4-05 4-16 4-27 

and neither Chatterton’s experiments ( Hydraulic E.xfierimejits in the Kistna 
Delta ) nor Rhind’s ( P.LC.E. , vol. 154, p. 292), markedly contradict these values. 

A more definite statement cannot be made. The values are probably safe, 
and are likely to be below the truth. 

No experiments are available on drowned weirs other than of the flat-topped, 
or sharp-edged type, except one on a rounded weir section (see Sketch No. 67, 
Fig. 4) with Di -f I) 2 = 6'6 feet ( Report of U?iited States Deep Waterways 
Board , p. 291). When undrowned, C x = 370, and diminishes as drowning 
proceeds, to : 

C x = 3*47, when the tail water is 3*3 feet above the crest 

The formulae are best treated by first calculating D 2 , from the equation for 
the channel discharge and then using the weir discharge equation to calculate 
D x , and thus obtaining the total depth over the weir. 

VALUES OF GOULD’S FUNCTION <p{r) (see Page 285 ), ARRANGED IN 
HORIZONTAL LINES FOR EACH TENTH, AND VERTICAL COLUMNS 


FOR EACH HUNDREDTH OF r=D~. 


H 

H« 

O'OO 

O'OI 

0*02 

0*03 

0*04 

0*05 

0*06 

0*07 

0*08 

1 

1 

0-09 

0*0 

0*0000 

0*0153 

0*0306 

0*0459 

0*0613 

0*0766 

0*0919 

0*1072 

I 

0*1 22610*1378 

o*i 

0*1532 

0*1685 

0*1838 

0*1992 

0*2155 

0*2319 

0*2483 

0*2646 

0*2810 

0*2973 

0*2 

0*3137 

°’ 33 01 

0*3464 

0*3628 

0*3791 

o *3955 

o* 4 I 37 

°* 43 I 9 

0 45 QI 

0*4683 

o *3 

0*4865 

0*5047 

0*5229 

o* 54 x 1 

o *5593 

o *5775 

o *5957 

0*6139 

0*6321 

°*6534 

°’4 0*6747 

0*6960 

0 * 7 I 73 

0*7386 

o *7598 

0*7811 

0*8024 

0*8237 

0*8450 0*8663 

07 

0*8876 

0*9137 

0*9399 

0*9660 

0*9921 

1*0183 

1 *0444 

1*0705 

1 *0966 

11*1128 

o*6 

1*1489 

1*1750 

1*2012 

1 *2322 

1*2674 

I * 3° 2 7 

i‘ 338 o 

i *3733 

1 *4086 

i *4439 

07 

i* 479 2 

i* 5 i 45 

1 ’5498 

1 ’ 5 8 5 1 

1 *6203 

1*6556 

1*7073 

i* 759 ° 

1*8107 

1*8624 

o*8 

i‘ 9 I 4 I 

1*9658 

2*01 76 

2*07I5 

2 * 1488 

2*2262 

2 * 3 ° 3 5 

2*3808 

2*4582 

2*5355 

°’9 

2*6129 

2*7681 

2*9233 

3 *° 7 8 5 

3*2347 

3*3889 

3 ' 544 i 

4*0096 

4 * 475 ° 

4*9405 


19 











































290 


CONTROL OF WATER 


In British practice D, and r/ l5 rarely exceed 3 feet. The limitation appears 
to be founded more on a desire to avoid waste of reservoir capacity than on 
considerations of safety. The design of the weir and the pitching of the 
escape channel follow the rules given when discussing Falls and Rapids (see 
pp. 655 and 721). In several of the newer German reservoirs the escape channel 
is broken up into a series of shallow water cushions, or the slope is even 
formed into waves. Since escape channels in general are usually dry, and 
rarely, if ever, run more than 6 inches deep for longer than a week, these 
designs do no harm, although the experience of irrigation canals shows that 
if severely tested they would probably be destroyed. The primary function 
of an escape channel, however, is to remove water, and these refinements 
obstruct the flow. Since ample opportunity exists for repairing any small 
erosion that may take place during floods, it appears best,’even in very steep 
channels, to make the channel smooth, and evenly graded, and to prevent 
erosion by means of a deep curtain wall at the actual weir, with such extra 
pitching as experience shows to be necessary. A somewhat steeper slope just 
after the weir does no harm. 

I purposely refrain from any discussion of the approximate rules for the 
determination of the length (channel breadth) of waste weirs. The Gould 
function method alone has any pretensions to accuracy. One of my earliest 
professional reminiscences relates to the rejection of a very excellent scheme, on 
the ground of insufficient waste weir capacity. The designer had, instinctively, 
applied the principles of Gould’s method, but, not being an expert mathematician, 
was unable to explain them clearly. Thus, what I now consider to have been a 
perfectly sufficient waste weir appeared far too small. The party I then adhered 
to was not only devoid of insight, but ignored a very cogent piece of natural 
evidence. The designed waste weir was an enlarged natural river channel, and 
no abnormal flood marks could be discovered above or near to the natural 
constriction. The designer, for want of funds, could merely propose to enlarge 
and regularise this constricted channel. We totally ignored the existing water 
marks, which showed clearly that a large temporary storage occurred above the 
constriction. 


CHAPTER VII.— (Section A) 
DAMS AND RESERVOIRS 


Stability of an Impermeable Dam and Cut-off Wall on a Permeable 
Foundation of Indefinite Depth.— Importance of tail erosion—Theory of the 
case where tail erosion is prevented—Tabulation of the values of the velocities of 
percolation—Effective depth of corewalls—Comparison of the theory with practice— 
Failure by piping—Fountain failure—Tail erosion and piping failure—Approximate 
theory when tail erosion occurs — Experimental data—General rules—Effect of 
gravity. 

Earthen Dams. —Impermeable cores of clay, masonry, etc.—Gritty and clayey 
material—Examples of the various types of dam—Classification— <£ Ordinary ” and 
“ Indian ” types—Drainage. 

General Design of Earthen Dams. 

Ordinary Type of Dam. —Slopes of the faces—Height of the dam—Possibility of 
steeper slopes. 

Construction. —(i) Preparation of the dam site — Specification—Criticism—(ii) Con¬ 
struction of the earth-work—Specification—Criticism—Preliminary experiments—• 
Practical results—Hump in the banks—(iii) Puddle trench and wall—Puddle clay 
versus concrete or masonry—Specification — Criticism—Tests for puddle clay— 
Criticism — Admixture of sand with puddle clay—Section of the puddle wall and 
trench—Filling of the puddle trench—Cases where water enters the puddle trench in 
large quantities—Junctions in concrete filling—Drainage of the puddle trench. 

Core Walls and Trenches of Materials other than Puddle.— Masonry or 
concrete—Thickness—Herschell’s rules—Bhim Thai failure—Wooden sheet piling— 
Cast iron or steel piling—Grouting in fissured rock. 

Position of the Impermeable Layer. —Liability to fracture owing to settlement. 

Indian Type of Dam. —( A) Dam with a thick core wall carried down to connect with 
an impermeable stratum—( B ) Dam in which the core wall is not connected with an 
impermeable stratum. 

(i) Preparation of the site.—Drainage—Reversed filters. 

(ii) Proportions of the puddle trench—Concrete base—Drains—Additional masonry 

. trenches. 

(iii) Construction of the earthwork—Modification of the face slopes—Dams over 40 

feet high—Dry stone walls and toes. 

Dams not joined to an Impermeable Stratum. —Depth of cut-off trench—Core 
walls versus an impermeable dam—Jacob’s sand dam—Criticism—Baroda dam— 
Leakage—Comparison with British practice. 

Casing of the Dam. —Function—Strange’s specification—Staines casing—Pitching— 
Construction—Thickness—Staines specification for concrete slab pitching—Outer 
slope pitching, or turfing—Walls on top of the dam—Generally regarding pitching and 
casing. 

Failure of Earth Dams. 

Top Width of the Dam. 

Outlet Works. _Bye pass drains for flood water—Valve towers—Undersluices—Pipe 

lines through the dam—Position of the valve—Syphons over the dam. 

Culverts. _Crossing the puddle trench — Slip joints—Tunnel outlet—Tunnels under 

"the puddle trencli_Theoretical proportions of a culvert under a puddle trench— 

29I 



292 


CONTROL OF WATER 


Practical proportions—Culvert stops, or plugs—Specification—Details of chases in 
the plugs—Creeping flanges. 

Valve Towers and Culverts. —Head wall and culvert—Central tower—Volume of 
water rejected when silting must be prevented—Undersluices—Discharge capacity 
of undersluices. 

Silting of Reservoirs. — Desarenador, or scouring gallery — Bombay practice— 
Assouan reservoir—Removal by dredging—Relation between reservoir capacity and 
mean annual run-off—Austin reservoir—British reservoir—Preliminary investiga¬ 
tions—Willcocks’ principles. 

Permeability of Earthen Dams. —Mean slope of the saturation plane — Bombay and 
Croton observations—Drop produced by a masonry core wall—British observations— 
Drop produced by a puddle wall—Experimental dams. 

Hydraulic Fill Dams. —Construction—Grading of material—Proportion of clay— 
Central drainage tower—Effect of moist climates—Necessity for special plant— 
Consolidation produced—Ratio of solids deposited to water used. 

Rock-fill Dams. —Construction—Initial settlement of the rock fill—Failures probably 
caused by bad construction—Fissured-rock foundations—Escondido dam—Wood and 
concrete diaphragm—Otay dam—Steel plate diaphragm. 


Stability of an Impermeable Dam and Cut-off Wall on a 
Permeable Foundation of Indefinite Depth.— An accurate mathe¬ 
matical solution of the above problem can be obtained, on the assumption 
that the upper boundary of the permeable stratum is a horizontal plane 
extending indefinitely in both directions from the ends of the dam, as shown in 
Sketch No. 68. In practice, this condition is sufficiently satisfied provided 
that marked erosion at the downstream end of the dam is prevented. Thus, 
the theory can be applied in order to investigate such cases as the following : 
(a) Earth dams which are never over-topped by the water that they retain. 

(< b ) Overflow masonry dams which are rarely exposed to the action of 
flowing water, so that the tail erosion is but small. 

(c) Regulators of canals where the action of the flowing water is under 
control, so that erosion is entirely stopped by the pitching, which is placed 
downstream of the work. 

In works such as weirs and undersluices, tail erosion cannot be kept 
within definite limits, and although the bed of the channel downstream of the 
work is pitched, deep scour holes may, and do, occur close to the downstream 
tail of the work. If certain assumptions are made which agree fairly well with 
the practical conditions, the theory can be modified so as to be applicable 
to these cases. Experimental investigations, however, show that the critical 
points where failure is most likely to begin are not the same as in works which 
are not exposed to erosion. If erosion does not occur the downstream tail of 
the dam is the point where failure commences. Whereas, if erosion occurs, 
failure begins in the neighbourhood of the bottom of the cut-off wall. Thus 
while the same theory suffices for the investigation of the two classes of cir¬ 
cumstances, the conditions for stability differ somewhat markedly, for in the 
first, or non-eroded class, a , the depth to which the core wall is sunk will be 
found to be the factor which mainly determines the stability. Whereas, in the 
scoured, or eroded class, the depth of the core wall has only an indirect 
influence on the stability which is almost entirely determined by 2 b, the width 
of the base of the dam. 

The circumstances assumed in the ideal case are shown in cross-section in 
Sketch No. 68, where the boundary of the impermeable area is hatched. 

Let 2b, be the breadth of the impermeable base of the dam, and let a, be the 



PERCOLATION UNDER A DAM 


293 


depth to which the impermeable core wall extends below the base of the dam. 
I ut A — b-— a 2 , and assume that the core wall lies in the centre of the base of 

the dam. b or the sake of simplicity, the action of gravity is neglected for 
the present. 

Then, assuming that the stratum below the dam is equally permeable at 
every point, and that no percolation occurs through the dam or core wall, the 
lines of flow are the series of confocal ellipses : 

-r 2 , y 2 _ 2 

cosh 2 a sinh 2 a 


and the lines of equal pressure are the confocal hyperbolas : 


cos 2 /3 sin 2 /3 







U mm 



Curve 

a . 

b . 



n EC 

100 

51 

o e -* c 0 

if 

J L M 

332 

60 

^0 6 Z - 4 , 


J , L , Mi 

350 

615 

oL * 0 66 +S 


IV l 

14 

- 4(1 

/} « 4 ° 


ELL , 

50 

O 

[3 - 90 * 


SNN , 

40 

-30 

p > -- gQ *3650 


s'n'n', 

30 

-40 

[b - 90 °' 55 IO 

5? 

5 "/vV 

!4 

-46 

p , » go'-i 6 ° 


Sketch No. 68. —Percolation under a Structure not subjected to Tail Erosion. 


Let us now consider one foot length of the dam. Let H, be the head of 
water which the dam holds up. Then the pressure at the hyperbola given by 
/3 — 7r {i.e. along the line AP), is H, and along the line CD {i.e. the hyperbola 
given by /3 = o) the pressure is o. Thus, the pressure along any intermediate 

hyperbola / 3 =/ 3 1 is H — 1 , feet of water. Also the quantity of water percolating 

7r 

along the imaginary tube bounded by the ellipses a = a x and « = a 2 is proportional 
to a 2 —and since the flow is capillary, the quantity delivered per second is : 

K^( a r a i) 

77 

where K, is the constant dependent on the effective size of the sand grains 
which occurs in Hazen’s formula (see p. 25). 

Thus, the rate of flow per square foot is not uniform, but becomes more 
intense as the normal distance between the ellipses a x and cq + S (where d is a 
small constant quantity) decreases. 


























294 


CONTROL OF WATER 


Now, let us consider two such ellipses, JLM, and JiLxMj, as given in 
Sketches Nos. 68 and 70. 

We have OJ =c cosh a x 

OJ 1 = c cosh (cq + S) 

Therefore, JJ x = rS sinh a x if § be small. 

OL=r sinh a x 
OL x = c sinh (cq-f-S) 

Therefore, LL 1 = ^S cosh <q, if 3 be small. 

Any other normal distance NN 1} plainly lies between the values JJ X , and 
LL X , for NN 1 = t’Sv'cosh 2 a 1 — cos 2 / 3 1? where / 3 =/ 3 X represents the hyperbola on 
which N, and N x , lie. 

Thus, the flow per square foot, or the effective velocity of percolation 
(see p. 25) along the tube JJiLLxMMj, varies between a maximum value: 


K — b 


V = 


7r 


JJl 


= K 


H 


ire sinh cq 


near JJ X , or MM X ; 


and a minimum value 


U=- 


K —S 

7r 


= K 


H 


LL X TrC cosh a x 


near LL X . 


As a numerical example, let us consider the values of V, and U, at points 
given by : 

y — o, x—pc ; for V 
x=o,y ~pc ; for U 

It will be plain that the values of V, and U, for the same value of/, do not 
then refer to the same tube (z>. a has not the same value in each case). The 
method of calculation adopted, however, is that which is best adapted to 
practical requirements. 

For the calculation of V, we have as follows : 


X 

cosh a— - —L 
C 


V = 


KH 

7r c sinh a 


p — cosh a 

a 

sinh a 

Vt tc 

KH 

I ‘O 

O'OO 

O'OOOO 

00 

I *5 

o ’96 

1T 44 

0*896 

2 "O 

1 * 3 2 

17182 

0*581 

3 ’° 

1 77 

2*8503 

o' 35 1 

5 *o 

2*29 

4*8868 

0*205 

10*0 

1 

2-99 

9*9 1 7 7 

0*101 


Vt TC 

The value j^"jq =co cannot occur in practice, for since c 2 = b 2 — a 2 , flow is 

b 

not possible until/, is at least equal to —=. 

V b 2 —a 2 

































VELOCITY OF PERCOLATION 


295 


For the calculation of U, we have as follows : 


• V 

sinh a = 

c 


U = 


KH 


7 TC COsh a 


p — sinh a 

a 

cosh a 

Uti r 

KH 

O’O 

O’OO 

I ’OOOO 

1*000 

°'5 

0-49 

1 ‘ I22 5 

0*893 

, i*o 

o*88 

1*4128 

0 7°9 


1*19 

17956 

0*557 

2 ‘O 

1-44 

2*2288 

0*448 

3 '° 

1 *82 

3*1669 

°‘3 I 5 


2*32 

5-137 

0*195 

10*0 

2-99 

9*9680 

0*100 


In this case fractional values of/, can occur because c, can be greater than <2, 

32 

provided that # 2 is less than —, say a less than 071A 

As an example of the values of V, and U, which occur in the same 
imaginary tube, we may take the following: 


a 

cosh a 

sinh a 

Uttc 

KH 

Wire 

KH 

, ) . 

.. . . s 

0*5 

• 

1*1276 

0*6211 

0*885 

i*6io 

I/O 

I ' 543 I 

1*1752 

0*649 

0*850 

1*5 

2 * 35 2 4 

2*1293 

0*426 

0*469 

2*0 

3*7622 

3*6269 

0*266 

0*276 

3*0 

I0*0678 

10*0179 

0*100 

0*100 

5 -o 

74*210 

74*203 

0*013 

0*013 


It will be seen that both V, and U, increase as a decreases. There is, 
however, a minimum value of a, say « 0 , which is that corresponding to the 
ellipse AEC, which passes through the two toes of the dam, and the bottom of 
the core wall, and is given by the equations : 

c cosh a 0 = b , and c sinh a 0 = a. 

Thus, the maximum values of U, and V, are obtained by putting a~a 0 
and are : 

T7 U 

v max = , in a vertical direction at A or C, either toe of the dam, and, 

na 

TC T-T 

U ma =-in a horizontal direction immediately below E, the bottom 

irb 

of the core wall. 



































296 


CONTROL OF WATER 


The upward pressure of the percolating water on the base of the dam is 
given by the formula : 

* = Co,.. £) 


7r 


where x, is positive when measured in the downstream direction. 

These formulae afford a measure of the likelihood of sand being removed 
from under the dam, and it will be evident that the dam is stable if the 
pressures and velocities thus determined are insufficient to remove the sand 
grains, or to blow up the dam. 

It is also evident that there is a limit to the total percolation per foot 
length of the dam, even if the permeable stratum is of very great depth. For, 
let a,j be the value of a for the ellipse that touches the bottom of the permeable 
stratum which is g feet deep. Then the total flow per foot length of the dam 
K H 

is - -(a g — a 0 ) } and since g, is assumed to be great, we can put 

7 T 

* 

cr 

cosh a 0 — e a o — sinh a 0 or ce a o = g. Therefore, a a = log<Aj 

Is 

and the total flow is ^ — ( log c ^- — do) which increases but slowly as g, increases. 

7 r \ c ' 

This investigation (at first sight) leads to the rather surprising result that 
the width of the base of a dam has no influence in stopping upward percolation 
at the downstream toe of the dam. 

This is possibly true in an ideal case, and suggests that the notorious 
weakness of dams with no core walls is not entirely due to “ Leakage along the 
seat of the dam,” or along the “line of junction.” In any practical case, there 
are core walls,—of shallow depth,—but still they exist, and it will be plain on 
looking at Sketch No. 68 that a shallow core wall, as shown at QR, would 
theoretically, be equally effective in stopping percolation as the deeper core 
wall OE, provided that R lies on the ellipse AEC (the dam itself is of 
course assumed to be impermeable). 

Now, take an example, and let us assume that b = 100 feet, and a =10 feet. 
Therefore c 2 = (99'5) 2 approximately. The equation of the ellipse AEC, is 

o o 

eL + iL =i 

9 1 9 1 • 

IOO 2 10- 

Now, put x = 90. Therefore j/ 2 = 100 x 0*19 = 19. y — 4*3 feet. 

Thus, a core wall with a depth of 4^3 feet at 90 feet from the centre of the 
base, is, theoretically, as effective as one which is 10 feet deep at the centre 
of the base. 

Again, if b — 50 and a = 10 feet, we get : 

Ti + y = I 

50 2 IO 2 

and when x = 40, —, = — ; and y — 6. 

’ 10 2 25 

So that a core wall 10 feet from the toe of the dam now requires to be 
6 feet deep, in order to have the same effect as a central core wall which is 
10 feet deep. 

Let us now treat the case of a blanket of puddle clay 3 feet thick, that 
starts at 3 feet from the toe of the dam, as shown in Sketch No. 69. 

Put b = 100. 






impermeable apron 


We have to determine a , where : 


297 


jf 2 , 

100 2 


= I 


and we know that x - 97, and y — 3 satisfy this equation ; for the ellipse must 
pass through the corners of the apron. 


Thus, 


°' 9 7 2 +~ 2 = 1. 

a 1 


a 


2 _ 9 


o*o6 


or, a = 12*3 feet. 

. . that in such a case a central core wall gives no extra advantage, unless 
it is more than 12*3 feet in depth. 

These figures are of course purely theoretical, but they serve to show the 
following principles : 

(i) A long, shallow blanket or apron is equivalent to a far deeper central 
core wall, and the theoretical depth of this core wall can be calculated as above. 

(11) The most advantageous position for a vertical core wall is as close to 
either toe of the dam as possible. This is of course subject to practical 


Top 


Water 


Level 


LOO 

Q 7 ‘ 


ffoutjp Stone of~offier Permeable Substance 

Clay or impe7a)table Masonry//Mti. 


-k 


Sluice Gate 
or Dam 


07 ’ 


wwmgsim?/ 


c/oe 


\ 


tel 

I 1 I 


ftpron BOO’wide * yaecp^orby Centra 1 Core Wall Seep 

Sketch No. 69.—Effect of a Shallow Apron in Stopping Percolation. 

considerations, and the two following conditions militate somewhat against a 
core wall being situated near to the toe of the dam. 


(a) If the core wall be too close to the water surface of the dam, it may 
be breached by burrowing animals (such as water-rats and crayfish). If it 
is too far removed, it may become dry during periods when the water 
is low in the reservoir, and crack. 

(b) The dam, in practice, is not wholly impermeable, and a wall of 
puddle, or other impermeable material, must be carried up above the top 
water level. Thus, if this wall is not placed vertically below the crest of 
the dam it must be laid on a slope. Puddle walls laid at a slope, or 
rather, beds of puddle facing a slope, are very difficult to lay clean and 
unmixed with earth or grit, and are extremely likely to burst and cause the 
water face of the dam to slip. While masonry walls laid on a newly 
made slope of earth are certain to crack. 


Consequently, I do not consider the fact that the theory does not show the 
position usually adopted for core walls to be the best, in any way decreases 
its value. 

In other respects, the theory agrees very well with advanced practice, for it 
clearly shows the raison d'etre of the reversed filters at the downstream toe, 
and the advantages of the concrete base of the core wall together with the 
accompanying drain and reversed filter. 


























CONTROL OF WATER 


298 


The practical application of these formulae greatly depends upon the 
conditions existing at the downstream toe of the dam. It will be plain that 
sand may be removed in the two following ways : 

(a) By piping, that is to say removing the sand in a horizontal direction, 
such as is indicated as likely to occur near the points L and below the 
core wall (see Sketch No. 68). 

This (as will later be shown) is largely influenced by the amount of erosion 

pj 

that takes place and otherwise mainly depends upon the ratio : 

(b) By fountaining, or the upward removal of sand, which is indicated as 
probable near the points J, and J x (see Sketch No. 68). This depends only 

H •! 

upon the ratio — 
a 

If these two actions are independently studied, we find experimentally that 
removal by piping is far more easily effected. In an actual dam, however, if a 
horizontal surface of sand exists below the downstream end of the dam, it is 
plain that piping cannot occur unless fountain failure has previously taken place. 
Thus, in earthen dams or head regulators, calculations regarding stability can 
be founded on the conditions for failure by fountaining ; and, consequently, 

the leading factor in the design of such dams is the ratio —. 

In a structure of the weir or undersluice type, on the other hand, deep holes 
may be scoured out below the tail of the work, and the conditions for piping 
failure will be found to determine the stability of the work. 

The case where the boundary of the sand downstream of the work is a 
sloping plane is not capable of exact mathematical solution. Where, however, 
the boundary is one of the confocal hyperbolae /3 = / 3 2 say, as shown in Sketch 
No. 70, an accurate solution can be obtained. The work need not be given, 
as it will be obvious to any one who has followed the original investigation 
that: 

U = khs 

(tt —/ 3 2 ) C cosh a 

and the velocity of percolation at any other point N is given by the equation : 


KHS 

V (»-«NN, 

where the symbols are those used on page 294. 

The exact point where failure is most likely to occur is doubtful. 
Immediately under the core wall at E (see Sketch No. 70) we have : 


U 


max 


KH 

(tt—/ i 2 ) b 


and here, the motion being horizontal, the stability entirely depends upon the 
friction of the grains of sand on one another. But as we proceed from E, to C, 
along the ellipse AEC, the velocity of percolation increases, and thus, were it 
not for the fact that the direction of flow becomes more and more inclined 
upwards, failure would occur sooner than at E. Consequently, the precise 
point where failure begins can only be determined experimentally, and it is 
probable that the weak spot is somewhere close to the line ST, the upstream 
face of the scour hole. In any case, it is found that the value of «, has but 





FOUNTAIN AND PIPING FAILURE 299 

little influence (and that only an indirect one due to the fact that /3 2 is depen¬ 
dent upon < 2 ), on the stability, and that the important quantities are b , and /3 2 . 
This last quantity is principally determined by the ease with which the sand is 
eroded, and by the amount of erosion which it has sustained. 

Actual experimental data are rare : 

If we put h , for the head in feet of water that produces removal of sand by 
fountaining (Sketch No. 71, Fig. 1) through a vertical height of l feet of sand, 
it will approximately be found that : 

(a) For sand of a mean diameter of o'o3 inch, / = 1 *2 h. 

(b) For sand of a mean diameter of o’oio inch, / = y 6 h. 

These figures are confirmed by Beresford ( P.l.C.E. , vol. 158, p. 77), who 
states that l = 3/z for sand ranging from o'oi inch to o'oo5 inch in diameter, and 
Russell ( Journ . Ass. of Eng. Socs ., 1909) (see p. 582) who states that / = for 
sand such as is used in mechanical filters. The figures are only approximat , 



Sketch No. 70. —Percolation under a Structure subject to Tail Erosion. 


and, so far as I can judge, the proportion of the smaller grains has a consider¬ 
able influence upon the question ( i.e. the value of zz, in the equation l — nil , 
probably depends not only on the effective size of the sand, but also on the 
uniformity coefficient). 

The results are, however, confirmed by practical rules, for we know that 


dams on coarse sand rarely fail unless 


, is less than and in fine sand unless 
a 


-, is less than 1. Now, the quantity /, considered above is equal to 7 ra, so that 

CL 

these rules give / = i' 6 /i, for coarse sand ; and / = yih , for fine sand, which is 
somewhat coarser than the finer of the two sands above experimented upon. 
Thus, the rules probably afford a margin of safety equivalent to 50 per cent. 

For piping failure, where /, now denotes a horizontal length of sand 
(Sketch No. 71, Fig. 2), we find that: 

(a) For sand of 0*03 inch mean diameter, / = 2*5 h. 

( b ) For sand of o’oi inch mean diameter, / = Zh. 















3 °° 


CONTROL OF WATER 


The experimental figures for piping failure are very irregular, and I do not 
consider that any great reliance can be placed on those given above. If the 
slightest void is left unfilled with sand in the top of the experimental tube a 
local flow of water is set up which rapidly removes the sand, and failures have 
been observed with o’oi inch sand in cases where / = 20 h. 

The time factor also appears to have a considerable influence, as I have 
found that if the pressure is left on for an hour or more piping occurs at heads 
which are easily resisted for 5 or 10 minutes. My apparatus, however, was 
not sufficiently perfect to enable me to assert that this was not caused by the 
sand gradually settling, and creating a small void which permitted a flow of 
water to commence, so starting the failure. 

The practical deductions are very clear. If erosion is permitted below the 
tail of the work failure can occur by piping, and the stability mainly depends 
upon 2b, the breadth of the dam. 

The failure is more or less fortuitous, as the liability to piping largely 
depends upon the depth and position of the eroded holes, and also on the 
occurrence of accidental void spaces in the sand below the dam. 



Sketch No. 71.—Piping and Fountain Failure of Sand. 


If tail erosion does not occur, the stability mainly depends upon the depth 
of the cut-off wall. Failure occurs by fountaining, and is less dependent upon 
accidental circumstances. 

Regarded in this manner, the figures given by Bligh and my distrust of 
shallow core walls (see p. 679) are both easily explicable. So also, the 
utility of shallow core walls for forming cut-offs to accidental vacuities under a 
dam or impermeable apron, and their probable ineffectiveness if the im¬ 
permeable apron is not of sufficient length, becomes plain. 

Effect of Gravity .— So far the effect of gravity has been neglected. Consider 
any point {x, y), where y, is positive, when measured downwards from the base 
of the dam. 

Then from the equations : 

* 2 ! = r 
COsh 2 a sinh 2 a 

jtr 2 y 2 _ ' ' .. .. ' \ ' ..) 

cos 2 /3 sin 2 j 3 1 
we calculate a and fi. , 


























EARTHEN DAMS 


3 QI 

The preceding investigation has shown us that the pressure at (,r, y), is 

H /3 

-7r * \ - - - ■' 

Super-adding the effect of gravity, we have a total pressure of: 

^Q+y, feet of water. 

7T • • 

The velocity of flow is represented by : 

KH 

-—- - • — and is unaltered by the action of gravity. 

c V cosh 2 a — cos 2 /3 

It will also be plain that the whole theory depends upon the permeability 
being constant over the whole layer, i.e. K = a constant. 

So far as I am aware, no variation in K, due to the pressure of superin¬ 
cumbent layers, has been observed; but variations in the size of the grains or 
in their freedom from dirt may have a considerable influence upon K (see p. 26). 

Earthen Dams. —The design of earthen dams is purely a matter of 
experience. The ruling factor is the means adopted for preventing water from 
traversing the dam. This is effected by the erection of some impermeable 
barrier in the substance of the dam. In British practice (including Indian), the 
impermeable substance is usually clay, or clayey earth ; but concrete (either 
of Portland cement or hydraulic lime), or masonry, has also been used. 

The older American engineers usually employed masonry “ core walls,” but 
at the present time concrete (sometimes reinforced with steel rods), steel plates 
protected with concrete or asphalt coatings, and the artificial clay formed by 
hydraulic sluicing, are also used. Similar devices are appearing in British practice. 

Such perishable barriers as wooden sheet piles will be referred to later. 

We will now consider the conditions affecting a dam composed of gritty 
material and clay. The properties of these materials may be thus defined : 

The “ grits ” are pervious to water in a high degree, but do not slip markedly 
when saturated with water, and a good Thames ballast consisting of sand 
and pebbles in almost equal proportions may be taken as the typical case. 
The “ clay,” when properly treated and deposited, is more or less impervious 
to water, but is almost incapable of supporting itself when saturated, and will 
slip until it attains slopes such as 1 in 5, or 1 in 7. London clay may be taken 
as the typical case. Thus, a “good gritty” material is capable of forming 
a stable embankment even when saturated with water ; and a thin layer of 
“good clay,” if properly deposited, will (for all practical purposes) stop the 
percolation of water, even if the head producing the percolation is large in 
comparison with the thickness of the layer. It is evident that the better the 
quality of the clay the thinner will be the clay wall or layer necessary to 
stop percolation, and therefore the smaller the danger of slips caused by the 
pressure of the clay setting the gritty material in motion. 

When good clay and good grits are obtainable the construction of a dam is 
fairly simple. The main body of the dam is composed of the gritty material, 
and the percolation of the water is stopped by a wall of puddled clay. 

When two such materials occur on the dam site, and a junction with a 
continuous layer of clay in the strata underlying the dam can be secured, the 
circumstances may be considered as highly favourable. A dam of this kind 
is shown in Sketch No. 72 (which represents the generalised section of the 
Staines reservoirs dam). Such dams are absolutely water-tight if the clay 








302 


CONTROL OF WATER 


layer is properly deposited, and, since the clay portion is small in comparison 
with the gritty portion, no danger from slips exists. 

Let us assume that such excellent clay as London clay cannot be procured, 
and (since core walls of other substances are too costly) that it is desired to 
make a dam of black cotton soil and shale. We now have a case resembling 
the Ashti dam (. P.I.C.E ., vol. 76, p. 288). The thin puddle wall that suffices 
in the case of the first class puddle made at Staines is no longer sufficiently 
thick to prevent leakage, and thus from one-third to one-half (or even more) of 
the bulk of the dam is made of “ clay.” The danger of slips is evidently far 



greater than in the first type, and increases as the bulk of the clay increases 
(see Sketch No. 73). 

As a matter of history such dams do slip, especially on the downstream 
face. (The Ashti dam has not slipped so far as I am aware.) 

Proceeding further in this direction, we come to the type of dam re¬ 
commended by Strange {Indian Storage Reservoirs , or P.I.C.E., vol. 132). 
Here, the whole dam is composed of a material which is somewhat more 



pervious to water than black cotton soil, but which is also less liable to slip. 
Strange’s specification is a mixture of one part of black cotton soil to one 


part of shale (Sketch No. 74) 
following : 

Coarse gravel 
Fine gravel 
Sand 
Clay 


In America, Fanning recommends the 


59 per cent. 
20 

9 
12 


» 


5 » 


55 


and tests the mixture by ramming it moist into a bucket, and then ascertaining 
if it will remain in the bucket when turned upside down. 




























TYPICAL PAMS 


3°3 


The above discussion illus¬ 
trates the variations in the 
relative proportions of gritty 
and clayey material that may 
occur in dams. 

We now come to the 
question of drainage. When 
saturated with water a pure 
clay is for all practical pur¬ 
poses absolutely unstable, and 
even the thinnest clay cores or 
puddle walls must be drained. 

Returning to our three 
typical sketches, the puddle 
wall of the Staines reservoirs 
was not artificially drained, but 
was erected in material which 
provided excellent drainage. 

The Ashti dam was drained 
in an unsystematic manner. 
Strange’s type is drained 
systematically in a way which 
will be later described. 

The principles affecting the 
design of a dam with a clay 
core may consequently be stated 
as follows : 

The thickness of the clay 
core depends on the quality 
of the available material, and 
must be sufficient to check 
detrimental leakage. On the 
other hand, the thicker the 
clay core, the greater the care 
that must be taken to prevent 
slips. As slips are caused by 
leakage of water, and especially 
by leakage through clayey 
material, the worse the quality 
of the clay core the greater 
is the necessity for systematic 
drainage. 

It will also be plain that 
the more the gritty material 
diverges from the ideal of a 
substance which is stable, when 
saturated with water, the 
greater is the liability to slips. 
The matter is not practically 
so important as the quality of 



Sketch No. 74.—Strange’s Design for an Earth Dam. 





































3°4 


CONTROL OF WATER 


the clay, for the simple reason that a good gritty substance is far more 
common than a good clay. 

(i) The Ordinary Type .—Here, the percolation or leakage through the dam 
should be almost negligible. This type can consequently be constructed 
when : 

(a) Material for forming a relatively thin impermeable core wall exists 
(eg. good puddle clay, concrete, masonry, or well protected steel plates), 
and its use is economically possible. 

(b) An impervious stratum of rock, or clay, must exist at the site of 
the dam at such a depth below the natural surface that it is economically 
feasible to make a practically water-tight junction between this stratum 
and the core wall. 

(ii) The Indian Type of Dam (although not exclusively confined to India), 
where percolation is an important factor. 

Here either : 

{a) The only material available for making the impermeable core is of 
such a quality that the core wall must be relatively so thick in proportion 
to the dam that a large fraction of the dam section is liable to slip when 
saturated ; or : 

(b) No impervious stratum exists at a reasonable depth beneath the 
dam, and percolation takes place under the bottom of the impermeable 
core (whether thick or thin), so that the whole of the dam must be con¬ 
sidered as liable to saturation. 

The term “Ordinary type 5 ’ is probably a misnomer. The circumstances 
permitting the construction of the ordinary type are common in the British 
Isles, but do not occur with the same frequency elsewhere. British engineers 
are therefore liable to consider such dams as the only type, and to believe that 
all others are risky and unsatisfactory. 

The actual facts are that a dam with a relatively thick core wall of clay 
which is not entirely impermeable to water is more liable to slip than one in 
which the core wall is thin and of almost impervious clay, but the slips only 
occur when drainage is not systematically attended to, and then almost 
invariably on the downstream face. Also, such slips (although in some cases 
causing the full supply level of the reservoir to be reduced) have never given 
rise to serious disasters. 

A dam with a thick clay centre, which is not carried down to an imper¬ 
meable stratum, is less safe, but with careful drainage can be rendered 
satisfactory. A dam with a thin core wall of good clay, masonry or concrete, 
is quite safe when exposed to percolation under the core wall, if properly 
designed, although it is by no means as water-tight as one of the ordinary 
type. 

In considering the above statements, it is as well to bear in mind that dams 
in which the core wall is not connected with an impermeable stratum exist 
in large numbers, and that outside the British Isles, cases where such construc¬ 
tion is unavoidable are very frequent. 

General Design of Earthen Dams. —The ruling factors in the design of an 
earth dam are therefore two in number. Good practice has led to the evolution 
of three types, which are entirely conditioned by these two factors. 


PROPORTIONS OF DAMS 


305 


The factors are as follows : 

(i) The material available for the construction of an impermeable core 
wall. This is either clay suitable for making good puddle, or a cheap 
supply of Portland cement, or hydraulic lime, for forming a good concrete, 
or masonry core wall. 

(ii) The presence of an impermeable stratum of unfissured rock or 
clay, at such a depth below the dam as to permit the core wall being sunk 
to form a secure junction with this stratum. 

Where both conditions are favourable, the “ ordinary type ” of dam has been 
evolved. Such dams are common in all countries, and are frequently held to 
be the only satisfactory construction. 

I shall later endeavour to show that too rigid an adherence to this type is 
not only very costly, but is unnecessary, whether safety, or the economical 
utilisation of the stored water, is considered. 

Where good core wall material is not available, or where impervious strata 
are not easily reached, another type of dam (which I propose to term the 
Indian type) has been evolved. 

In this type, percolation under the dam is guarded against by careful 
drainage, and in some cases the dam itself is porous. While engineers 
accustomed to the careful and expensive methods employed in the ordinary 
dam to prevent all percolation, may consider such dams as makeshifts at the 
best, many satisfactory examples exist. I consider that this type will probably 
be largely adopted in the future. 

The hydraulic-fill dam in theory is essentially an attempt to manufacture 
an artificial clay by a water-sorting process, analogous to that which on a 
large scale, and over long periods of time, actually produces clay in Nature. 

Ordinary Type of Dam.—The proportions of earthen dams are solely derived 
from practical experience. Under the conditions usually obtaining, i.e. practically 
no percolation through, or under the core wall, and very little artificial drainage 
of any portion of the dam except perhaps the puddle trench (see p. 317) slopes 
of 3 to 1 on the water face, and 2 to 1 on the downstream face, are found to be 
stable. 

The dam is generally carried up at least 5 feet above full supply level, and its 
width at the top varies from 6 feet in low, to 10, or 12 feet, and even more in 
high dams, especially if the top of the dam is intended to carry a road, or even 

a cart track. 

The most economical height can be determined by balancing the expense of 
an extra foot in height of the dam against the cost of the extra excavation 
required to increase the width of the waste weir in order to pass off the same 
quantity of water at 1 foot less head. As an example, let us suppose that the 
length of the waste weir is 200 feet and that the maximum flood likely to occur 
can be passed off under a 3 feet head. The top of the dam would require to be 
at least 3 feet above flood level, or 6 feet above the normal full supply level. 

If the waste weir length is increased to 200 x ^5 =368 feet, overtopping will be 

equally well guarded against with a dam 1 foot lower than that designed. 
Comparative estimates can be made, and the cheaper solution may be selected. 

The matter can be expressed in general terms by stating that when a site 
suitable for a long waste weir exists, and the depression crossed by the dam 

20 


it 


CONTROL OF WATER 


3°6 

is such as to require a long bank to close it, the elevation over the full supply 
level is least, and as small a value as 4 feet may prove economical. 

On the other hand, in localities where the configuration of the ground is 
precipitous, a long waste weir may prove very costly ; and, similarly, it will 
usually be found that the dam is a short one. 

Thus, an elevation of 10, or even 12 feet, above full supply level, may be 
advisable. 

The matter is influenced by the temporary storage of the flood volume in the 
reservoir. The principles discussed under Flood Discharge (see p. 284) must 
be considered in drawing up the final design. 

A comparison with the designs for an Indian type dam will at once suggest 
the possibility of a slope steeper than 2 : 1 being employed on the downstream 
side, provided that drainage is carefully attended to. The question can only 
be settled by experiments with the actual materials it is proposed to use. 

A study of British dams suggests that 2 : 1 is a minimum value in cases 
where drainage is left to Nature, and 2^ : 1 is frequently adopted ; but it must 
be remembered that British (and to a less degree French and German) practice 
is still greatly influenced by vague fears resulting from the Dale Dyke failure. 

In low dams, the rules given by Strange (see p. 332) may be considered as 
perfectly safe, and the slopes could be made steeper in good, well drained 
material, were it not that the economy thus secured is usually quite inappreciable. 

Construction. —The practical details of the construction of a dam, in¬ 
cluding minutiae, which at first sight appear to be unimportant, have, in reality, 
a decisive effect on its stability. 

Taking the details in order, we have as follows : 

(i) Preparation of the dam site. 

(ii) Construction of the earthwork. (Drainage will be considered in the 

section on Indian dams.) 

(iii) Construction of the puddle trench and wall, including its drainage. 

(iv) Pitching and casing of the dam. 

(v) Outlet passages or tunnels, and valve tower. 

CONSTRUCTION. — Preparation of the Dam Site. —The following specification 
gives first class work. 

(a) The whole base of the dam shall be excavated at least 6 inches deep, 
and as much deeper as may be directed, in order to remove all turf, mould, 
roots, and vegetable matter, (and pervious soil if directed). The turf and 
mould to be preserved, and to be used for soiling the outer face of the dam. 

(h) All tree stumps and roots to be removed, and the voids thus pro¬ 
duced to be filled in with well-rammed material, as specified under the 
heading Embankment. 

(e) All field drains crossing the site of the dam to be traced out, com¬ 
pletely excavated, and to be refilled with puddled clay, as specified under 
the heading Puddle. 

(d) The base of the completed excavation to be harrowed in a direction 
parallel to the length of the dam, so as to promote a satisfactory union 
between the natural earth and the embankment. 

The following comments may be made : 

Clause {a). —The phrase in brackets is occasionally required in order to 
enforce the removal of localised pockets or beds of sand or gravel. 


EARTHWORK 


307 

Clause ( c ).—This clause is required in cases where the land is artificially 
drained. It is not usually needed in hill reservoirs. 

Clause ( d ).—This clause is of somewhat doubtful utility. It is usually put in 
in order to prevent the bottom of the stripping being left smooth and polished 
by the ploughshare, in cases when the turf, etc. is removed by means of 
ploughs. 

The least preparation which can possibly be regarded as good practice 
consists in the removal of the top 6 inches of the surface soil, and harrowing 
the surface thus exposed at least twice in directions at right angles to each other. 

For small banks holding water up to a height of 5 to 6 feet above ground 
level, at the most, removal of all growing plants by ploughing and harrowing 
has been found sufficient. In such instances, the base of the dam is consider¬ 
ably wider in proportion to the depth of water retained than is usually the case. 
In spite of the fact that the earthwork is by no means so well constructed as is 
customary in the case of larger dams, breaches almost invariably start with a 
leak running along the old ground surface. 

The junction between the dam and the natural surface is always a weak 
point, and if there is any doubt as to the quality of the soil exposed by the 
ordinary 6 or 9 inches of stripping, it is always better to go deeper still. In one 
example, where work was executed under a specification corresponding to that 
given, it was considered necessary to remove a quantity of earth equal to 
14^ inches over the whole base of the dam, in place of the 9 inches specified. 

(ii) Construction of the Earthwork .—“ Earthen dams rarely fail from any 
fault in the artificial earthwork, and seldom from any defect in the natural soil 
—which may leak, but not sufficiently to endanger the dam. In nine-tenths 
of the cases the dam is breached along the line of the water outlet passages ” 
(MacAlpine). 

This dictum forms a very valuable guide in the design of earthen dams. 

Nevertheless, in order to secure water-tightness, and to minimise the settle¬ 
ment of the dam after construction, it is necessary to deposit the earth in 
regular layers, and to roll each layer well, with sufficient watering to ensure 
adequate consolidation under the rolling. 

The following specification is very complete, and certain clauses can usually 

be omitted: 

(a) The embankment to be formed in regularlayers not exceeding 9 inches 
in depth at the heart of the embankment, and 18 inches at the outer parts 
and slopes when spread out. (These thicknesses to be measured before 
rolling.) The layers are to slope from the outer sides down to the centre 
at an inclination of 1 in 12. The slope of the earthwork in a longitudinal 
direction during progress must not exceed 1 in 100. 

(b) The earth for embanking may be obtained from the excavation for 
the puddle trench, waste weir channel, etc. so far as it is available, provided 
that the material is in accordance with the specification. The remainder 
of the necessary earth must be taken from excavations (from inside the 
reservoir) as directed, (below top water level), and the excavations are to 
be left with slopes dressed not steeper than 4 horizontal to 1 vertical, and 
so as to drain into the main water-course. 

(c) There is to be no excavation within 100 feet of the toe of the em¬ 
bankment. 

(d) The most clayey portion of the material is to be used for the heart 


3o8 


CONTROL OF WATER 


of the embankment, and more especially on the water side of the puddle 
wall. The more stoney, gravelly, and sandy portion is to be used in forming 
the outer parts and slopes, but more especially for the outer side of the 
I embankment. 

(e) No turf, peat, moss, mud or vegetable matter is to be put into the 
(heart of the) embankment. 

( f) The material for embanking may be brought up to the bank site in 
waggons on rails, but no rails are to be laid above any portion of the 
embankment site. 

(g) Every layer must be carefully spread out to the proper thickness, 
and is to be rolled with a heavy grooved roller, at least 2 tons in weight, 
till quite consolidated, being kept thoroughly moist by watering as required 
during the process. 

(h) In any case when stones are laid on the embankment they must be 
deposited in a regular layer, each stone being laid on its flattest bed, the 
rounded side or pointed end being uppermost, no stone being closer to 
another than 4 inches. The next layer must consist of such material as 
will bind and entirely fill up the crevices, and the whole must form a com¬ 
pact mass, so as not to be liable to subsidence. 

(z) The embanking will be measured and paid for to the slopes and 
sections shown, but the contractor without extra charge is to leave it 
12 inches higher than the levels shown at the highest portion, and at corres¬ 
ponding extra heights, according to the depth, in order to allow for 
subsidence. 

The following comments may be made : 

Clause (a ).—As it stands this is first class work, and is probably too stringent. 
In good practice the sentence in brackets is frequently omitted, and layers 12 
inches at the heart, and 2 feet at the slopes, are not really detrimental. 

If a deep gorge is left in the bank (e.g. in order to pass one year’s floods), 
it is usual to specify that the layers shall slope downwards away from the 
temporary scar end at 1 in 20, or 1 in 30. Slips are consequently less likely, 
but the gorge method of disposing of floods is not advisable if it can be 
avoided. 

Clause (fr ).—The bracketed clauses are not always required. In tropical 
countries,/* drainage to the main water-course ” may produce erosion, although 
stagnant water is liable to induce fever, and should therefore be avoided. 

Clause (c).—The distance depends on the height of the bank, and “two” 
or “ three times this height ” appears to be a more logical method of specification. 

Clause (d ).—This is very good practice, but unless marked variations in 
the quality of the earth procured are anticipated, it must be realised that the 
contractor will charge from one-eighth to one-sixth extra rates for this clause. 

Clause (*?).—It would be better to entirely reject these materials, using the 
turf for sodding the outer slopes of the bank. In some cases, “ all vegetable 
earth or mould” is rejected, and there is little doubt that better work is thus 
produced. 

Clause (/).—The use of rails on an embankment gives rise to difficulty in 
spreading and rolling the layers. If good inspection can be relied upon it 
appears preferable to permit the use of rails, and to specify that they must be 
shifted at least 6 feet sideways at every rise of two layers. 

Rails should not be permitted within 10 or 15 (preferably 20 or 30) feet of 


WEIGHT OF EARTHWORK 


3°9 

the edge of the puddle trench or wall. The erection of trestles on the bank to 
carry rails should be entirely prohibited. 

Clause (g ).—In some cases, the number of rollings is specified, and rolling 
across the breadth of the bank by lighter rollers is required. 

Clause ( h ).—Stones should be used for the stone drains, and toe wall referred 
to on page 325. If an excess of stones remains, this clause is useful. 

Clause (z).—The shrinkage allowed is usually at the rate of 1 foot in 40 or 
50 feet height. 

The correct fulfilment of the above specification is costly, and, in order to 
minimise the uncertainties which the contractor has to face, it would seem 
advisable to systematically investigate the amount of rolling and watering 
necessary to produce satisfactory consolidation in the manner indicated below, 
and to append a statement of the results to the specification as an indication 
of the probable cost. The legal technicalities which must be observed, in 
order to prevent the experiments being construed as part of the specification 
are not discussed. 

As an indication of the increased expense over ordinary earthwork, I may 
state that this bank cost about four times as much as the same contractors, in 
the same locality, charged for ordinary earthwork constructed under somewhat 
less favourable conditions as regards the quantity of earth per yard forward of 
the bank ; and, judging by other tenders, the reservoir bank prices were closely 
cut with a view to obtaining the contract. 

Since the object of this somewhat costly treatment is to obtain a thorough 
consolidation of the earthwork, systematic tests should be made by excavating 
test pits of measured size, in the natural earth and bank, and weighing the 
excavated material. 

The results should be approximately as follows : 



Weight in Lbs. 

per Cube Foot. 

‘ ' ' 1 1 1 • , • 

First Example. 
Mean of 23 Experi¬ 
ments 

As given by Bassell 
[Earth Dams). 

Natural earth as found in borrow 


; > 1 ' ['■ (P* *» ; \('| , , r 

pits • • • • • 

Ditto., as thrown into wag- 

11S 

116*5 

gons ..... 
Earth in dam as found in trial 

co 

r-^ 

8o'o 

pits ..... 

136 

i 33 '° j 


I am inclined to believe that anything less than 12 per cent, extra weight per 
cube foot of the dam, when compared with the natural earth, is an indication 
of bad work, but the fairest method is to compare the results in the dam with 
those of carefully superintended ramming, carried out in a bricked pit about 
6 feet X 6 feet x 18 inches deep (a smaller size is undesirable, as the earth 
packs against the sides), with smoothly cemented sides and bottom (see p. 322). 

It is very important to prevent any lumps being left on the slopes of an em¬ 
bankment, outside the finished section, even as a temporary expedient. Such 
humps set up stresses, and cracks are likely to occur in the bank just above the 













3 IQ 


CONTROL OF WATER 


hump, as per Sketch No. 75. In one particular case, where a hump some 100 
yards long had been made, on which to lay rails for the transport of earth, a 
crack, approximately one-eighth of an inch wide, and some 50 yards long, formed 
in the spot marked A, and was in certain places more than 6 feet deep, as tested 
by probing with a cane. No doubt the shocks of the locomotives and exposure 
to a temperature of 120° F, had some effect, but the crack occurred in the exact 
position that theory would indicate. Such a crack may form a starting-point 
for a slip, even after the hump is removed and forgotten, and two cases where 
a bad slip in the side of a cutting has been traced to a hump left temporarily in 
the excavation slope have occurred in my own experience. 

(iii) Puddle Trench and Wall .—A bank constructed according to the above 
specifications is by no means water-tight in itself, except under very favourable 
circumstances ; and in order to prevent leakage it is necessary to provide a core 
wall, or impermeable partition. This is carried up say, 3 feet above the maximum 
high-water level, and down to solid rock, or other impervious stratum. 

While a wall of either puddle clay or concrete, or a masonry core wall (when 


Hand Cast from banks C UD. 



of proper construction and proportions) will produce a perfectly satisfactory 
result, the general practice of engineers appears to favour a puddle wall, wherever 
clay capable of forming a good puddle is obtainable. 

I he pi actice seems logical if the portion of the impervious wall above ground 
level is alone considered. This is embedded in the dam, and is exposed to 
stresses and deformations caused by the settlement of the dam. Such actions 
are best resisted by an easily yielding substance, such as good puddle clay, 
rather than by rigid, and therefore more easily fractured materials, such as 
concrete or masonry. If, however, we also consider the filling of the trench, the 
advantages of puddle are not so manifest, and concrete or masonry may be 
regarded as equally sound from a constructional point of view. 

The following specification shows the method by which first class puddle is 
made, and laid in position in a temperate climate : 

(a) The puddle to be made from clay approved by the engineers. 

O All stones (exceeding three inches in maximum dimensions) to be 
removed, and the clay to be left exposed in layers not more than 12 inches 
thick for at least 24 hours, and to be watered once or more as directed. 














PUDDLE CLAY 


3 T1 

(c) The soured clay to be passed through an approved pug mill, or to be 
otherwise reduced to a homogeneous mass. 

(d) The broken clay to be deposited in layers, and watered as directed, 
and to be allowed to weather for at least a week. 

(e) The puddled clay to be deposited in the trench or wall in layers not 
exceeding 3 inches in thickness, and to be well cut up by an appropriate tool at 
least 6 inches long, so as to be incorporated with the lower layer. 

(_/) All clay surfaces in the puddle wall or trench to be covered with bags, 
or to be otherwise protected against drying, and falling materials. The old 
surfaces to be well heeled over, or to be otherwise cut up before new puddle 
is deposited. All puddle which has become dry, cracked, or muddy, or mixed 
with impurities, to be replaced by approved puddle. 

(g) The filling of the puddle trench to commence at the deepest point, and 
to be carried on right and left continuously, but no portion of the trench bottom 
to be covered up until it has been inspected and passed by the engineers. 

(h) The filling of the puddle wall to be carried up simultaneously with the 
construction of the bank, and between properly supported timbers. The top 
of the puddle clay to be at least 3 inches, and not more than 12 inches, above 
the earthwork. 

(f) All timber stringers and walings to be removed from the puddle trench, 
or wall, as the clay is deposited. 

The following comments may be made : 

Clause (a ).—The tests for suitable clay are described on page 312. 

Clause (b ).— The period of “ souring ” and the amount of watering depend 
on the properties of the clay. The period specified is a usual one. 

{d) —This process is very variable. As a rule, a week’s weathering in thin 
layers, with watering three or four times, suffices in a moist climate, like 
England ; but in some cases better material is secured if the puddle is taken 
direct from the pug mill and deposited in the trench. 

Clause (<?).—Three-inch layers are, if anything, somewhat thin. A 6-inch 
layer, if well cut up and spaded during deposition, gives good results. The 
best results are attained when the puddle is cut into blocks about the size of a 
brick, which are forcibly thrown into place, while a gang of men cut up the 
surface of the lower layer with spades, or by means of their heels. 

Clause (/).—Old surfaces should, as far as possible, be avoided. If puddle 
has to be deposited on an old surface, a paring, say half an inch thick, should 
be taken off so as to expose a clean surface. The bags will usually need 
watering daily, and any mud thus produced should be removed before fresh 
puddle is deposited. 

Clause (/i ).—Unless the puddle is carefully supported both during and 
after deposition, it is liable to split, and fall asunder. A puddle wall, built 
between walls of sods, has been known to burst, almost as badly as a wall of 
water. The clay was probably too wet, but puddle which has once cracked 
will not re-unite, unless taken out and again kneaded up. 

Clause (i ).—The runners, or poling boards, should be lifted so that their 
bottoms are slightly above the top of the layer which is being deposited, and 
lumps of puddle should be thrown into the space thus left vacant. If the 
runners are drawn after puddle is deposited against them, cracks may be set 
up. In unstable soil this work may be dangerous, and in such cases concrete 
is usually employed for filling the “puddle” trench. 


312 


CONTROL OF WATER 


The most important tests for clay, suitable for puddle, are those for 
tenacity, and impermeability. For tenacity, after weathering, watering, and 
carefully working up, make a roll i to inch in diameter, and io to 12 inches 
long. This should not fall apart when held up by one end. For impermeability, 

1 to 2 cube yards, properly prepared, as above, should be formed into a basin 
to hold 4 to 5 gallons of water, and the loss after 24 hours observed ; evaporation 
being determined in an equal impermeable basin. 

Earth suitable for puddle generally gives a clayey odour when breathed 
upon ; is opaque, and not crystalline in fracture ; is unctuous to the touch, and 
when kneaded for three minutes and then formed into balls about 3 inch in 
diameter does not fall apart under less than 48 hours’ soaking in water. 

I would, however, point out that the above are the crystallised experience of 
generations of British Clerks of Works regarding British clays, and that 
(especially in foreign countries) puddle can be obtained from clay which does 
not entirely pass these tests. 

As an example ;—so far as I am aware, no clay exists in the Punjab which 
passes these tests in a perfectly satisfactory manner ; yet I have found that 
by careful treatment (and especially by a longer weathering than is usually 
required with British clays) a very fine puddle can be obtained from material 
which in the raw state looks like a clayey loam ; but which, when weathered 
for three months, with watering every third day, produces a puddle which, in a 
thickness of one foot only, allowed water to percolate, under 6 feet head, at a 
rate of o’3 to o - 6 cusec per million square feet. The earth was not unctuous 
to the touch, and contained some grit. When rolled for the tenacity tests, the 
greatest length that could support itself was 6 inches, and 3-inch balls fell in 
pieces after 30 hours at the most. 

It may be noted that, while pure clay forms the best puddle, provided that 
it is never exposed to evaporation, or to drying by capillary action, yet, where 
drying by evaporation can occur, a certain admixture of sand, varying from 
10 to even 25 per cent, is advisable, in order to prevent cracking. The exact 
ratio is easily found by experiments on a small scale. 

The section of the puddle wall is generally either uniform throughout, or 
is sloped as in Sketch No. 72. The slope is advantageous, as any slight 
settlements only tend to consolidate the wall. The minimum thickness in 
usual practice, (the clay at Staines was exceptionally good) is 5 to 6 feet at 
the top of the wall, and one-fifth the depth of the water retained at ground 
level. 

Where the clay is not considered to be of first class quality, these thick¬ 
nesses may be increased to 8 feet, and one-third the depth of the water 
retained. 

Where, as is occasionally the case, screened gravel is mixed with clay, the 
thickness must be still further increased, but such examples are approaching 
the Indian type of dam and should consequently be considered under that 
section. 

The puddle trench is carried down at least 2 feet, (and preferably 4 
feet) into the impermeable stratum. The width of the excavation will depend 
on the depth of the trench, and is estimated from the ordinary rules for 
timbering trenches. Roughly speaking, a timbered trench has a minimum 

width of ^ 5 T feet, an d such a width is usually amply sufficient for 



PUDDLE TRENCH 


the puddle thickness required to prevent percolation. If a smaller width is 
advisable, the rules for puddle walls may be followed,— e.g. one-third the depth 
of water at the top, tapering to 5 feet at the bottom. 

It is extremely important that right angles should not appear either in the 
cross, or longitudinal section of the puddle trench. Sketch No. 76 shows what 
happens during settlement, and further comment is unnecessary. Thus, the 
section of a trench timbered after the usual walings and runner method 
(Sketch No. 77) is badly suited for filling with puddle, and certain risky and even 
dangerous trimming has to be effected. The poling board method (Sketch 
No. 129) produces a better section, but the actual excavation is less easily effected. 
When the trench has been taken out to such a width that the puddle would be 



Rock., 

or other 
hard Material 


Sketch No. 76.—Fissures in Puddle produced by Irregularities in the 

Face of the Trench. 


abnormally thick if the whole trench were re-filled with puddle, engineers have 
in some cases re-filled the trench with a thinner wall of concrete, as being a 
substance less easily rendered permeable by mixture with the earth or gravel 
used for re-filling the surplus width. The substitution is quite justifiable, as 
settlement stresses of a character sufficiently intense to rupture a 5 or 6-foot 
wall of good concrete are unlikely to occur in a narrow trench below ground 
level. The only weak points are the junction with the puddle wall above, or 
near to ground level, and the general impermeability of the concrete. These 
will be discussed later. 

The minutiae connected with laying the first layer of puddle deserve con¬ 
sideration* In all cases a 9-inch layer should be carefully laid over the whole 




3 1 4 


CONTROL OF WATER 


bottom of the trench, in order to ensure a junction, and should then be 
removed. This produces a very effective removal of all loose matter and 
dirt from the bottom of the trench, which might otherwise form a line of 
weakness. 

In cases where the quantity of water flowing into a puddle trench is large, 
the puddle should not be washed over by the flowing water. 



It is sometimes enough to make a small grip or trench in the puddle, on one 
side of the trench (or on both if the water enters on two sides), and to allow 
the water to collect and run off to the nearest pump. If the quantity of water 
is sufficient to damage or wash away the clay by thus running over it, special 
devices must be employed. 

The ideal method is of course a garland of timber and clay, formed all 






























FILLING OF TRENCH 


3i5 

along the trench at the level of the bottom of the lowest water-yielding stratum. 
Sketch No. 77 shows the details. This is costly, and either the width of the 
trench may prove insufficient, or the water may issue in large quantities, almost 
down to the bottom of the trench. 

In one case, the problem was solved by laying 6-inch agricultural drain 
pipes with open joints, on each side of the bottom of the puddle trench, which 



conducted the water to a pump sump. In front (see Sketch No. 78) two walls 
of 14-inch brickwork in cement were built, which were carried up above the top 
of the water-bearing stratum. The space between the walls, to about 3 feet 
below their top, was filled in with concrete consisting of 1 Portland cement, 
2 ballast, and 1 sand. The puddle wall was laid on top of this. When the 
puddle wall had reached ground level, pumping was stopped ; and after the 
ground water had ceased to rise, the whole of the pump pipes and drains were 

























CONTROL OF WATER 


316 


filled with cement grout. It is open to doubt whether the drain pipes were 
either properly filled, or really required to be filled. 

In another case (Sketch No. 79), where due to some miscalculation, the 
pump shaft had been sunk on that side of the puddle trench from which the 
water did not issue, a 9-inch cast-iron pipe with a creeping collar was laid 
across the trench, and the whole bottom of the trench was then covered with 
concrete, consisting of 1 Portland cement to 3 gravel and sand, to a depth of 
about 3 feet, i.e. to a height of about 1 foot above the level of the main entrance 
of the water. When this was set, a brick and concrete wall was built on top of 
it, the water being led by grips and drains (usually lined with wooden launders) 
to cast iron pipes, connected with the 9-inch pipe, and carried up as the puddle 
wall rose. When the work was finished, a dead end was fixed to the lower end 
of the pipe in the pump shaft, and the whole pipe was filled in with cement 
grout. The tunnel between the puddle trench and the pump shaft, together 
with the lower 10 feet of the pump shaft, were built up in brick and concrete, 
well grouted, and the rest of the pump shaft was filled with puddle. 

\ \ 1 r 


Puddle Filling 


: ‘ v . 


6*6' Pump Sump 
filled in w'th P C. 

»• 'Concrete 


• • % 
\ v • ; 


1 .if- 


Puddle 


1 . 


Filling 

L 


Soft Loam 


If 


T 


T 


6 


4*5' Heading filled 
m Hitti Qncks m CcmenFi. -' .c * - 


Filled in 
witti 

1 Bk-mrkU conc\et\ I fissured b 
- 6 ' 


Concrete^ Fillingy 


Large Stones 

I Wooden 0 rain to Pipe 
'learned up Hifp filling 


Grit Pock 
fissured 
[^carrying water 


,i|j 9" Pipe filled in Hitt) grput 

T* . v.q, ■,. . . l:-b ____ 

F\ Ocad end serened on pipe Duck foot Send 


Sketch No. 79.—Filling of a Puddle Trench. 


The only remark, that it is necessary to make, is that when modern Portland 
cement is used, a well-proportioned concrete will probably be water-tight, with 
less than one part cement to three parts of sand and gravel. In cases where 
the whole puddle ” trench is to be filled with concrete (as now seems to be 
coming into fashion), similar precautions are necessary ; but the real weakness 
lies in the possibility of the concrete failing to join propqrly at the end of each 
days woik. In spite of the obvious disadvantages of night work, wherever 
possible it is best to lay the concrete day and night, without intermission, 
until finished. This is, however, frequently quite impracticable, and in such 
cases the following specification may be adopted : 


“ All concrete surfaces over 24 hours old to be picked over, washed 
with water under 150 lbs. per square inch pressure, and all loose chips 
removed. Over this surface spread and carefully work into all corners 
1 a 1-inch layer of cement mortar (1 cement to 2 of sand), and upon this 
lay the new concrete, working it well with forks.” 

































CONCRETE FILLING 


3 i 7 

Even this amount of precaution, combined with very close inspection, may. 
fail to procure a proper union. On examination of the defective spot a hollow 
(say ^ to 1 inch deep), will be found in the old work, in which water tends to 
collect. This water may prove sufficient to drown and wash away the cement 
from the mortar placed upon it ; and small pockets of sand (it may be only 
lV> or 3V °f an inch in thickness) will remain. The action only occurs in 
shallow, basin-shaped depressions, with sides the slope of which is not steep 
enough to prevent the pressure of the new mortar forcing the water away 
against gravity, with a velocity adequate to carry off the finer particles of 
cement (which, as is well known, alone possess cementing properties). I have 
therefore found it best to direct that all surfaces on which concrete will later be 
deposited shall be laid to a slope of 1 in 12, or 15 ; either towards the edge of 
the trench, or better still, towards the scar end of the work. The mortar should 
be as dry as is consistent with filling the small interstices of the old work. 
Vertical sides of old work also need picking over, and should be laid with 
chases, which are easily formed by the insertion of a log of timber behind 
the shuttering. Such precautions, combined with careful inspection, prevent all 
leakage. 

The above described methods may be regarded as applicable to cases where 
artificial drainage of the puddle trench is considered necessary. In British 
work, drainage is far more common than is usually reported. There is a 
general belief that leakage through, or under a well made puddle wall, is dis¬ 
creditable. Such a standard of workmanship is laudable, but water (whether 
leakage or otherwise) has only a certain value ; and it is far better to provide 
for such leakage than to ignore it, more especially as (if collected) such leakage 
can be credited to the compensation water allocated by Parliament. 

Hill ( P.I.C.E ., vol. 132, p. 208) acknowledged the existence of leakage, and 
put in a pipe which for some years delivered, as compensation water, about o'8 
cusec, which leaked through fissures below the puddle trench. Finally, the 
pipe silted up, and ceased to flow. We may therefore consider that Hill in this 
manner gradually stanched the leakage. Such stanchings are most desirable ; 
since, if any leakage continues through puddle, the effect is to gradually wash 
away the clay particles, replacing them by sand. Cases have occurred where 
vertical, sand filled fissures 2 inches wide, and 40 feet high, have been found 
when old puddle trenches or walls were opened. The fact that the pipe silted 
up rather suggests that some such action began in this case, and was arrested 
before any harm occurred. If this be so, the design should be regarded as 
productive of a very desirable result. 

Core Walls and Trenches of Materials other than Puddle.— In 
India, and in some parts of America, good puddle clay is not easily obtainable. 
The water-tightness of a dam is then usually secured by a core wall of masonry 
or concrete. In late years, armed concrete, asphalte and concrete, or steel 
plates buried in concrete, have also been used. All these seem to give satis¬ 
factory results when proper workmanship is obtained, and no method gives 
satisfactory results if carelessly applied. 

Considerations of cost, together with the available labour and materials, 
must determine the choice. These walls, unlike puddle, being rigid, do not 
adapt themselves to the settlement of the earth bank, and must consequently 
be made of sufficient strength to resist the stresses induced by settlement. 

The following investigation, although by no means complete, leads to a 


CONTROL OF WATER 


3i8 

satisfactory section, provided that the earth bank is carefully constructed,— i.e. 
is deposited in thin layers (say 18 inches to 2 feet thick at the most); the layers 
being laid horizontally, or slightly inclined towards the core wall, and being 
well rolled and watered according to some such specification as that already 
quoted. 

Draw from the base of the core wall (Sketch No. 80) : 

(i) On the waterside a line ab , inclined to the horizontal, at an angle 
(f) equal to the angle of repose of the saturated earth, i.e. cf) = 20 to 23 degrees. 

(ii) On the downstream side a line cd , inclined at 8 to the horizontal, where 
8 is the angle of repose of the rammed earth, i.e. 8 = 45 to 55 degrees. 

Calculate the areas of the portions of the cross-section of the dam cut off 
by these lines. Roughly they are,—with (f) = 20 degrees, and a 3 : 1 slope, 

h 2 

4/z 2 , on the water side ; and with $ = 45 degrees, and a 2: 1 slope, -, on the 
downstream side, where h, is the height of the core wall. The weights of the 



earth may be assumed as 160, and 132 lbs. per cubic foot, so that the core 
wall has to sustain a thrust of 

/z 2 ( 160 x 2 — 132 x J) lbs. per foot run, 

or 76/z 2 , lbs. say; and if the thickness of the wall is x, feet, its ultimate re¬ 
sistance to shear when composed of concrete is about 30,000 x lbs. per foot 
run. 

fid 

Thus, for strength only, x = ^ where f is the factor of safety, equal say 

to 2, in view of the extremely adverse assumptions made. Unless It, be great, 
this will usually lead to smaller values of x, than those indicated by practical 
experience, as requisite to stop percolation through the wall. 

Such rules are given by Herschell ( P.I.C.E ., vol. 132, p. 255) as follows: 

In first class work, 4 to 5 feet thick at the bottom of the trench, enlarging 
to 8 feet at the natural surface, and tapering off to 4 feet at the top of the wall. 

Wegmann (ibid., p. 267) designs the core wall of a proposed dam retaining 
96 feet of water, as 6 feet wide at the top, i.e. 100 feet above ground level • 
enlarging to 15 feet at the ground, and 18 feet at 33-33 feet below this level, 
and then continuing at the same width to the bottom of the trench. 

As a contrast, Herschell states that a wall 2 feet thick over its whole height 
has sufficed to form a satisfactory stop for percolation. 













MASONRY CORE WALLS 


3*9 


Sketch No. 81 shows a design founded on Wegmann’s design (ibid.), but 
modified in accordance with the results of the experiments on permeability 
referred to on page 348. There is no doubt that a dam of this type can retain 
70 feet of water, and a priori there is no reason why it should not be as 
safe as puddle-cored dams which already retain 80 to 90 feet of water satis¬ 
factorily. The slopes will be seen to differ considerably from those adopted 
in puddle cored dams. So far as can be judged these differences are 
allowable. 

Since the masonry core wall is presumably more permeable than a puddle 
wall, the water face is better drained and therefore less likely to slip, and is 
partially supported by a rigid wall. Hence, a slope steeper than 3 to 1 is 
permissible, although whether so steep a slope as 2 to 1 is advisable in a 
high dam is doubtful. Similarly, the downstream side is likely to be more 
saturated than in a puddle cored dam ; thus, the paved and drained berms 
form a rational precaution. The core walls should increase in thickness 
below the natural surface level, until a stable (although not necessarily 
impermeable) stratum is reached. The earthwork should be constructed with 


mve breaker at 

top of Pitching JaAT' 


11 - 1 R.L.85 


80. top of Pitching, 
LUL-M 


— . >?' Paving on 
56. Top of Pi tchin g) 16" broken Stone 

<V Pitching. 

IS"Paving on 
“broken Stone 



S' Concrete thm 


Detail of terms. 


Stable Soil 

mot Imperm eableStratum 


Sketch No. 81.—Dam with Masonry Core. 


precautions similar to those adopted in puddle core dams, and some such 
mixture as Fanning’s (see p. 302) appears advisable. The wall being rigid 
is probably less fitted than a good puddle wall to sustain large differences in 
water pressure. Thus, some arrangement of pipes through the wall connected 
with drains might be advisable to prevent large differences of water pressure 
existing on either side of the wall. 

The rules given above will probably not suffice if direct water pressure is 
permitted to act on the core wall, which may happen if the bank is not 
properly consolidated. The stresses thus developed in a core wall may be 
approximately estimated by a consideration of the results of the Croton 
observations (see p. 348). 

It appears that if the dam is well made, a pressure equivalent to 10 or 
15 feet head of water must be sustained. Thus, calculations on a basis of 
resisting the bending moment produced by 1500 to 1600 lbs. per square foot 
over the whole area of the wall will probably lead to a sufficient margin, even 
if the earth is only moderately well consolidated. 

It may be suspected that some such action occurred in the old Bhim Thai 
Dam core wall, which Ashhurst ( PJ.C.E ., vol. 75, p. 202) describes as 40 feet 


















320 


CONTROL OF WATER 


high, io feet wide at the bottom, and 4 feet wide at the top, buried in a dam 
25 feet wide on the top, which failed near the outlet tunnel. Consequently, 
core walls cannot be considered as substitutes for good workmanship in the 
earth work ; although, if the dam is overtopped, they may save a disaster by 
temporarily preventing the entire destruction of the dam by erosion. 

It is also necessary to refer to the old American method of constructing a 
core wall and cut off of wooden sheet piling. See Sketch No. 101 for best 
details. The tendency to eventual decay is obvious ; but, in view of the 
present price of timber, such construction is unlikely to be adopted in the 
future. Nevertheless, when adopted as a temporary measure (and where 
the silt content of the stored water is sufficient to ensure eventual stanching 
by interstitial silt deposit, due to percolation), the construction appears to 
be justifiable, provided that its limitations are thoroughly realised by the 
designer. 




- 

V' 


-5t-3 - 






TV 

(— 


-'15- 

-dr 


* r > 

1 



1<-*£- 






±. 


This space cleared out by hater jet £ men grouted 
Sketch No. 82.—Cast-Iron Piles used in Egypt. 


jv \> t ■ rrrv: ‘‘ tvn 1 . ... - > ., rt. v o im/ic 

The flat, cast iron piles (Sketch No. 82) used in Egyptian weirs (eg. the 
Esneh barrage) may be considered as a modern and permanent equivalent of 
the above construction. The interstices being filled with cement grout, the 
life of the work is that of thick cast iron under somewhat favourable circum¬ 
stances, as far as corrosion is concerned. For shallow depths (say not over 
25 feet) the method may prove less costly than trenching and filling the trench 
with puddle or concrete. Visual proof of complete junction with the clay 
stratum is of course impossible. 

Piling built up of rolled steel sections has lately been introduced. The 
driving gave some trouble at Hodbarrow ( P.I.C.E ., vol. 165, p. 167), but newer 
patented and specially rolled sections permit of very good work being done. 

The durability of steel is less than that of cast iron, but I doubt if this can 
be regarded as a serious defect. 

In a few instances fissured rock has been rendered “ watertight ” at small 
cost by boring a line of vertical holes, say 2 inches in diameter, and 8 inches 
apart, along the centre line of the dam, and injecting cement grout under 



































INDIAN TYPE OF DAM 


3 21 


pressure. When ocular proof is obtained (such as is afforded by the appear¬ 
ance of new springs above the grouted line), the process may be considered as 
satisfactory, otherwise a certain amount of distrust is advisable. 

Position of the Impermeable Layer. —Theoretically speaking, the 
best position for any impermeable septum is as close to the water face of the 
dam as is possible. In nearly all modern dams the core wall or septum is placed 
vertically below the top of the dam. Thus, the whole water side of the dam 
is useless qua providing stability. This must be regarded as a defect, but 
practical considerations compel the designer to adopt the central position. 

If a layer of puddle clay is laid on the water face, it will be found to be 
perforated by burrowing animals such as crayfish, or rats ; and consequently 
the early designs of Telford have rarely been copied in this respect. 

If masonry or concrete is placed, instead of puddle, in a similar position, the 
settlement of the dam invariably causes fractures which permit leakage to 
occur. 

The question deserves investigation, and if an elastic impermeable coating 
can be found which is not liable to damage from burrowing animals, it should 
certainly be placed on, or near to, the water face. In small works of a 
temporary nature economy in earthwork can be secured by the use of bitumen 
sheeting ; but, so far as I am aware, no large dams have yet been constructed 
on this principle. 

The above discussion includes all work in which different methods are 
employed in the ordinary and Indian type of dam. As the Indian methods 
permit good results to be obtained with somewhat worse material, it appears 
advisable to discuss them before considering the casing, pitching, and outlet 
works of dams, which are constructed on the same principles in both types. 
It must also be remembered that the adoption of the precautions used in India 
is never detrimental to a dam, and it is only under very favourable circum¬ 
stances that they can be entirely dispensed with. 

Indian Type of Dam.—A dam of the Indian type is constructed so as 

to sustain appreciable percolation. This may arise from two causes, as 

follows : 

(i) Either the available material or the climatic conditions do not permit of 
a good puddle clay, or other substance providing a relatively thin impermeable 
core, being procured. 

(ii) Or, whether the impermeable core be thick or thin, the geological 
conditions are such that the cut-off trench beneath the dam cannot be 
carried down to a sufficient depth to unite the impermeable septum (formed 
by the core wall and trench filling) with an impermeable stratum of clay or 

unfissured rock. 

We thus have two routes by which the percolating water may travel, i.e. 

corresponding to case (i) through the dam itself, or as in case (ii) under the 

bottom of the cut-off wall or trench sunk below the dam. 

As will be seen later, dams exist which are subjected to percolation in both 
ways, but such dams must be considered as more severely tested than the more 
normal examples in which material percolation occurs by only one of the above 

paths. 

The typical Indian dam falls under case (i), and for some reason which I 
am unable to understand, it is held to be safer than a dam which is water¬ 
tight in itself, but which is subject to percolation below the cut-off trench. 

21 


3 22 


CONTROL OF WATER 


The circumstances under which the Indian dam is generally constructed are 
as follows : 

“Clay” of a second or third rate quality exists, and can be made into fair 
puddle in the trench, but the climate is such that the manufacture of puddle in 
the open air (as is required in building the puddle wall) is a difficult matter. 

The typical earlier design is well illustrated by Burke’s Ashti dam ( P.I.C.E ., 
vol. 76, p. 288), see Sketch No. 73. Here there is a puddle trench approxim¬ 
ately 10 feet in thickness, carried down to a bed of trap rock. Above the 
ground level, however, the narrow core wall usually found in British designs is 
replaced by a triangular mass of puddled “ black cotton soil,” (i.e. 2nd or 3rd 
class puddle) some 60 feet wide at the base. Outside this is a mixture of 
weathered trap rock (“ Muram ”) and earth, which may be considered as 
pervious, but stable, when exposed to water (i.e. the Indian equivalent of 
“ gritty material ”). 

As a matter of experience, such dams are pervious to water to a more or 
less marked degree. Unless the very best workmanship is used during con¬ 
struction, they are apt to slip. Burke followed a specification of practically the 
same type as that given on page 307, and his finished dam appears to have 
weighed about 7 per cent, more than the natural earth, and consequently the 
Ashti dam has not slipped, but slips in the older Indian dams are nevertheless 
common. 

The younger school of Indian engineers have therefore developed the 
system described by Strange (Indian Storage Reservoirs , and P.I.C.E ., vol. 
132). Percolation through the dam is accepted as a fact, and it is realised that 
slips occur, not because percolation takes place, but because the percolated 
water stagnates and saturates the bank, and finally finds its easiest path of 
escape to be through the dam towards the outer slope, which then slips or 
cracks. 

The following description of a modern Indian dam should be read with 
reference to Sketches Nos. 74 and 84. 

(i) Preparation of the Site .—In dams not exceeding 40 feet in height the 
usual British practice is followed, but drains are constructed. Sketch No. 74 
shows a complicated method, where the foundation is cut into angular waves 
4 feet in height, and 20 feet from crest to crest, with 4 feet x 5 feet blocks of 
puddle in the trough of each w r ave upstream of the puddle trench. This may 
be considered far too “niggling” where machinery, or even ploughs, are 
employed for excavation. The downstream portion of the base should be cut 
into ridges and hollows, approximately as shown, and should be provided with 
dry stone drains wffiich are connected by a cross drain to the main downstream 
drain, at all points where the slope of the ground permits. 

The principle of these drains resembles that of a filter. It is desired to 
carry off the percolation w'ater in an absolutely clear state, and to prevent all 
the silt and clay particles from passing away through the drains. A 4-inch 
agricultural drain pipe is consequently laid, or a 6 inch by 4 inch dry stone drain 
is formed, in each of the drain excavations, and this drain is covered by graded 
layers of gravel or broken stone. On top of these layers from 7 inches to 1 foot 
of fine sand is placed. The main dowmstream drain is similarly constructed, 
but must be proportioned so as to carry off more w-ater. A 12-inch pipe, or a 
dry stone drain 9 inch by 9 inch usually suffices. 

Sketch No. 74, which shows the most systematic drainage system I know of, 


INDIAN PUDDLE TRENCHES 


3 2 3 


may be regarded as too costly unless very heavy percolation is anticipated. As 
a rule, one or at the most two longitudinal drains in the cross-section of the 
dam will suffice, and dry stone walls are frequently built on top of these in 
order to collect all water passing over them (see Sketch No. 74). 

The correct location of the cross drains, at each valley in the longitudinal 
section of the dam site, is probably far more important than the number of 
longitudinal drains, provided that the latter are laid to a uniform grade, and 
are well constructed. 

(ii) The Proportions of the Puddle Trench. —Strange’s recommendations 
are shown in Sketch No. 74. In applying these in other localities, it should be 
remembered that: 

(1) The trench is not timbered during excavation, hence the side slopes of J-, 
or -J- to 1. 

(2) The raw material available for puddle is not of first class quality, and 
owing to the climate the puddle is made by chopping, watering, and rolling the 


■Plan at Top —-Planbelow Top 


Water Side 





c 


3“ 


‘0\ 


t 


>0 

Y- 


r- 

/ 

JL 

/ 

C _/ 


/1 


Ni 




L. 


:j 


fill Batters / in 16 
Useless if h/gtier than !B 

Sketch No. 83.—Grooving of Concrete Walls at Junction with Puddle. 


clay in the trench. The width of 14 feet, which Strange adopts, is consequently 
needed in order to permit the use of horse rollers. 

A trench filled with good puddle, concrete, or masonry, could therefore be 
made narrower, and the usual British practice might be followed. 

The puddle trench is drained in a similar manner to the dam foundation. 
In order to prevent the localisation of percolation which might possibly occur 
near the drain from setting up erosion of the base of the puddle wall, this base 
is made of concrete about 4 feet by 10 feet, well keyed into the puddle wall 
(these details in Sketch No. 74 differ from those given by Strange, being my 
own). 

The drain is constructed of dry stone, of say 4x6 inches internal dimen¬ 
sions, surrounded by about 4x3 feet of clean rubble, and this in turn by a 
1 foot layer of clean gravel, or coarse sand. 

Strange recommends that the puddle trench should be supplemented by 
masonry walls at points where it is excavated to an unusual depth, e.g. across 
the bed of the river that previously drained the valley. The method seems 
rational, but local conditions must determine whether it is required. Rules for 
such walls are given on page 318 (Sketch No. 94 gives details of the junction). 































CONTROL OF WATER 


3 2 4 


<3 



Q 

o 

o 

C 

rt 


V- 

d 

w 

c 

s 

o 

a 

g 

o 

U 

c 

.2 

c 


Tf 

00 

6 

£ 

a 

o 

H 

a 

a 

in 


The junction of the puddle with 
this masonry needs careful con¬ 
sideration. The masonry should 
batter outwards in all directions, 
so as to prevent shrinkage cracks 
in the puddle at the line of junction. 
Consequently, the masonry should 
be a frustrum of a cone. So also, 
chases should be formed at every 
possible point, as shown in Sketch 
No. 83. The sketch is a complete 
solution of the problem, and the 
chases are easily made in concrete. 
In brickwork, much cutting ofbricks 
is required, but is unavoidable. 
Inspection during construction and 
deposition of the puddle should 
be unremitting. It will also be 
plain that an arrangement of 
silting tanks above the deeper 
portions of the trench, in order 
that stanching by percolation may 
occur during construction, quite 
justifies any small cost entailed. 
The puddle filling is carried up 
to about 3 feet above the ground 
level, and is then stopped; the 
climate being such that puddle 
made in the open will crack and 
split if formed of pure clay. 

(iii) Construction of the Earth¬ 
work .—As a general rule Strange 
recommends that the whole bodv 

J 

of the dam should be made of 
equal parts of clay and weathered 
shale (i.e. clay and grits), but in 
any given case experiment must 
decide the exact proportions. 
The specification of workman¬ 
ship closely resembles that already 
given, the small variations being 
due to local conditions. The con¬ 
solidation obtained with such mix¬ 
tures is considerably less than is 
usual with the more gritty materials 
employed in British practice. 
Strange states that 106 cube feet 
of excavation from borrow pits will 
be required for 100 cube feet of 
bank. My own experiments give 





















DRAINAGE OF DAMS 325 

figures ranging from 109 to 105 cube feet, as against 116 to 111 cube feet for 
purely gritty material. 

Dams constructed in this manner are found to be permeable (see p. 348) ; 
and, in consequence, slips are of frequent occurrence. These slips always take 
place on the downstream face (except when local slips are caused at the water 
face by sudden lowering of the water surface). The slopes adopted (3 : 1 water 
face, 2 : 1 downstream face) might therefore be modified with advantage ; and 
such values as to 1, on both faces, or 2f : 1, for the water face, and 2^:1, for 
the downstream face have been suggested. 

In general practice, it is usual to provide against slips by means of 
berms on the downstream slope, and to form a heavy toe wall at the lower toe 
of the dam. Sketch No. 86 shows Jacob’s design at Jaipur, which attains 
stability by a reversed filter at the toe. 

The most systematic application of the method is that given by Strange 
(see Sketch No. 84), whose final design for dams more than 40 feet high consists 
of a dry stone toe of the roughest obtainable rubble, laid in beds normal to the 
slope, with one or two cross chace walls of concrete, with a view to increasing 
the resistance to slipping. Where the dam is joined to an impermeable stratum, 
the interstices are packed with clayey schist, and a solid facing of concrete is 
also built at the upper end, as at the water face toe of Sketch No. 84. Where 
impermeable strata are not reached, it might be preferable to lay a reversed filter 
in place of the concrete facing, starting with say 12 inches of road metal, followed 
by 12 inches of gravel, and then 12 inches of coarse sand as at the outer toe 
of Sketch No. 84. Localisation of the percolation must be avoided at all costs. 
It will be noticed that this design very closely resembles the combined rock- 
fill and earth dams of America. The real difference is that in the case of the 
Indian dam, earth forms the bulk of the dam, and the rock work is of less 
importance ; whereas in the American dam the earth filling is the minor 
factor. 

Dams not joined to an Impermeable Stratum. —The principles of the 
design of dams subject to percolation having been thus laid down, their extension 
to cases where the core trench does not join an impermeable stratum are 
fairly plain. 

The cut-off trench should be carried down about 30 feet (which was 
Rawlinson’s design where the depth of water retained was 30 feet); or, as 
Strange suggests, in good compact soils, to a depth equal to one half the depth 
of water stored ; and when the soil is fairly compact, to a depth equal to the 
depth of water stored, provided that all sandy and highly pervious layers are 
cut by the puddle trench. 

So far as I can ascertain, no failure due to percolation under the puddle 
wall has as yet occurred, when the depth of the trench exceeded three quarters 
of the depth of the water stored ; and in most of the older dams the concrete 
base of the puddle trench and a systematic drainage were not adopted. No 
failure due to insufficient depth of puddle trench is recorded in the case of dams 
founded on permeable soil, provided that the drainage had been properly 
attended to. 

The drainage system is quite as necessary to prevent slips as the toe wall, 
and while less carefully drained dams have not failed, Strange’s design should 
not be departed from unless the circumstances are otherwise extremely 
favourable. 


CONTROL OF WATER 


326 



Sketch No. 85.—Balanced Gate Outlet. 















































































3 27 


JACOB'S TYPE OF DAM 

This Sketch shows the outlines of the arrangements adopted by Pennycuick at 
Periyar, to pass 1600 cusecs under a pressure which may attain 49 feet when the gates 
are closed. In view of the great liability to wear of the upper gate the lower gates 
must be considered as an integral portion of the design. Since they are hung from 
rods passing through pipes, these lower gates can never be raised for repair. As a rule 
this must be considered as a defect. At Periyar these lower gates are only worked 
when the reservoir is at a low level, never pass more than 500 cusecs, and when 
open are never exposed to more than 20 feet head ; the regulation then being also 
mainly effected by means of a Stoney sluice at the tunnel portal. Thus, in general 
the lower gates would need to be replaced by a second balanced gate. The design is 
an excellent solution of the local problem, and the principles might be generally adopted, 
since it may be presumed that when discharges computed in hundreds of cusecs are 
dealt with, slight leakage is permissible. If no leakage can be allowed the gates of 
the Roosevelt dam (Wilson, Irrigation Engineering ) may be taken as a basis for 
design, but the increased cost indicates that as a rule leakage should be permitted. 
If either type is adopted in a culvert outlet not surrounded by hard rock the stresses 
in the masonry will plainly require very careful calculation. 


The filling of the core trench needs careful thought. Strange is apparently 
of the opinion that his 14 feet wide trench with 4, or g- to 1, side slopes will suffice, 
when filled with puddle, and with the concrete base usually adopted. Personally, 
I favour concrete, or a double wall of concrete and puddle in two layers. 

The dam itself may either be of Strange’s type, Sketch No. 84, or if good 
puddle is procurable water-tightness may be secured by a puddle wall, say 33 p.c. 
thicker than the usual rules indicate. The fact that settlement will certainly 
occur seems to preclude the use of masonry or concrete for the core wall. 

On referring to the preliminary section, it will be seen that the provision of 
an impermeable carpet over the whole base of the dam stops percolation almost 
as effectually as a vertical cut-off trench, and while a good wall of puddle clay 
or other non-rigid substance gives satisfactory results, there is little doubt that 
if the whole dam be made of fairly impermeable earthwork, the effect in 
preventing percolation through the dam is almost equally good; and the 
percolation under the cut-off trench is probably less than if the thinner wall of 
more impermeable material forms the only impermeable portion of the dam. 

The real dividing line is fixed by the value of labour. In countries such as 
India, where labour is cheap, the best solution (when good puddle clay is not 
available) is to roll and puddle the whole dam very carefully. Compare the 
Ashti dam, and Strange’s general section, with the Staines dam. 

If labour is dear, a thin wall of strong material is indicated, as in the case 
of some American dams, where impermeability is secured by thin steel plating, 
averaging fths of an inch in thickness, protected from rust by a 4-inch coating 
of asphalte on each side. 

Such a dam cannot be considered as an innovation in constructional design. 
Hundreds of examples exist in Ceylon and Southern India, without any puddle 
trench at all, and are often of great age. As an example of a modern dam subject 
to heavy percolation, I would instance the Amani Shah dam at Jeypore (Rajputana) 
constructed by Col. (now Gen.) Jacob. This has no core wall, and is formed 
of sand, resting on sand and mud. Its dimensions are (/ ./.C.A., \ol. 11 5 ? P- 5 )• 


Height . 

Breadth at top 
Breadth at base 
Inner slope, i.e. water face 
Outer slope • 


61 feet. 
30 
396 
4 to 1 
2 to 1 


35 


33 






328 CONTROL OF WATER 

The toe wall was constructed,—to quote Gen. Jacob : 

“ Next to the earth a layer of sharp sand about 10 feet wide and 5 feet 
deep was placed, outside of this a similar layer of small broken stone ; and 
finally a similar mass of large rubble.” 

It was anticipated that: 

“ It would act as a filtering medium, keeping back the earth, but allow¬ 
ing the water to percolate out free from silt.” 

“The highest water level yet reached is 31^ feet.” 

If I may criticise a singularly successful design, I should be inclined to 
recommend that the water slope should be 3 to 1, or as steep as stability allows ; 
and that the outer slope should be made 3 to 1. My reasons are, that it is 



//■ /5 doubtful if the ndter tent ever 
exceeds 4t, even during floods 


S<and l Mud 


Sketch No. 86.—Jaipur Dam ; for Culvert see Sketch No. 90, Fig. 1. 



evident that the dam is saturated up to a line sloping away from top water level 
at 1 in 7, or perhaps even 1 in 6 ; and, as at present designed, a line at 1 in 6 
drawn from the designed full supply level of 41 feet cuts the outer slope at about 
3 feet above the toe ; whereas if the slopes were reversed, or were even made 
1 in 3, on both sides, the 1 in 6 line would pass well below (about 8 feet for 1 in 
3 slopes) the outer toe. (Sketch No. 86.) 

The dam at Baroda (see Sketch No. 87), described by Sadasewjee 
( P.I.C.E ., vol. 115, p. 43), shows a more typical section. The dam is of clay 
and grit mixed, and the puddle trench is filled with good (Indian) puddle, 
carried down to a clay stratum except for a length of 200 feet, where it stops 
at depths varying from 25, to 40 feet, being 5 feet wide at the base. 

No systematic provision being made for drainage of the dam itself, slips 
occurred, and an open drain 10, to 12 feet deep was cut just outside the outer 















BARODA DAM 


3 2 9 

toe of the dam for a length of 2900 feet. This discharged a quantity of water 
varying from 06, to o’9 cusec. 

The question was considered by Latham ( P.I.C.E ., vol. 115, pp. 44 and 122), 
who gives a rather interesting piece of reasoning. He says that when the 
leakage takes place below the puddle wall, the apertures by which the water 
escapes will always be of the same size ; if, however, leakage occurs over the 
puddle wall, the total area of the apertures will vary with the height of the 
water in the reservoir. 

Thus, since : 

“ The law which governed the flow of underground water was similar 
to that which governed the flow of water in pipes and channels,” 

a leakage, proportional to the 

“ Square root of the height of water above the point at which it was 
escaping,” 

would indicate leakage under, and through, the core wall. But since : 

“ By taking into consideration another factor, i.e. the actual height of 
water in the reservoir above the top of the puddle wall,” 

it was possible to calculate the escaping water with exactitude, Latham 
therefore deduces that the leakage was through the body of the dam, and over 
the top of the core wall. 

The reasoning is well worth bearing in mind when leakage occurs ; and 
since Latham is a very accurate experimenter, it would appear that definite 
channels of escape existed in this particular dam, or that so large a proportion 
of big stone was present that the usual relation for capillary channels {i.e. 
volume escaping varies as the pressure), did not hold good. A priori , we 
may usually expect to employ the reasoning: Volume escaping varies as the 
height of the water above the point of escape,—as indicating leakage under, 
and through, the core wall. While, if the second factor—height of the water 
above the top of the core wall—also manifests itself, the leakage is over the 
core wall. 

I reproduce the original drawing given by Sadasewjee {lit supra), as 
Latham’s observations show that a dam of this type will stand leakage to the 
extent of o'85 cusec over a length not greatly in excess of 200 feet without 
slipping. 

The remedies consisted of a clay wall at the outer toe, 12 feet wide, flatten¬ 
ing the outer slope near the toe to 3 to 1, and a system of. surface drains to 
carry off rain water falling on the outer slope. 

The above may be considered as representing the worst that can happen in 
dams of this type, when properly constructed, whether the core trench is joined 
to an impermeable stratum or not. 

In order to obtain any instance of a partial failure (such as the above) I 
have been obliged to include a case where drainage was not well attended to. 
So far as I am aware, no properly drained dam has failed by reason of per¬ 
colation. The failures of the older Indian and Cingalese native made dams 
can almost invariably be traced to over-topping by floods, and no undoubted 
case of failure due to percolation has yet been recorded. 

The following appears to be a fair view of the question. The ordinary 


CONTROL OF WATER 


33° 

English practice relies too exclusively on puddle and impermeable strata, which 
can usually be obtained in England at a certain price, owing to the small scale 
of English geological features. Indian practice is more logical, in that when 
the above advantages cannot be obtained except at a prohibitive cost, the 
difficulty is surmounted without any pretence of ignoring it. 

Personal experience leads me to believe that puddle clay passing English 
specifications, or cheap concrete and masonry, combined with easily reached 
impermeable strata, occur only exceptionally. I confidently look forward to an 
extensive use of the Indian type of dam in other countries ; all the more so 
since any engineer who has to cope with less favourable climatic conditions 
and more intense floods than those of India, may consider himself most 
unfortunate. 

The whole matter is one of balance between the dam and the puddle trench ; 
where, (as in the case of the ordinary English dam, great care is taken to 
produce an absolute junction between the puddle trench and an impermeable 
stratum), the dam may be considered as not very greatly affected by percolation, 
and a thin wall of puddle clay is sufficient to stop percolation. Where the 
puddle trench is known to be carried to an insufficient (according to English 
ideas) depth, more care and pains must be devoted in order to make the dam 
as a whole partially impervious by mixing some clay with the gritty materials. 
A proper system of drainage must be constructed in order to overcome the 
tendency to slips which exists in this mixture when saturated. 

The differences between the above two types having been considered, we 
can proceed to examine the various portions of the dam that depend not so 
much on the amount of percolation, as on climatic conditions. These are : 

The Casing. 

The Pitching. 

Casing of the Dam. —The casing of modern dams is thin, and can best 
be regarded as a layer of stone or gravel which affords a means of draining the 
pitching. 

Strange says that we should construct the casing of one part clay and two 
parts of shale, and make it 2 feet wide from the top down to full supply 
level; and below, the width should be increased 1 foot for every 10 feet of 
vertical height. 

This specification is for a climate where the rain-fall, although intense, is 
limited to about four months in the year. In a country where rain is less 
heavy, so great a thickness is perhaps useless ; but on the other hand, if the 
rain-fall is distributed over the whole year, the proportion of clay seems exces¬ 
sive, and might produce turbidity in the water. 

At Staines (where the rain-fall is about 25 inches annually, and occurs over 
the whole year), 6 to 9 inches of pure gravel sufficed. 

Pitching. —The necessity for pitching is obvious. The most usual type is a 
layer of roughly hammer-dressed stones, laid on their large ends, and dressed 
so as to meet all round their bases for a depth of 3 to 4 inches. 

The thickness may vary from 6 inches at the bottom, to 18 inches at the 
top, in reservoirs some 6 square miles in area ; and say 9 inches at the bottom, 
to 2 feet at the top in the case of reservoirs 20 square miles in area. 

The following specification of Messrs Hunter & Middleton has produced 
very satisfactory results at Staines : 


PITCHING OF DAMS 331 

1 he inner face of the embankment to a depth of 15 feet below the top 
water level is to be protected by concrete slabs made in situ of 4 to 1 
concrete, 4 feet square, and 5 inches thick, worked to a good face and 
resting on 6 inches of gravel; every alternate slab being left out in each 
line until the subsidence has ceased, when those in position will be packed 
up to the line of slope, and the work completed. At the foot of the 
concrete facing there is to be a step or berm 3 feet wide, and below that 
line the embankments are to be covered with a 9-inch layer of gravel. 

I he fetch is but small (1^ mile at the most), but the reservoirs are greatly 
exposed to wind, and it is doubtful whether any thickness less than 9 inches 
would have sufficed had the pitching been composed of smaller and rougher 
material. 

In the actual construction, a 3 feetx 18 inch concrete toe wall was built at 
the bottom of the concrete slabs (Sketch No. 72). The appearance is good, 
and similar (although probably somewhat thicker) slabs deserve consideration 
wherever stone is not easily available. Being smooth, and of large size, the 
thickness need hardly exceed one half of that given by Stevenson’s rule, which 
is obtained from experience in very windy localities. 

The following is a good rule :—Thickness=£ height of waves likely to 
occur. For this height Stevenson gives : 

Height in feet= 1*5 VF + (2 - 5 — 4 VF) 

where F, is the “fetch ” of the wind in miles. 

In cases where stone is not procurable, hard burnt blocks of clinkered bricks 
(say 6 bricks in a block), can occasionally be procured. Pavings of brick, on 
edge, or on end, are usual in the Punjab, but they are not strong enough if the 
waves are high, as is likely to be the case if F, is much over a mile. 

The wall or wave breaker at the top of the dam (as shown in Sketches 
Nos. 74 and 81), has been recommended as an effective means of preventing 
waves from washing over the dam, but is rarely employed. Careful drainage 
of the top of the dam with drains extending down the side slopes at frequent 
intervals seems to be a better method of dealing with waves and spray. 

The outer slope of the dam requires to be protected from rain wash. This 
is usually effected in England by covering the slope with vegetable earth, and 
sowing with grass ; or sodding with the sods removed from the base of the 
dam, special provision for drainage usually being unnecessary. In less equable 
climates, turf of this character is difficult to maintain, and either careful plant¬ 
ing with fleshy plants, or coating with gravel, or small stone, is consequently 
required. The practice of planting with shrubs, or worse still, with trees, 
should not be followed, as these conceal leakage if it occurs. Cases have been 
met with where cracks and fissures in dams have been traced to the action of 
wind on trees growing on the dam. 

The Staines specification gives the usual British practice : 

The whole of the outer slope of the embankment is to be covered with 
a layer of soil 6 inches thick, resting on 3 inches of gravel, and sown with 
clean rye grass and white clover seeds. 

In hotter climates, a deeper layer of soil, and a more fleshy grass, or even 
such plants as Mesambryanthemum, are advisable. 

A little consideration will make it plain that both the casing and pitching of 


CONTROL OF WATER 


33 2 

a dam should in reality be determined by the quality of the gritty material. 
At Staines, if appearance could be entirely neglected, there appears to be no 
real necessity for either. Taking the other end of the scale, a dam constructed 
according to Fanning’s or Strange’s specification requires thick casing and 
good pitching to prevent the slopes from being guttered and damaged by rain 
or waves. 

Top Width of a Dam. —The top width is usually taken as io to 14 feet. 
There is very little doubt that in all dams, except the very lowest, it should be 
of sufficient width to carry a cart road, as the extra cost is rapidly saved by the 
ease with which repairs and maintenance are carried out. If there is the 
slightest doubt about the sufficiency of the waste weir ( e.g . owing to the avail¬ 
able records of flood discharges being for a short period only) 14 feet should be 
considered as the minimum width. To my own personal knowledge, one dam 
at least has been saved, and a bad disaster averted by temporary heaps of 
earth erected along the crest, which just sufficed to prevent the destruction of 
the dam by overtopping during an abnormal and sudden flood. 

While the chief credit is due to the local labour which took the risk of 
accompanying the dam down the valley, the earth was finally secured by 
excavation in the top of the dam, and, had the top width been insufficient to 
permit this, procuring the necessary earth from the downstream slope, would 
have been more tedious and more likely to create a weak spot. 

Low Dams .—The previous discussion mainly refers to dams of considerable 
height. The following proportions are suggested by Strange (.Indian Storage 
Reservoirs ) for dams under favourable circumstances : 


Height of Dam. 

' , 1 

Height above 
High Flood 
Level. 

Top Width. 

Slope of 
Water Face. 

■( ‘ 

Slope of 
Downstream 
Face. 

Less than 15 feet 

4 to 5 feet 

6 feet 

2 : 1 

f*(() l 

l 2 1 1 

15 feet to 25 feet 

5 to 6 „ 

6 „ 

2J : 1 

2 : 1 

25 „ 5 ° » 

6 feet 

8 „ 

3 : 1 

2 : 1 


Failures of Earth Dams. —The usual cause of a bad failure is the in¬ 
sufficient capacity of the waste weir, as was the case in the Johnstown dam, 
which is discussed under Floods. 

The Holmfirth failure (P./.C.E., vol. 59, pp. 51 and 57), where the dam had 
been allowed to settle until its crest was but little above the waste weir sill, can 
only be regarded as the result of careless maintenance. 

Among other disastrous failures the Dale Dyke may be mentioned. 
This was apparently caused by the bursting of an unprotected line of pipes 
laid through the dam. Since, however, the earthwork is described as very 
loose, and more like a quarry tip than a dam, it is difficult to allocate the 
responsibility accurately. 

Small failures usually consist of slips or sloughing of the downstream slope ; 
and if the water in the reservoir is rapidly lowered, similar, but usually more 
localised slips, may occur on the water face. 




















VALVE TOWERS 


333 

Outlet Works. —The crucial point in the design of the earth dam of a 
reservoir is the method employed for drawing off the water. 

The more intensely a catchment area is developed, by increasing the 
storage on it, the more important it becomes to arrange the outlet so that water 
can be drawn off at any level. If we in any way limit the depth from which 
water can be drawn, it is evident that, pro tanto , we diminish the effective 
storage capacity. On the other hand, a large reservoir capacity, (if properly 
used) entails the reception of large volumes of flood water into the reservoir, 
and this water, except under very favourable circumstances, is bound to be 
turbid. It is therefore necessary to be able to draw off the upper layers of the 
water, which will more quickly become clear, and to reject the lower layers, if 
abnormally silted. Thus, it is absolutely essential to provide some method of 
running off large quantities of water when the reservoir is nearly empty, unless it 
is possible to systematically reject turbid water by means of bye-pass drains. 
Even then, it is quite possible that the cost of such bye-pass drains may exceed 
that of a draw-off system, which will permit an equally satisfactory rejection of 
silt-bearing water, combined with the selection of clear water for use when required. 

The systems adopted are as follows : 

(i) A valve tower which permits water to be drawn off at any level. 

(ii) A series of undersluices at a low level for rejecting silty water, and these 
(or a separate set), or a valve tower, may be employed for the delivery of water 
for use. 

Valve towers (see Sketch No. 88) are usually constructed of stone or 
masonry, and while a cast iron valve tower may be cheaper, it is exposed to 
greater risk of injury by ice. Where the formation of thick ice is unlikely, the 
question of cost may be allowed to determine the material selected. 

The valve tower must be sufficiently far removed from the dam to be safe 
from injury, either by settling of its foundations, due to the pressure of the dam, 
or by slips of the dam itself. A line of pipes, or a tunnel, is required to carry 
away the water from the valve tower. 

The most obvious and the cheapest method is a line of pipes laid in the dam 
or in a trench below the base of the dam. It is doubtful whether this con¬ 
struction is ever permanently successful, and it should never be adopted except 
for temporary work, and even then only in cases where failure of the dam will 
result in but little harm. Sketch No. 89, shows the nearest approximation to 
this construction existing in permanent work with which I am acquainted. The 
pipes are 3 feet in diameter, and are surrounded by 18 inches of concrete. The 
design cannot be recommended, although the general arrangements which 
permit water being drawn off at any level without opening any valve under 
more than 15 feet head are excellent. The weak point is admirably illustrated 
by the statement that the dome valves Aj, A2, etc., cannot be opened unless the 
lower valves V, are partially closed. Thus, if any serious break occurred in the 
concrete and pipes in the dam, it might become impossible to close the dome 
valves (see Fig. No. 3), and then the destruction of the dam would merely be a 
matter of hours. The pole and plug type of valve (see I lg. No. 4) would leally 
be safer, since it is more certainly closed should any displacement of the pipes 
occur. The difficulty of opening these valves may' be overcome by the bye-pass 
shown in Fig. No. 2. It is, however, plain that the pipes would be far safer 
against fracture if they were carried in a culveit. 

In certain very early designs the only valves were located at V, and the 


334 


CONTROL OF WATER 


inner orifices A, could not be closed. Such designs are extremely dangerous, 
and I believe that no examples exist at present. The life of a dam with this 
type of outlet may usually be reckoned by months. 










































































































CULVERTS THROUGH A DAM 


335 


Even in temporary construction an unprotected line of pipes with the valves 
correctly placed is extremely objectionable. The line is very liable to fracture ; 
and although the leak can be stopped by shutting the upper valve, repairs are 
difficult, and may entail letting off all the water in the reservoir. It is also 
quite evident that the outer skin of the pipe line forms a possible line of leakage 
for the water, and that the puddle wall crossing may also be breached by the 
puddle below the pipes settling from beneath the pipes. While wide creeping 
flanges surrounded by puddle form a fairly efficient stop against leakage along 
the pipe line, nothing except a concrete wall, built up from the foundation of 
the puddle trench to the pipe, (as in the method used in carrying the concrete 
lined channel into the Hampton service reservoir, shown in Sketch No. 83, or 
that shown in No. 88) is effective against settlement of the puddle. 

In pioneer work, where every penny must be saved, it has occasionally been 
found advantageous to carry a line of pipes through the dam, at or a little (say 



15 feet as a maximum) below the top water level. Under these circumstances 
the pipe line usually works as a syphon, and is only rarely under pressure. 
Fractures of the pipes may therefore prove troublesome, but need not be 
disastrous, and the method has proved very efficient. It is, of course, obvious 
that any later attempt to utilise more than, say, the top 20 to 30 feet of the 
reservoir content will entail very expensive works, and the whole of the water 
in the reservoir may have to be run to waste before a culvert situated at a low 
level can be constructed. 

The next method is to build a culvert of ashlar masonry, or brickwork, in 
which the pipes are laid (Sketches Nos. 88, 90). A plug of ashlar masonry, or 
best bricks, is placed across the culvert; usually near the foot of the inner slope 
of the dam. Both the culvert, and the pipes where they cross the plug, require 
creeping flanges to prevent the water from leaking along their outer skin. The 
method is unobjectionable, but the culvert is liable to be fractured by settlement 































































CONTROL OF WATER 



of the earth of the dam, and puddle wall. In high dams, even the best ashlar 
has proved too weak to resist the forces thus brought into play. 

Where (see Sketch No. 88) the culvert lies above the level of the bottom of 
the puddle trench (as is frequently the case) this action is intensified by the 
necessity of supporting the culvert where it crosses the puddle trench, on a 
rigid concrete or masonry pillar, in order to prevent a hollow occurring in the 
puddle clay beneath the culvert, just as was pointed out when dealing with the 
pipe crossings. For typical culvert sections see Sketch No. 90. 

In some cases the culvert has been built with a slip joint at this point ; but 
even this precaution has not met with invariable success, possibly owing to the 
pressures produced by settlement being by no means entirely vertical (Sketch 
No. 88). 

The effect of the various failures,—or it would be more correct to say, of the 





Sketch No. 90.— Sections of Culverts. 


possibilities of failure,—thus disclosed, has led many engineers to consider it 
preferable to drive a tunnel through the undisturbed hills on one side of the 
dam, and to lay the outlet pipe in this. The advantages are obvious :—the 
valve tower and culvert are entirely separate from the dam, and cannot be 
injured by its settlement, nor can the culvert form a line of weakness in the dam. 

On the other hand, the cost is greatly increased, and tunnel work requires 
a special class of labour, not always easily procurable. It is also quite 
evident that work done in tunnels, in the dark, is far more liable to be 
scamped than in a culvert, which is built in the open, and can be inspected 
inside and out at every stage of construction. 

Summarising these points :—It would appear that the tunnel plan should 
be adopted in large works where skilled labour is abundant. Where unskilled 
labour only is piocurable it is quite possible that bad workmanship may 














































































SECTION OF CULVERTS 


337 


result in unseen defects, which prevent the attainment of the almost absolute 
safety which the tunnel plan (if well executed) undoubtedly secures. 

It must also be remembered that even though a culvert should be slightly 
fractured by settlement, the defect is by no means irremediable, and probably 
merely entails the injection of three or four barrels of cement grout under 
pressure. 

I may also mention the method adopted at Staines reservoirs, which 
seems almost ideal where an impermeable stratum of sufficient thickness is 
known to exist at a small depth. Here the culvert was carried not only under 
the dam, but also under the puddle wall, with its top at a depth of some 7 feet 
below the top of an impermeable stratum of London clay. It was thus possible 
to combine all the advantages of undisturbed ground secured by the tunnel 
system, with a length of culvert but slightly in excess of that required to 
traverse the dam at its base. 

The design of the draw-off passage (whether constructed under the dam 
as a culvert, or as a tunnel through the hillside from the dam) needs 
consideration. 

In the first place, if the culvert is surrounded by puddle, the stresses on 
the arch are unusually great, since well made puddle is practically a heavy 
fluid as regards vertical pressures, but cannot be relied upon to give the 
same horizontal support at the springing of the arch as that which is afforded 
by a perfect fluid. 

The severity of the conditions to which a culvert loaded with puddle is 
exposed, are best realised by the following investigation. (See Sketch No. 90, 
Fig. 4-) 

Let /, be the span of the arch, in feet, measured to the intrados. 

Let h, be its rise in feet, measured to the intrados. 

Let d 0 , be the arch thickness at the crown in feet. 

Let D 0 = 4 +^ where z , is the height of any rigid non-moving filling 
that exists above the arch crown, i.e. in good work z=o , so as to 
avoid leakage. 

Let /, be the height of the puddle above the crown of the arch 
in feet, or above the top of the filling if z, is not equal to 
nothing. 

If the weight of the puddle per cube foot differs materially from that of the 
arch masonry, put : 


Weight of puddle per cube foot 


p — Height of puddle x 


Weight of masonry per cube foot* 


Then, owing to the fact that the puddle may sink unequally, we must 
consider the arch as exposed to a moving load equivalent to p, feet of masonry 
per foot run. 

For such a case, Tolkmitt (Entwerfen der Gewoblten Brucken) finds that: 


d, = _ °’ 5 I _ > 

h o‘5/+o'i ^h-\- D 0 


Hence, d 0 = h approximately, if z = o, whatever value of p be assumed ; for 
we cannot assume that p, is very much less than 20 feet, since, although it may 
be doubtful whether the top portions of the puddle move sufficiently to be 


22 





CONTROL OF WATER 


33 8 

considered as a live load, there is no doubt that the first 20 feet above the 
culvert must be treated as a live load. This condition secures that there is no 
tension in the arch, and then the equation : 

k 0 = i*S lbs. per square foot 

h \ d 0 / 

gives the pressure at the crown of the arch ; where w, is the weight of a cubic 
foot of masonry. The maximum pressure in any portion of the arch does not 
exceed 2 k 0 . 

Now, let / l3 be the span, and # l5 the rise of the arch, as measured to the 
centre line of the arch ; and the arch thickness at the springing measured 
perpendicular to the centre line. Muller-Breslau ( Elastizitatstheone der 
Tonnengewolbe) finds that k x , the pressure at the springing, is given by : 

*1 = 5'2 (Do+o’5/+o‘i4^) ^ec tj> + ^5—^ +°'75/ lbs. per sq. ft. 

Ah\ D 0 +o m sp+o'S& 


+1 


where tan 2 cf) ■ 


/ 2 i D 0 +o* Sp +0-14/2 


■ COS cf) 


The result obtained with the upper sign must not be negative ; and with 
the lower sign must not be greater than the permissible working pressure. 

As a rule, we can put ( ~r — \ \ but if cos cf) be greater than take 

«i " a i 

for the first trial. 

These rules are founded on formulae deduced by drawing the lines of 
resistance of various arches ; and the arches investigated were mainly parabolic, 
or three centered. 

Existing culverts are usually constructed with semicircular arches, and 
h h 

d 0 =~r, and <^i = - is a fair indication of their proportions. 

It may be inferred, that these dimensions are probably of excessive strength 
for the portions of the culvert which are loaded with well rammed firm earth, 
and that they are too weak for the portions under the puddle wall. 

I have been unable to find one case where the culvert arches did not crack 
or settle if the side filling was of puddle clay ; while few appear to have 
cracked when covered with puddle, and supported at the sides by solid 
material. The cracking cannot be considered as amounting to a failure, and 
in most cases was scarcely of such a magnitude as to cause uneasiness to the 
engineers. It is, however, evident that a side coating of puddle forms an 
unfavourable condition. I therefore recommend that, wherever possible, the 
culvert should be bedded in undisturbed material up to the haunch level, and 
that a water-tight junction between the culvert walls and this material should 
be secured by heavy and systematic grouting with cement as the side walls are 
built up. In cases where this method is not practicable, it appears wisest to 
design the top of the culvert as an arch to carry a pressure equal to that 
produced by the puddle load; and to spread out the sides as shown in 
Sketch No. 88. 

While no existing culvert has been constructed of reinforced concrete, this 
material seems admirably adapted for sustaining the tensile stresses produced 







S39 


CULVERT PLUGS 

by the unequal pressures on the arch. It may be objected that the circum¬ 
stances are such as to favour corrosion of the reinforcement, but it must be 
remembered that the tensile stresses probably only act during the settlement 
of the puddle, so that corrosion of the reinforcement at a later date is of little 
importance. 

The stops, or plugs, which close the water end of the culvert or tunnel, 
lequire careful construction, as they are exposed to a head of water equal to 
the total available depth of the reservoir. Sketch No. 91 shows details. 



Half Plans of Brickmrk l Grouted Ashlar Fl ues. . 


Sketch No. 91. —Details of Plug between Valve Tower and Culvert. 

It is doubtful whether the general form of the ashlar plug is as satisfactory as that of 
the brickwork plug. The structure from which the sketch is made gives satisfaction. 

The following specification is not only suitable for such work, but may 
(with the obvious exception of radiated joints) be employed for all brickwork or 
masonry which is intendecj to retain a high head of water. 

“ The plug to be faced on the water side with 1 foot 9 inches of granite 
ashlar, radiated on beds and joints, having V grooves in the same, run 
full of pure cement grout, and behind the ashlar there is to be 8 feet 
3 inches of blue brickwork in cement. 

“ The brickwork must be very carefully set in cement mortar, and 
grouted in the vertical joints. The sides, floor, and arch of the tunnel are 
to be roughened so as to make a good bond with the brickwork, which is 
to be well forced into soft mortar all round the sides and arch. 

“ Three circumferential chases, are to be cut or formed in the arch 
masonry, and concrete, one to fit the radiated ashlar, and the other two to 
make a good stopping chase with the brickwork. 

<k The whole to be made perfectly watertight, and the contractor to cut 
all bricks to fit the pipes and creeping flanges, grouting in the same in pure 
cement. All launders, troughs, and cofferdams required to pass the water 
over the plug during erection, and until the mortar is sufficiently set to 
allow the water being passed through the pipes, to be provided bv the 
contractor.” 













































































CONTROL OF WATER 


34 ° 

Any rule for the thickness of the plugs, or stops, must obviously take into 
account the area of the exposed surface, as influencing the stresses developed 
by the water pressure. But it would appear that a thickness of ^th to yth 
of the head of water is sufficient to prevent any undue percolation, provided 
that the stresses are not so heavy as to produce tension in the brickwork. In 
cases where the stress formulae indicate a smaller thickness, water-tightness 
is economically secured by means of a layer of asphalte, or bitumen sheeting 



sandwiched into the plug. Specifications for such work are given on page 978, 
and a very excellent detail appears under the head of Service Reservoirs. 
(See Sketch No. 156.) 

The details of the chases deserve consideration. The work is not easily 
inspected, and necessitates a large quantity of bricks being cut. Thus, there 
is a great tendency for the masons to fill the chases with a mixture of bats and 
mortar. The chases should therefore be carefully spaced, so that they will 

























VALVE TOWERS 


34i 

marry easily with courses of the actual bricks used (not with the theory of four 
courses per foot, etc.). The shape should also be that of a half-brick, so as to 
encourage the masons to fill in with whole bricks ; and experience leads me to 
believe that bricklayers (as distinct from really skilled masons) make a better 
job when allowed to lay bricks in mortar, and to fill in the interstices with pure 
grout at the end of, say, each hour’s work. 

Creeping Flanges .— The general proportions of creeping flanges for pipes 
in concrete are shown in Sketch No. 92. The usual error (especially in the 
case of the creeping flanges to pipes) is to make the radial breadth of the 
flange too small. For creeping flanges in concrete a width, say, five times 
the thickness of the pipe suffices. This width will not suffice for creeping 
flanges for pipes in puddle. The width should be fixed by a consideration of 
the amount of settlement likely to occur in the puddle. From certain failures 
it may be inferred that the radial breadth should be at least ^ 0 -th (or better 
2Vth) °f the height or depth of the puddle (whichever is the greater) 
above or below the pipe or culvert. The real object of such a creeping flange 
is, of course, to provide against slip and movement of the puddle ; and the 



above rule roughly indicates the probable magnitude. Where the flanges are 
not cast solid with the pipes, they should be united with the pipe by means of 
a caulked lead joint resembling that used to joint pipes ; or else should be 
bolted in between the two flanges of a flanged joint. 

Valve Towers and Culverts. —The .typical valve tower and culvert 
arrangement, with the tower at some distance from the centre of the dam, is 
shown in Sketch No. 88. The head wall and sluices (see Sketch No. 94) is 
a somewhat cheaper method of passing the same discharge, but only permits 
water to be drawn from one, or at the most two levels, and can only be used 
when firm foundations exist at a shallow depth. 

The culvert with a central valve tower and open approach channel is exposed 
to fracture by settlement of the dam, and can only be considered as good 
design when the circumstances are such as to favour the construction of a 
masonry core wall. In such cases it is probably the cheapest solution of the 
problem ; since the valve tower forms part of, and is built with, the masonry 
core wall. 

The various positions of the valve tower produce a design which is well 
























































































































342 


CONTROL OF WATER 


suited for drawing' off the quantity of water usually delivered from the reservoir 
for use either in town supply or in irrigation, i.e. a daily volume equal to soth 
or itjoth °f tf> e content of the reservoir. 

When it is desirable to prevent silting by the rejection of all turbid water 
through an outlet at a low level (diversion channels being too expensive) the 
volumes of water to be dealt with are far larger. Broadly speaking, the problem 
is to reject, if necessary in one day, a quantity of water equal to a large fraction 
(one-third, one-half, or possibly even the whole) of the maximum daily flow 
that usually occurs in each year. This last may be considered as about one- 
sixth of the maximum flood (which occurs at intervals’of 20, or 30 years). In 



Section 



Sketch No. 94.—Head-wall Outlet. 

cases where the reservoir capacity is small compared with the average yearly 
run-off of the catchment area, it may amount to one-tenth, or to one-twentieth 
of the capacity of the reservoir. The outlet should, therefore, be large enough 
to discharge about ^th to ^th °f the total reservoir capacity even when the 
leseivoii is neaily empty, so that no marked ponding up of silty water need be 
permitted. For preliminary designs, the quantity rejected may be considered 
as that coiresponding to the bank stage of the stream draining the catchment 
aiea, and the effective head under which the orifices work may be taken as 
5, or 10 feet. Ihe final studies will of course take into account the silt content, 
and the regime of the natural stream. 

































































SCO URING B V SL UICES 


343 

The problem is not as yet fully understood, and the difficulties attending 
the preliminary investigations and the preparation of the final designs are very 
great. 

Considerations of cost prevent a valve tower being used for dealing with 
such large quantities of water, and the present solution usually consist of under¬ 
sluices of the type shown in Sketch No. 94. The great difficulty is that the 
system can hardly be adopted unless a firm rock foundation exists at a moderate 
depth. Typical examples are the Assouan masonry dam, and the Maladevi 
earth dam. 

Sketch No. 95 shows the present (1910) section of the Assouan dam, and 
No. 94 the methods used by Strange to connect a head-wall of similar section 
with an earthen bank. The design is costly, but enables the waste weir either to 
be shortened, or to be entirely dispensed with. All silt deposits are prevented, 
so that (correctly regarded) the comparative cost in relation to that of a valve 
tower is materially reduced. 



Sketch No. 95.—Assouan Dam and Repairs below Sluices. 

The sketch shows a typical section. On the average the repairs shown are some¬ 
what more bulky, and the stone facing is somewhat thicker than is usually the case. 
The rock downstream of the dam was cleared out until perfectly sound, and the excava¬ 
tion up to a level of 9'84 feet (3 m.) below the sluice bottom was filled in with 
rubble masonry in i c : 6 s mortar. Above this level the mortar was i c : 4 s . The 
cut stone facing is'usually 1'32 feet (o‘4 m.) thick, laid in i c :2 s mortar, and the 
bond stones are 2‘65 feet (o'8 metre) deep, and at the most exposed points are 
spaced 5*25 feet (i‘6 metre) centre to centre. The quantities of work are stated as 
about: 

47 cube yards masonry, and 19 square yards facing, per foot run of dam containing 
sluices. 

Very intense erosion is likely to occur in the escape channel, and for this 
reason alone a rock foundation must be considered almost indispensable. The 
various sketches of under-sluices (see p. 695) may be consulted for the details 
of protection against erosion, and the aprons put in at Assouan in 1901-3, are 
shown in Sketch No. 95. 

The design of the wall (see Section in Sketch No. 94) needs careful 
consideration, since, owing to the existence of the large sluice openings the 
unit pressures are likely to exceed the permissible values if the height much 




















344 CONTROL OF WATER 

exceeds 60 feet. For this reason, if for no other, rock foundations undei the 
wall form a necessary condition. 

According to the present Indian practice, such under, or scouring sluices, 
can usually pass off about one-seventh of the maximum flood ; and the le- 
mainder is dealt with by an escape weir, either drowned, or with a clear ovei- 
fa.ll. This indicates a method which is economically feasible ; and since the 
problem of silt deposit is forcibly brought before the notice of all Indian 
designers by the large number of old and abandoned silt-filled reservoirs now in 
existence, this capacity is probably the largest that is financially profitable. 
Any scouring sluice of a larger capacity is likely to prove too costly for the 
advantages reaped, except in unusually favourable circumstances. 

Silting of Reservoirs. —It is very hard to state general rules for this 
subject. Silt deposits can be readily removed in certain cases by means of a 
scouring gallery, such as is known in Spain as a “ desarenador.” 


• 7 - 3 ? I 



e- 46 ’sq. 


Plan of Working. Galley. 



The typical, and most successful example, is the Alicante reservoir. Sketch 
No. 96 shows the dimensions of this gallery, but the upper working gallery is 
copied from the arrangements existing at Elche. The method of working is 
very clearly described by Aymard (.Irrigations du Midi de PEspagne , pp. 145 and 
196). About every fourth year, when the deposits are well consolidated, as 
is ascertained by boring a hole through the wooden gate, the cross-beams a , a , 
are sawn through on both sides, leaving the gate supported only by the inclined 
struts. Workmen then enter the upper gallery, and cut away these struts by 
means of long chisels, and remove the beams and gate by hooks. The silt deposits 
in front of the gallery are then pierced and stirred up by long, iron-shod poles, 
worked by pulleys from the top of the dam. Once the flow is started, the deposits 
(which are usually about forty feet thick in front of the dam), are rapidly scoured 
out, the water initially standing about forty feet above the top of the silt deposits. 























































SCOURING GALLERIES 


345 

So far as can be gathered from the information given by Aymard and 
Willcocks (which is avowedly approximate only, since no surveys exist), the four 
years silt deposits represent about 3 to 4 per cent., and the water used to clear it 
away about 30 per cent, of the reservoir capacity. Such a result indicates very 
good working, and the proportions of the gallery are important; for in. the case 
of the Elche reservoir, where the gallery is of the same section throughout its 
length, the process is relatively so unsuccessful that the reservoir filled up in 
about fifty years ; while the Alicante reservoir is some 300 years old. Aymard 
gives the general slope of the Alicante bed as 43-, and the reservoir is narrow, 
being about 1000 feet wide as a maximum. 

It would consequently appear that this method is only applicable to 
reservoirs situated on steep sites ; and certain of the earlier Algerian reservoirs, 
the bed slopes of which appear to have been about 3^3, are now silted up, 
although provided with similar scouring galleries. I cannot, however, state 
that these galleries were well adapted to local circumstances (as the Alicante 
proportions were slavishly copied, and this, unless special investigations were 
made, would appear illogical), or carefully worked, as the records show that 
the dams themselves gave trouble by cracks and fissures during the whole 
history of the reservoirs. Under such circumstances, it is doubtful whether 
any engineer would feel justified in opening a scouring gallery which “works 
with a noise like cannon.” 

It is plain that these galleries are only'applicable where the reservoir can be 
completely emptied at more or less frequent intervals ; and that the bed of the 
reservoir must be steeper than would be deemed advantageous if storage 
capacity alone were considered. 

Thus, reservoirs which can be cleared of silt by a scouring gallery are by 
no means satisfactory from other points of view, since the cost of the dam per 
cube yard of water stored will obviously be comparatively large. 

Many large reservoirs exist in the Bombay Presidency, some of which are 
subject to silt deposits. In the earlier designs it was considered sufficient to 
allow about 10 per cent, extra capacity for silting. Later designs, however (the 
oldest British built reservoir dates from 1868), treat the matter more system¬ 
atically. The waste weir is supplemented by a set of powerful under-sluices, 
which pass away the silted water brought down by the early monsoon floods, 
and it is hoped that this method (if carefully applied) will suffice. Inspection 
of the large number of ancient silted reservoirs existing in India is not very 
encouraging. It may be anticipated that existing reservoirs (unless provided 
with very powerful under-sluices) will also slowly silt up ; although it is quite 
possible that the period necessary for silting to cause appreciable damage may 
be measured in centuries, rather than years. The final results will probably 
depend more on the quantity of water which can be passed to waste, 
than on the actual discharge capacity of the under-sluices. No amount 
of sluice capacity will prevent marked silting in those reservoirs which store 
water for two or more years, and are supplied by a catchment area the mini¬ 
mum annual flow of which is insufficient to fill them. 

The Nile reservoir at Assouan is worked on the principle of rejecting the 
silted water of the rising flood, and retaining only clearer after waters. The 
circumstances, however, are far more favourable than is usual in India. The 
Nile floods are so regular, and the system of up-river gauge reports so excellent, 
that it is. very rarely necessary for any silted water to be even temporarily 


CONTROL OF WATER 


346 

retained in the reservoir. While in Indian reservoirs, owing to uncertainty 
as to the future supply of water, it is frequently necessary to store heavily silted 
water. Also the Assouan under-sluices can pass off the flood discharge of the 
river at a mean velocity of about 20 feet per second, so that hardly any ponding 
up of silted water (and consequent deposition of silt) takes place. 

It would therefore appear that designs on similar lines will permit reservoirs 
to be kept clear of silt ; but the practical difficulties of sacrificing all the high 
flood water in reservoirs the capacity of which is any large fraction of the mean 
yield of the catchment area, are obvious. 

It must also be noted that the Assouan dam is founded on hard granite. 
Even under these extremely favourable circumstances, extensive and costly 
repairs have been found necessary below the under-sluices, and it is doubtful 
whether they will not have to be repeated at frequent intervals. (See Sketch 
No. 95.) 

Suggestions have been made for the mechanical removal of silt by dredging, 
the requisite power being obtained from turbines worked by the stored-up water 
and transmitted electrically. The principle is a good one, and it must be 
remembered that the power obtainable from a storage reservoir the main 
function of which is irrigation, will rarely be found of much value for manu¬ 
facturing purposes, owing to the variability both of the discharge, and of the 
available head of water. 

In the case where this electrical dredging was proposed, the local con¬ 
ditions were somewhat peculiar. As a general rule, where such an installation 
proves necessary, a more economical form of power would undoubtedly be 
steam, or oil engines, carried on the dredger itself. 

It will be seen that there is a certain relation between the ratio which the 
capacity of the reservoir bears to the mean annual flow of the catchment area, 
and the probability of damage by silt. 

Let us assume that a river (over the whole of the year) deposits in the form 
of silt o’5 per cent, of the volume of water entering the reservoir. 

Let us first consider a very unfavourable case, such as the Austin reservoir 
in Texas. Here the volume of the reservoir was - 4 ^th that of the mean annual 
flow, and the dam being of the overflow type, circumstances favoured the dis¬ 
position of silt. Under the above assumption the yearly silt deposit would be 
2u°n = ith of the volume of the reservoir. As a matter of fact, in seven years 
about 49 per cent, of the volume of the reservoir appears to have been silted 
up. 

A reservoir of 40 times the capacity would probably have caused the deposit 
of a greater proportion of the silt entering it. The deposit in seven years would 
theoretically have amounted to 7xo’5 = 3’5 per cent, of the volume of the 
reservoir, and in practice it might be expected to be at least iVty x 3'5 = I ’3 P er 
cent, say, and either figure is (comparatively speaking) small, although not very 
satisfactory. 

Consequently, an overflow dam, or, in fact, any dam without powerful under¬ 
sluices, is quite unsuited for a reservoir of which the capacity is so small a 
fraction of the mean annual flow as was the case in the Austin dam. The 
Hamiz and Habra dams are similarly defective. 

On the other hand, the average British town water supply reservoir holds 
about 33 to 50 per cent, of the mean flow ; and although the floods are turbid, it 
is doubtful whether the mean turbidity over the year amounts to even o’oi per 


RESERVOIR CAPACITY AND SILT 


347 

cent. However, let us assume that o'i per cent, is possible. The yearly 

deposit is at most o‘2 to 0*3 per cent, of the volume of the reservoir, and is pro¬ 

bably less than one-tenth of these figures. 

1 hus, an overflow dam, or a high level escape weir, is quite allowable in 
such cases. 

The general principles are evident. 

When the reservoir volume is small in comparison with the mean annual 
flow (or rather, with the yearly volume of silt carried by the river), the dam 
must be of the Assouan type, i.e. provided with powerful under-sluices. These 
must be systematically employed during the high water season to pass off 
heavily silted water, and to scour out deposits. Later on, the clearer waters 

can be retained. In fact, we should endeavour to store what is mostly ground 

water flow, coming down after the flood season is finished. 

1 he process is not difficult where the volume of the reservoir is ^th or ^th of 
the mean annual run-off of a fairly permanent river, such as occurs in tolerably 
damp climates. Difficulties begin when the volume is one-tenth, or one-fifth of 
the mean annual flow of a variable river. Even in a fairly moist continental 
climate, the minimum annual flow may be only about two-fifths of the mean. 
In such a year, any error in judgment might entail starting the dry season with 
the reservoir only partially filled ; and in a dry continental climate matters are 
even more difficult. The correct procedure, nevertheless, is plain. Systematic 
rain-fall observations and gaugings must be carried out during the construction 
of the reservoir. It should then be possible to estimate the quantity of rain-fall 
falling towards the end of the rainy season that will certainly produce enough 
run-off to fill the reservoir, and to determine the relation that this bears to the 
minimum yearly rain-fall. 

Thus, assume a case where the flow of the stream usually ceases in October, 
and let it be found (by actual observation) that 4 inches of rain falling in August 
or in September, is sufficient to fill the reservoir, and that the minimum fall 
between May and October (which is assumed as the flood season) is 12 inches. 
Then it will be plain that if the under-sluices are closed each year when 8 
inches of rain have fallen, it is extremely improbable that the reservoir will not 
fill, and the longer the records are maintained, the more closely the limit can 
be fixed. A study of the ground water storage on the methods laid down by 
Vermeule should be extremely useful in such cases. The important matter is 
that the designer should state his principles, and should definitely order the 
required observations to be made, so that the records may be available when 
the question becomes acute. 

Thus, in all cases where the flow of the driest year can be relied upon to 
fill the reservoir, silt deposits can be materially diminished, or can possibly 
be entirely prevented if the under-sluices are sufficiently powerful. At present, 
the experience which would permit any definite rule being given, does not exist. 
However, this is not very material, as a preliminary stanching of the reservoir 
bed by silt deposits is actually advantageous, since it will minimise leakage. 

The general principles both of design and of observations are very concisely 
stated by Wilcocks {Nile Reservoir Dam at Assouan), as follows : 

“The obstruction to the flood was not to be greater than that of a 
cataract like Semne.” 

The natural stream bed must be studied, and if any unusually contracted 


CONTROL OF WATER 


348 

portions exist, above which silt deposits are not produced, the area of the stream 
channel in these places can be taken as a basis for the design of the under¬ 
sluices. In other cases it appears best to assume an area for the under-sluices, 
to calculate the heading up necessary in order to pass the greatest flood through 
this area, correcting for the velocity of approach indicated by the cross-sections 
of the reservoir, and then to examine the possibilities of silt deposit in the pond 
formed above the dam. It must always be remembered that a certain amount 
of silt deposit may be expected in the early years of the life of the reservoir, 
which is harmless unless it bears too large a ratio to the reservoir capacity. 

Permeability of Earthen Dams. —All earth dams are saturated by 
water up to a plane sloping more or less irregularly away from the water surface. 
The most exhaustive series of observations on the subject are those made by 
the Bombay Irrigation Department (.Experiments on the Saturation of High 
Embankments). The earlier and less complete observations on the Croton 
(N.Y.) watershed dams are most useful, as showing that differences in the 
methods of construction and climatic conditions have little effect on the general 
results. 

The slope of the saturation plane, measured over a short distance, is very 
irregular, is obviously greatly influenced by accidental circumstances, and 
fluctuates as the water in the reservoir rises and falls. The average slope 
measured from the water surface to the saturation level at a point below the 
downstream toe of the dam, is fairly constant, and its mean value for seven 
dams (which are practically of uniform material all through) is o'32, the maxi¬ 
mum being 0*46, and the minimum (about which there is some doubt) o'12. 

In dams composed of thick clay cores with more permeable outer casings, 
the slope in the clay is about o'32 to 0*35, and in the casings 0H4 to o'i6. In 
three dams which are very well drained, and are composed of clayey material, 
the value is o'2o, o'22, and 0*28. 

The figures for the Croton dams are almost identical, ranging from 0*14 to 
0*40 ; the higher figure indicating the very best construction ; while the mean 
is about o'23, which agrees very fairly with the mean for the whole section of the 
Bombay dams in which the hearting only is of clay. 

The Croton dams have masonry core walls, and although the observation 
pipes were not spaced sufficiently closely to allow of a definite statement being 
made, the engineers who made the observations (see Engineering News , 
Nov. 28, 1901) considered that the core wall produced a drop of 10 to 12 feet in 
the plane of saturation. 

My own observations on a well made British dam indicate slopes of 0*30 to 
o‘37, and that a good puddle wall produces a drop of about 20 to 30 feet. The 
figures are hardly comparable with the above-mentioned Indian and American 
results, as the dam was newly made, and the Indian observations show that 
steeper slopes may be expected in older dams. 

The banks of the Punjab irrigation canals are very badly made when com¬ 
pared with the work required in the case of high dams. Slopes as flat as o'oy 
and 0'o9 occur. Under these circumstances a bank in which the slope of the 
line joining the full supply level at the water face, and the outer toe, is steeper 
than 0M5, or o'i6, usually gives trouble by seepage on the outer face, which 
(if the soil is of a bad quality originally) may cause a slip. (See Sketch 
No. 217.) 

The engineers reporting on the Croton dams make certain deductions from 


STABILITY OF DAMS 349 

their observations regarding the stability of earth dams. I have submitted their 
deductions to systematic small scale tests, and believe that they are unwarranted. 
So far as my observations go, an earth bank is perfectly stable under percolation 
(however great), provided that the water issuing from the bank does not carry 
away more particles of the earth than it deposits in the dam. The question of 
the stability of a dam is therefore intimately connected with the silt content of 
the water in the reservoir. Putting aside the extreme, and unpractical cases 
where the leakage is so great as to appreciably reduce the volume, stored in the 
reservoir, the problem is merely to dispose of the leakage in such a manner that 
the finer particles are not reduced in number. If therefore, the water entering 
the dam contains much silt, the reversed filter may permit the more minute 
particles to pass away, provided that a larger volume of similar particles 
is deposited inside the dam. If the water is very clear, even the slightest 
removal of fine particles may finally cause a breach. 

The stability of barrages or weirs such as are found on the Nile and Punjab 
rivers, is only explicable by the deposition of silt above the barrage compensating 
for the removal of finer particles below. The application of such principles to 
dams may be considered to be risky. It will, however, be plain that if the finest 
particles can be retained, the dam will lie stable whether the water is clear or 
silted. Thus, a reversed filter properly graded so as to retain the finest particles, 
will render very intense percolation harmless. 

In this connection the very interesting experiments of Saville (Engineering 
News , Dec. 24, 1908) may be referred to. Here an experimental dam about 11 
feet high and 6 feet in length was constructed, and its permeability and satura¬ 
tion plane were determined. The figures are not quoted, as they refer to a dam 
deposited by the hydraulic-fill method, but the whole investigation and the 
mechanical analysis of the material form a model piece of work. Similar trials 
should certainly be made by any engineer contemplating the construction of a 
hydraulic-fill dam, and would also afford valuable information even when the 
ordinary methods of dam construction are adopted, since the results thus 
obtained, combined with a survey of the natural ground water levels, permit the 
leakage through and the stability of the proposed dam to be scientifically 
determined. 

Hydraulic-fill Dams. —Hydraulic-fill dams are earthen dams in which 
the earth is deposited hydraulically. 

Water is pumped or delivered from reservoirs, at a high pressure, through 
a nozzle against a bed of earthy material situated at a higher level than the site 
of the proposed dam. The water is thus charged with a mixture of earth, 
stones and clay, and is conducted by flumes, or pipes, to the dam site, where it 
is allowed to deposit its charge of material, and escape. 

The principle of the method is plain, but the details of execution require 
consideration. 

In the first place, the earth used should be somewhat carefully selected. 
What is really required is a mixture of particles of all sizes, ranging from the 
finest clay up to rocks which can barely be moved by the water. Clay alone 
cannot be utilised, and earth without any admixture of stones is liable to give 
trouble by slipping. 

It is also stated that when the clay exceeds 50 per cent, of the whole volume, 
trouble is likely to occur by slips, even when stones and rock form almost the 
whole of the remaining volume. 


9-ffll Wl 


35° 


CONTROL OF WATER 



Angular rock is detrimental, 
since it is not easily moved by 
the water, and when moved is 
liable to injure the flumes. 

The process evidently very 
closely imitates the manner in 
which beds of clay and sand are 
deposited by rivers ; and, if well 
carried out, mayibe relied upon to 
produce a good bank. Indeed, the 
chemical composition and phys¬ 
ical properties of the clay portion 
of the deposit markedly resemble 
those of good puddle clay. 

As we wish to obtain a 
section of material in grades re¬ 
sembling that of an Indian earth 
dam with a puddle hearting, it 
is plain that the loaded water 
I should be delivered at the edges 
^ of the bank, so that it may there 
deposit the heavier material, 
3 forming a pitching, or rip-rap 
(see Sketch No. 97). The water 
should be drawn off near the 
centre of the dam by a sub- 
stantial tower, so that clayey 
o particles may be deposited at the 
^ place where a puddle hearting 
would usually be situated, 
w The method has been prin¬ 
ce cipally employed in dry climates. 

Certain phenomena in hydraulic- 
fill dams now under construction 
in climates where rain is some¬ 
what more frequent, lead me to 
believe that the method will 
either prove impracticable in a 
moist climate, or will only be 
possible with material contain¬ 
ing a somewhat smaller pro¬ 
portion of clay than that stated 
above. But it is evident that 
each material should be separ¬ 
ately considered, and all that 
can be definitely said is that the 
more moist the climate, the 
smaller the proportion of clayey 
or saturable material that can 
easily be dealt with. 




























HYDRA ULIC FILL-DAMS 


35* 


The danger of slipping being greatest just after deposit (while excess water 
is oozing from the bank) it is plain that there is a certain element of luck, in that 
the accidental coincidence of a spell of wet weather with the delivery of material 
containing a larger proportion of clay, may lead to a partial slip. 

It is but fair to the process to state that bad failures have only occurred 
when the method has been recklessly applied (the fill being deposited on im¬ 
properly prepared foundations, with inadequate provision ' for drainage). It 
would appear that if systematic drainage were universally adopted, after the 
manner provided for in Indian practice, the proportion of clay at present found 
advantageous might be greatly exceeded. 

I may here refer to the porous conduit adopted in the Crane Valley dam, 
and described by Schuyler (Trans. Am. Soc of C.E., vol. 58, p. 218), and would 
remark that the minor accident that occurred was plainly not due to the conduit, 
which appears to have done its work admirably. 

The real advantage of a hydraulic-fill dam is its low cost per cubic yard, 
when the total quantity of earthwork is large. 

The construction of such a dam requires certain somewhat unusual local 
conditions, and a comparatively large investment in plant of a rather special 
type. Thus, its adoption is unlikely, except in countries where hydraulic 
mining is practised, or in the case of large dams where a certain amount of 
expenditure in preliminary studies is permissible. Under such circumstances, 
I believe that the method deserves consideration, and if the problem of obtain¬ 
ing good drainage of the base of the dam is properly dealt with, and the available 
material contains a sufficient proportion of sand, gravel and stones (in order to 
secure stable slopes), with enough clay to form an impermeable core, the dam 
should not only be cheaply constructed, but it would appear that a more satis¬ 
factory result can be secured than by any other method. 

According to Schuyler, the earth deposited in the dam is packed into about 
90 per cent, of the volume that it occupied before being washed down, and only 
the very best rolling and after-consolidation has secured equally good results. 

If the method is considered sufficiently infallible to permit of the total 
neglect of all ordinary drainage and preparation of foundations, the inevitable 
penalties of bad work can be anticipated. 

Very few reliable figures as to the power required can be given at present. 

In the Lake Francis dam (ut supra , p. 212), the percentage of ,solids 
deposited varied from 6 to 48 per cent, and averaged 17 per cent, of the volume 
of water pumped. About 5 per cent, of the solids washed down were not 
deposited in the dam. 

The friction in the pipes, or flumes, varies so greatly with the material used 
that no rules can be given. In some cases, a 6 per cent, grade is found to be 
small, while in others 2, or 3 feet per 1000 suffices. 

Similarly, the best shape of the flumes appears to be entirely dependent 
upon the properties of the material. 

It may also be noted, that where stable material is deficient, good results 
have been obtained by placing brushwood in the slopes. Where sand is in 
excess, and tends to form layers across the bank, stirring with spades or poles 
is advisable. 

Rock-fill Dams .—In rock-fill dams the body of the dam is constructed 
of loose rock, and impermeability is secured by a core wall and cut off of earth, 
clay, steel plates, concrete, masonry, or other material. Sketch No. 98 shows a 


mi. 42 ' usually not above 


52 


CONTROL OF WATER 



e 


I 

<0 


• <0 

t 

1 I 

Q 




' o 
o 

p< 


ts 

c§ 


^3 

I 

<0 

A) 

•s 

.^f. 


00 

cr. 

6 

£ 

w 

u 

H 

W 

W 

m 


typical section, and also illus¬ 
trates the fact that an imper¬ 
meable core wall cannot be 
dispensed with. 

Schuyler (Reservoirs for Irri¬ 
gation , etc.) enumerates seven 
types of core wall. Study of 
the examples leads me to be¬ 
lieve that, as a rule, the method 
of constructing the rock work is 
such that settlements as large 
as (and in the case of bad work 
many times larger than) those 
which occur in earthen dams 
take place in the rock fill when 
water is first admitted into the 
reservoir. Thus, rupture of the 
impermeable coating has to be 
guarded against. In the success¬ 
ful examples the impermeable 
coating is either of earth or clay, 
and is consequently elastic, and 
is of considerable thickness ; or 
else it consists of a vertical wall 
of steel or reinforced concrete of 
sufficient strength to resist the 
stresses produced by settlement. 
Success has also attended the 
use of thin masonry, concrete, or 
wooden diaphragms, but only 
when these are laid against, or 
are buried in, hand laid rubble 
walls of considerable thickness. 

The rock-fill type of dam is 
at present somewhat discredited, 
owing to numerous failures hav¬ 
ing occurred. Such failures, 
however, are usually clearly 
traceable to bad construction, 
and are most frequently caused 
by the cut-off trench not being 
taken down to a sufficient depth. 
Indeed, in most cases, no other 
type of dam would have been 
expected to stand such treatment, 
and the rock-fill dam “made a 
better show” than could have 
appeared possible. 

It may consequently be stated 
that the type is serviceable, and 

























ROCK-FILL DAMS 


353 

appears admirably adapted to cases where the foundation is hard, but perme¬ 
able, eg. of thick beds of deeply fissured rock. 

Percolation must then occur, and so long as it is not sufficient to remove 
either the foundation rock, or the rockwork of the dam, the dam will stand 
where an earth dam would be eroded, or where a masonry structure would be 
destroyed by upward pressure. 

The resemblance between such dams as the typical rock-fill dam (see 
Sketch No. 98), and the Indian composite dam with a dry stone toe, is obvious. 
Owing to the more careful methods of construction employed in India, the 
Indian type (height for height) is less bulky. 

The sketches of the Escondido and Otay dams are typical of good American 
practice, although the Otay dam has not yet sustained the full depth of 
water. 



The Escondido dam (Sketch No. 99) is founded on partly disintegrated 
granite, containing large boulders. The cut-off trench at the upper toe is from 
3 to 12 feet deep, and is filled with 5 feet thick rubble masonry in Portland 
cement. The facing is composed of two layers of redwood planks, each three 
inches thick, for depths of 50 to 76 feet below top water level; 2 inches thick 
between 25 feet and 5° feet below 5 and I2 inch thick when less than 25 feet 
below. The planks are spiked to 5x6 inch vertical timbers, 5 feet 4 inches 
apart, embedded in the hand-laid dry rubble facing wall so as to project 
2 inches beyond it. This 2 inches of space was filled as the planks were laid 
with rammed Portland cement concrete. The dry rubble wall was 15 feet 

thick at the bottom, and 5 fe e t thick at the top. 

If we assume that the cut-off trench is carried down to a sufficient depth, 
and regard the plank facing as a temporary expedient which is to be leplaced 

2 3 




















CONTROL OF WATER 


354 

by permanent work later on (as local conditions permit), the design may be 
considered to be first class, and to be well adapted to the locality. 

It is somewhat difficult to criticise the Otay dam (Sketch No. ioo), as, judg¬ 
ing from the foundation, either a masonry, or an earth dam, could have been 
erected. I shall therefore merely describe the steel core wall. This is of three 
steel plates, each 0*33 inch thick for the first 15 feet; then j inch thick to 5° 
feet high, getting thinner towards the top. 



The plates were riveted together, and were caulked on the water face side. 
They were then brushed over on each side with hot asphalt of a somewhat 
liquid consistency. On this was placed burlap, which held the soft asphalte in 
place. The whole was then coated with a harder grade of asphalte, and was 
then enclosed in a wall of “rubble masonry in Portland cement concrete” {i.e. 
probably concrete with “plums”), 2 feet in thickness, the plate lying in the 
centre. 

The shuttering of the wall (made of 1 inch boards on 2 inch by 6 inch 



































ROCK-FILL DAMS 


355 

posts) was left in place, and the rock fill was built against it on each 
side. 

The success or failure obviously depends upon the manner in which the rock- 
work was laid, and since the dam has not yet filled, the case remains unproved. 

The details of the steel plating and its treatment are plainly good, although 
they are capable of improvement if expense has not to be considered. 


CHAPTER VIII.— (Section B) 
MASONRY DAMS 


Masonry Dams. —Gravity and arch dams. 

Distribution of Stresses in a Masonry Dam. —Deduction of the “ Middle Third ” 
rule—General theory—Application to the calculation of the stresses on a horizontal 
section of a dam. 

Working Units. —Specific gravity of the masonry—Theoretical condition for the 
minimum section—Preliminary design of the minimum section—Rectangular and 
parabolic topped dams—Batters and overhangs—Alteration of the thickness when 
these are neglected—Preliminary estimation of the total volume of the dam—Calcula- 
tion of the pressures from the preliminary design—Example. 

High Dams. —Limiting values of the pressures—Examples— Shearing Stresses. 

Very High Dams. —Approximate equations—Accurate equation. 

Further Theory of Masonry Dams. 

Atcherley’s Theory —General conditions—Diagram of stresses on a horizontal section 
—Parabolic distribution of shears on a horizontal section—Diagram of stresses on a 
vertical section according to Atcherley’s theory—Uniform distribution of horizontal 
shears—Criticism. 

Experimental Results. —Tension near water face toe of dam—Construction at and 
near the water face toe—Values of the tension—Rules for dam design—Algebraic 
investigation of Atcherley’s theory—Tail thickening—General conclusions—Effect 
of earth pressures. 

Fissures in Dams. —General theory—Case of a weak dam—Case where no tension 
exists in the cracked masonry—Case where the stress vanishes at a point nearer to 
the water face than the inner end of the crack—Case where the inner end of the 
crack is exposed to tension—Practical considerations—Permissible length of a crack 
—Example. 

Failures of Masonry Dams. 

Puentes Dam. —Failure by Percolation. 

Bouzey Dam. —Failure by uplifting pressures due to cracks. 

Austin Dam. —Failure by horizontal shear. 

Abnormal Loads on Dams. 


Practical Construction of Dams — Weak points—Rubble masonry versus concrete 
with plums—Portland cement versus hydraulic lime—Water-tightness—Intze’s 
designs—Hollow concrete facings—Jack arch facings—Rich concrete and pure 
cement facings — Pointing — Dry versus wet concrete—Lias lime concrete—“Shear¬ 
ing” and “compressive” strength—Disposition of material with regard to shearing 
stresses. 

Temperature Stresses in Dams. —Theory—Coefficient of expansion of concrete— 
Practical observations—American observations—Coefficient of expansion of large 
masses of masonry—Internal temperature variations. 

Form of the Downstream Face of Overflow Dams. —Nappe boundaries—Tail 
portion of the curve—Practical considerations—Flashboards. 

Theory of Curved Dams.— Approximate theory — Wade’s practice — Values of the 
compressive stress—Bellet’s corrections for the slope of the dam faces—Combined 

X 

theory of gravity and arch stresses—Values of the ratio- Dome-shaped dams. 


Arch and Buttress Dams. 


35 6 


NOTATION 


357 


Reinforced Concrete Dams. —General principles'—Bending moments and shearing 
forces—Preliminary design of reinforced concrete beam—Graphic diagram of 
forces. 

Foundations. —Core walls—Flooring of the dam. 

Earth Pressures on Retaining Walls. —Approximate theory—Graphical determina¬ 
tion of the maximum pressure—Practical details. 


SYMBOLS 


For suffix notation, see page 365. 

a, is the distance in feet of the mass centre of the area A, from the water face of the 
dam. 

A, is the area in square feet of the cross-section of the dam above the level x. 
b n , is the area in square feet of the cross-section of the dam between the levels 
and x n . 

e, is the vertical “ tail ” thickness of the dam in feet (see p. 380). 

C (see p. 365). 

d , is used for the depth in feet below top water level when investigating Atcherley’s 
theory (see p. 381). 

E (see p. 365). ^2 

H, is the horizontal force acting on the area A. H = — in the working units. 

K (see p. 381). 
k (see p. 365). 

/, is a suffix (see p. 373). 
ni (see p. 364). 

M,„ is the moment of A n about the water face end of t n -\ while, 

N m , is the moment of A„ about the water face end of t n ; thus, 

N n _ x , is the moment of A w _ x , about the water face end of / M _ x . (See pp. 358 and 368.) 
n, when a suffix denotes the section actually considered. 

ns= j “7 ( See P ' 385) * 

/, is the vertical pressure at the water face of the section t. For unit used, see p. 362. 

P (see p. 385). 
p e (see p. 363). 
p 0 (see p. 373). 
p f (see p. 383). 

q, is the vertical pressure at the downstream face of t. See under p, for units, and for 

q e , q 0 , q', and Q. . 

r n , is the batter, i.e. the distance in feet which the water face end of t n is shifted towards 
the water relative to the water face of t n _ v 

r, is used for the vertical pressure at any point distant x , from the water face of t. 

(See p. 360.) 

S, and S x , are used for horizontal shears in Atcherley’s investigation. (See p. 3 ^°-) 

s, is used for the water pressure existing in a crack when investigating fissures, i.e. from 

page 383 onwards. 

/, is the horizontal thickness of a dam at a level x, or d (p. 381), below the highest water 
level. 

u (see p. 367). 

V, is the vertical force acting on the section t. V = Ap. 

W (see p. 380). 

x, is used for the depth of the section t, below top water level, x, is also used as a 
running co-ordinate on page 360 and 380. 

x, and y (see p. 381). 

y, is the distance of the point where the resultant of H, and V cuts the section /, from 

the water face end of /. y, is also used as a running co-ordinate on page 3 ^°- 

z, is the length of the crack in feet. 

X = JL 

t 

0 , is the angle between the downstream face of the dam and the vertical, 
p, is the specific gravity of the masonry. 


35 ^ 


CONTROL OF WATER 

SUMMARY OF EQUATIONS 


X 

Vertical pressures. — r—p + {(j[ —p) -y V = A p 



2 V , 
t 1 

ft'-o 

M 

X 3 


a =A 

^6pA 



o> 

II 

1 N 
H < 

ft-) 


Approximate Section of the Dam.— 


x° 


X 3 


X 


Eh /h \ 3 


t- 


kJ p (x* — i 6 A 4 + 4 pAi 3 ) \V (.v 4 + E/z 4 ) \ P 2 v/> 


(iy 


A i_ ^ 4 -i6A 4 + A 1 g 
4 P 

Ah = A 


N m _i = An-^n-i* M m = N m _j + g{^n ^] 2 + tn-\tn + At 2 — ^n(Ai-i + 2 G)} — A n a f n y~A n (a n r n ). 
n =M w + A/« = N w ._ 1 + An—+ 7 '! A—Y + 4i-i4* + G* + r n (t n 4- 2 t n _P)f — A n a n . 


N 


Batter Equations .— 


«"=- - 2 r « 

__ 2 Ant n — 6M m 

6A„_j + ( 2 t n _ l + t n )h 

High Dams .— 

Maximum pressure — q sec 2 6 , or p t sec 2 6 

= 3 ' 2 $x approximately 
= 203.* lbs. per square inch. 
Maximum shear — ioi lbs. per square inch. 

Very High Dams .— 

— (s-sn 

t = A l 2 P e qo 

lo 

Fissures .— 

(l ^ )2=r ^{ I ' I2 ( 3w + X )"^ X (4~ x )} 

The other cases are not summarised, since they but rarely occur. 


Masonry Dams. —Masonry dams for retaining water are divided into two 
classes : 

(a) Gravity dams, in which the water pressures are resisted by forces brought 
into action by the weight of the dam only. 

(h) Arched dams, in which the dam forms an arch, and resists the water 
pressures in the same manner as an arch sustains the load which is placed 
upon it. 















FUNDAMENTAL ASSUMPTIONS 359 

As a matter of fact, all arched dams act partly as gravity dams, and most 
gravity dams are curved in plan, and are therefore subject, in a greater or 
smaller degree, to arch stresses. 

As a preliminary to the theoretical investigation of the stresses in either 
type of dam, it is necessary to investigate the internal stresses produced in any 
section of a gravity dam. 

Distribution of Pressures in a Masonry Dam. —Suppose a force R, 
to act across a section of unit breadth, perpendicular to the plane of the paper, 
represented by the line ED, and for the sake of simplicity drawn as horizontal. 
Let V, and H, be the vertical and horizontal components of R {i.e. perpendicular 
and parallel to ED), and let the line of action of R, cut ED, in P. 

Let ED = t, and EP — y. 

The ordinary rules of statics tell us that reactions exist at every point in ED, 
which may be resolved into vertical pressures and horizontal shears. 



We also know that the resultant of the shears is equal and opposite to H, 
and that the resultant of the pressures is equal and opposite to V. 

Further than this our knowledge does not extend, and any approximate 
solutions, as yet theoretically obtained, are of somewhat doubtful validity, 
except under such restrictions that the results are useless for practical purposes. 

It is therefore necessary to make some assumption. The assumption 
selected by engineers finally leads to the result that the pressures vary uniformly 
across the section ED, as shown by the trapezoidal stress diagram. (See 
Sketch No. 102.) 

This is a simple assumption, and is one which is familiar to engineers, but 
it cartnot be said to have any very strong theoretical foundation. Its real 
claim to respect lies in the number of satisfactory dams calculated according to 
its results, and the less numerous unsatisfactory ones which must be considered 
unsafe when the results of the assumption are applied. 

Of late years a certain amount of experimental evidence has been accumul- 

































































360 control of water 

ated, which indicates that the assumption leads to smaller stresses than are 
found experimentally. 

Let therefore : 

q, be the pressure in lbs. per square foot at D, 
ft, be the pressure in lbs. per square foot at E. 

Then, at any point Q, where EQ = x, the pressure is : 

. < i • • . i > ., • 'p j / y ~ .' | i 

r=ft+{q~ft)] ' ■ 


and we can at once determine/, and q, as follows : 

(i) The algebraic sum of the pressures is equal to V, or : 

V = (P +?) ( 2 



Sketch No. 102.—Diagram showing Vertical Pressures on a Horizontal 

Section of a Dam. 


(ii) The moment of the pressures about any point is equal to the moment of 
V, about that point : 

Or, taking moments about E ;— 

V y=P;+to-P)j=£(P+tt) 

Hence, we have ; 



an d is evidently the mean value of the pressure if distributed uniformly over 
the area ED. 















361 


VERTICAL PRESSURES 


Now, consider P, to move along the line ED, from E, to D, we have ; 

• • » { 

Remarks — 

P, coincides with E. /, is a pressure, but <7, is a 
tension. 

P, enters the middle third, q, is zero, but is changing 
from a tension to a pressure. 

P, is at the mid point of ED. Both /, and q, are 
pressures, and p = q. 

P, leaves the middle third, p , is zero, and is changing 
from a pressure to a tension. 

P, coincides with D. /, is a tension, q, is a pressure. 

In all investigations connected with dams the symbol/, is employed to 
denote the pressure at the water face, and q, to denote the pressure at the 
downstream face of the dam. 

It is therefore quite evident that the only positions of the point P, where 
both /, and q, are positive and no part of the section ED, is exposed to tension, 
are those that lie between : 

y 1 y 2 . 

- = -, and That is to say, P, is inside the middle third of the section. 

1 3 t 3 

We thus obtain the usual “ Middle Third Rule ” ; 

“ In order to secure that no tension occurs at any point of a rectangular 
section, it is requisite that the line of action of the resultant pressure on 
that section should fall within the middle third of the section.” 

Although it is not usually stated, the component of the resultant force in the 
plane of the section should be parallel to one of the sides of the section. 

General Theory. —This question does not frequently occur in practice, but 
let us assume that ED, no longer represents a rectangular section, but a section 
the area of which is represented by A. Let, the mass centre of this area be 
distant d , from E, and the moment of inertia about a line through the mass 
centre and perpendicular to the projection of H on the plane of ED, be A r 2 . 

We at once have the following equations : 


y 

t 

P 

Q 

r\ 

4 v 

2V 

U 

/ 

t 

1 

2V 

t 

0 

1 

V 

V 

2 

t 

/ 

2 


2V 

J 

0 

t 

T _ 

2V 

4 v 

1 

t 

t 


V =pA~{P~q ) and Vy=pSd-(p-q) 


Put ~ = 


,=m; and we have : 

L 


V 




m 2 -\-n 2 \ m 2 -\-n 2 _Vy 


A'- 7T~)+t 


?l 


Ad 


and these equations can be treated just as the simpler equations for a rect¬ 
angular section were ; and are open to similar theoretical objections. 

Application to the Calculation of the Stresses on a Horizontal Section of a 
Dam. —In this case, if we consider ED, to be a horizontal section of a dam, say 
1 foot broad for simplicity, we see that: 





CONTROL OF WATER 


362 

V, is the weight of the masonry above ED, and is equal to the area of cross- 
section of the dam above ED x the weight of 1 cube foot of masonry. 

H, is the horizontal thrust of the water on the water face of the dam above 
ED, and, for the present, we neglect all other forces, such as the vertical com¬ 
ponent of the water pressure that may exist owing either to the water face of 
the dam not being vertical, or to cracks in the masonry. So also, such 
matters as ice pressure, and wave action, etc. are excluded. 

Let us take as the unit of weight the weight of one cube foot of water (/. e. 
62*5 lbs. approx.). 



Then, if p be the specific gravity of the masonry of the dam, one cube foot 
of masonry weighs p of these units. 

In actual piactice, p varies from i"8 (112 lbs. per cube foot), or perhaps a 
little less, up to 2-5 (156 lbs. per cube foot), or perhaps a little more. The 
lower figure indicates materials unsuitable for dam construction, and calling for 
special precautions. The higher figure indicates very good materials, and very 
careful workmanship. 

In preliminary studies, p — 2 25 (140 6 lbs. per cube foot) is a fair value to 
assume. 



























































PRELIMINARY THEORY 


363 


Now, (Sketch No. 103) let A, be the area of the dam section above EF. 
Then V=Ap is the weight of the masonry above EF. Also let the mass centre 
of this masonry lie at a horizontal distance d, from E, which is assumed to be 
the water face of the dam. 


Now, if x, be the depth of E, below the maximum water level in the 
reservoir : 



x 

and H,acts^ vertically above E. 


Hence, referring to the figure, we easily see that R, the resultant of H and 
V, cuts EF at P, where EP=j/ } and : 


_ . x H x 3 

J '~ a + 3V~ a + fyA 

Hence, if /, be given, /, and £, can be calculated. 

Now, it is evident that economy in material is best secured if the dam be so 
designed that/, and q, are always, and only just, positive. Hence, we see that 


2 1 

y = — So that 
o 


1= O, q = 2 ^- 


Next, consider the reservoir as empty down to E. Then H=o. Then, 


t 

if a= 

O 7 

3 


P e ~^~- and q e — o 


where / e , and y e , represent, the values of/, and q, when the reservoir is empty. 


Now ,y = a -\-^——. Hence, we get: 


*•3 


2pA 


as the value of the minimum thickness of the dam that is consistent with the 
condition that no vertical tensions shall exist across the horizontal section EF. 

It is plain that cases can be conceived in which this condition would not 
suffice to produce a satisfactory dam section, and (see p. 375) it is probable that 
a high dam designed solely in accordance with this condition would fail either 
by shearing near its base, or by horizontal tension across vertical sections. 
Nevertheless, under practical conditions a dam of which the horizontal thickness 
at each vertical depth is "calculated by this rule will be found to form a very 
close approach to the final design, and it is therefore advisable to discuss the 
methods of laying out such a section before entering into the modifications of 
the theory. The design of a dam from these conditions is evidently a matter 
of trial and error. Such methods are laborious, and if once introduced an error 
will be carried forward, and will affect all the later work. It is consequently 
advisable to sketch out a preliminary design by a less rigid plan, and to use the 
exact equations for checking and modifying this design only. 

Prof. Kreuter ( P.I.C.E ., vol. 115, p. 63) has shown how a section, theoretically 
exact in form, can be laid down. In practical work, it will save time to sketch 
out such a section, and afterwards to introduce any modifications that practical 
conditions require. 




CONTROL OF WATER 


364 

Let ABCG, (Sketch No. 103, Figs. 2-4) be the upper portion of the dam, 
which may either be rectangular (Fig. 2), or shaped to an overfall form (Fig. 3). 
In cases where the dam carries arches for a roadway the pressure produced by 
the weight of the arches and piers must be combined with the load due to the 
visible section of the dam. 

Let t 0 , be the width of the section CG. 

Then, if h, be the height of this first section, and p the specific gravity of the 
masonry of the dam : 

We have, taking moments about the end of a 0 (Fig. 4), when the line of 
pressure falls at the end of the middle third, for a rectangular top : 

7 * to ^ 
p lf °6~ 6 

or: h — to^p 

and, for a parabolic top : h = t 0 -- 

where in each case h , and t 0 , represent the height and bottom width of this first 

section. And, as a general rule, if the resultant of all vertical loads above the 

line CG, be V 0 — npt 0 h say, and act at a distance a 0 , from the point G, where 

a 0 — mt 0 (Fig. 4) : then, taking moments about the end of a 0 ; 

/ 2 \ - 

7 ipt^h or, h — toLnp (4 — 6;/z). 

Next, consider a section below this, cut off at a depth 2 h, and assume the 
intermediate portion of the dam to be trapezoidal. 

The width t lt necessary to ensure that the centre of pressure lies within the 
middle third, both when the reservoir is full, and empty, is obtained as 
follows : 

In the case of a rectangular top : 

The total weight is, pht 0 -\-ph — =-p ^ (3/0 + /1), and by hypothesis its mass 

centre lies at ~ from the water face. Thus, its moment about the other tri- 
3 

section of / l3 is : 

P ~ ( 34 + 4 ) “ 

and this is equal to the overturning moment of the water pressure. 

Therefore, pt 1 (st 0 +t 1 ) = S/i 2 
Hence, since /i 2 = pt 0 2 , we have : 

4 2 + 344 —S/ 0 2 =o or, fi — vyt 0 , 

k 2 

and the total area to the depth 2 h, is A! = 2'35 —z_. And r i} the batter of the 

V p 

water face required to cause the mass centre to be at a distance —, from the end 

3 

of A, is given by : 

/>- + />('-. p i- n) 

2 \ 2 3 2 3 / 2 ' 3 / 

_ 24 (4-24,) 

1 84 +/, ~ 0054 


which gives : 





KREUTER'S EQUATIONS 


365 


Thus, the top portion of the dam should overhang slightly towards the water. 
This is known to be undesirable, and in practice the thickness /, must be slightly 
in excess of 17 1 0 . 

11 the top ot the dam is parabolic, the overhang is not required, for : 
r Proceeding on similar lines : 


A = 2*1 1 0 


2 

Af= 2 *o8^ 

v p 


and, 




= 0-04/0 


6^1 + 36 to 

I he upper portion of the dam being thus determined, let /, be the thickness 
of the dam at a depth x, below the highest water level, and A the total area of 
the cross-section to that depth. Sketch No. 104. 

Then, reasoning just as before, we have : 


Hence, 


A/ x 3 
P a 


2A.t = 


//A 7A 

Now, plainly -^- = t. Therefore, 2A — = — i or integrating, A 2 


x 4 +a 


X' 

-c or integrating, A a =— 

P 4 P 

We can determine C, by considering that when x=2/i, then A, is the sum of 

the two sections already calculated, A — A x say, so that we finally get 

x 3 


or 


t= 


t- 


I p (x 4 — 16h 4 + 4 p Aj 2 ) 


x J 


for a rectangular top, 


and : 


t- 


I p(.r 4 + 6-o9// 4 ) 
x 3 

V p(x 4 + r 2 8N) for a P arabolIc t0 P- 

In practice, the suffixes must be carefully attended to. A 1} is the area down 
to the level x = 2/1= x 1} and, except in very wide-topped dams, we usually find 
that x n — Xn-j, can conveniently be taken as equal to k. Thus, b 2 , is the area 
between x x — 2h , and -*2 = 3//, and A 2 , is the total area = A 1 + ^ 2 ) down to the 
level x 2 = 3 h. 

If for any reason it is desirable to take x n —x n - x as not equal to h , but say, 
x n —x n -i = 5 feet, then b 2 , is the area between x x = 2k, and x 2 = 2h-\-$, and A 2 , 
is the total area down to the level x 2 = 2h + S- 

Similarly t x , is the horizontal thickness at the level x x = 2 /z, and / 2 , is the 
horizontal thickness at the level x 2 — 3/1, or x 2 — 2/^ + 5 feet. 

The zero of x, depends on circumstances. In an overflow dam x = o, at say 
5 feet above the crest of the dam. In a non-submerged dam it is usual to take 
x = o, at the crest of the dam. In final calculations, the allowances made for 
ice pressure and shocks by floating bodies (see p. 394) must be considered in 
determining the level x—o. 

This equation permits a preliminary section of the dam to be set out at any 
depth ; and if 4pA x 2 — \6/i 4 = E/i 4 , we have approximately : 

x E h ^ h\^ _ x_ _ kh 


In 2 I 


IP 


(I)' 


which is quite sufficiently exact when exceeds 5, or 6, 











366 CONTROL OF WATER 

This method is very convenient for studying the effects of modifications in 
the upper portion of the dam, and saves a good deal of tedious tiial and eiror 
in any case. 

The section obtained, however, is an ideal minimum (subject to the con¬ 
dition that the two upper portions are as assumed), and only satisfies both the 
middle third conditions if the batter or overhang of the water face is properly 

adjusted at each of the levels ar l5 x 2 , . . . and x n . 

The necessary batter, or overhang, at any depth x n , can be approximately 

calculated as follows : 

Let b n , be the area of the nth. section, i.e. between the levels x n -i, and x n . 
Let A,^, bejthe totaljarea down to the level x n ^. 



Now, assume that x n —x n -i, is so small that the area b n , may be regarded as 
a parallelogram. Then, taking moments about the water face end of 4 , if the 
section above x n -i is correctly adjusted, we have : 



r„)+J„(!) = (A„- 1 +^n)“= A„ 

A _A ^ l_1 


4 

3 


r n = 


7 4 
' bn 




where r n , is positive for a batter, and negative for an overhang. 

The above equation is merely a first approximation, and the corrections are 























































WATER FACE BATTER 


3 6 7 


obvious when the upper section is not accurately adjusted, or when the mass 
centre of b nj is not at the mid point of t n (see p. 370). 

The utility of these batter calculations may be regarded as doubtful, in view 
of the relatively small importance of the middle third law when the reservoir is 
empty. When they are not observed, the thickness of the dam is somewhat 
altered, as is indicated by the following investigation. 

Measure all abscissas from the water face end of 4 -i- In the usual notation 
let unaccented letters refer to the properly adjusted section, and accented letters 
to a section where t n , has neither batter nor overhang, and is in consequence 
increased to t n -\-u n . 

Put M„, as the moment of A n , about the end of 4 -1, and h — x n — x n -\' 

We have in the properly adjusted section : 


, _M m . x n ° 

yn ~ R/fyA ; 


— ..4 
3 


And, in the modified section, without batter or overhang : 

M'» 


\h 


and, neglecting such terms as r n ^t we have : 


k 

M 4 = M n -\-t n u n — 
2 


A» 


uji 


Therefore : 

2 

3 


/, \ \ M n( , tyjl h 

(4 T Un) — y I T Un_ tv k Mfi 


-If . 

3 " 


for : 


rn+-^{ 


n 2M„ n 2Aj 1 6 pA n 

1 11 ( U n tjl 2 U,Jl 


\ . xA / u n h\ 
)^6pK n \ 2A J 


2M) 


- n 

3 f 
in 


2A, 


0 


= £~ — = — + small terms. 
A n bp A n 3 


Now, the section of the dam is nearly triangular in form. Approximately, 
therefore : 

X n tn nil tn 2 


M n = 


A« — 


6 

X n t n 


6 

flht n 


and, in any given case, if the small corrections are required^ they can be 
calculated. 


Therefore 


— U n — — ?n + ^n 

3 

= - r n + u, 


( 


tnll 2t n h 

nht n 2 3 nt n h 


) 


I'n + 


Uji 

3 n 


or 


Un — 


3 nr n _ 


2 n -1 


— — r. 


») 


approximately. 


Thus, when a positive batter is required, we could theoretically diminish the 
thickness, in place of putting in the batter, and still satisfy the middle third 


















CONTROL OL WATER 


368 


condition when the reservoir is full ; but in consequence the condition would be 
violated when the reservoir is empty. 

When an overhang, or negative batter, is required, as for example in the 
second section of a rectangular topped dam, we must increase the thickness, 
since overhangs are not allowable (see p. 378). 

In trial designs, it is best to ignore batters, and any consequent decrease in 
thickness ; but overhangs, or rather the consequent increase in the thickness 
should be calculated. The nett result is an increase of 2 or 3 per cent, at the 
most, in the volume of the dam. Whatever method of adjustment, other than 
a rigid adherence to the calculated batters and overhangs, be adopted, the 
total volume must be increased if the middle third condition is to hold with the 
reservoir full and empty. 

The whole volume of a dam of varying height is very rapidly approximated 
to as follows : 


We have : 



a' 4 — 16/z 4 
4 P 


,r 4 + E/z 4 
4 p 


and we have calculated E/z 4 = 6^09/z 4 for a rectangular top. 

E/z 4 = i*28/z 4 for a parabolic top. 


Hence, A 2 = 


,r 4 +a known quantity 

4 P 


We therefore take the longitudinal section of the dam site, and calculate the 
fourth powers of the height at each point shown on the section, add the con¬ 
stant quantity, and after division by four times the specific gravity of the 
masonry, take the square root of the result and sum up by any of the ordinary 
rules. 

In two practical cases, I found that the result agreed within 2 per cent, of 
that obtained from an accurately calculated table of areas and heights. The 
approximate result is always somewhat less than the final value. 

The preliminary sketch being obtained as above, equations below and 
p. 369 should be used to calculate the pressures when the reservoir is full and 
empty: and any slight modifications required to keep p positive; and where 
advisable q e , also positive, can easily be made. 

When the water face of 4 -i is taken as the origin, the required formulas 


are : 


A n — An—1 + nl h, 


1 — ZZ ?i — iA ?i —1 


AT _ XT 1 zA—1 + 4 f n t n 2 V n M n 

M n - N n-i + il - —z -4-1 + k 7 4 +n = “ 

U 

Thus, measuring from the water face of 4 : 

Nn = A n -i(zZn_i + ^n) + g 4 -i( 4 -i + 4 + 2 ^») + ^ 4(4 + Vii) = Mn + An^n = A n a n 

-v 3 
n 


6>pJ\ n 


a n — a„+r n and y n — a H - j- 

and the conditions are : 

*n x *n 7 In v hi * 

and if p is positive, q e , may be slightly negative without any great detriment. 












FINAL CALCULATIONS 


369 


Also, q 

fie 


2 P A n f 3/n 1 = 2 pA n 

1 tn 


in 

2 pA n j ^ 

~t 7 \ 2 


J 

3 a n\ 


~fi 


*n 

2pA, 


tn J 


and the work can be carried on with certainty, as any great divergence from 
the preliminary values of t n , shows that an error is likely to have occurred. 

The final determination of the dam section requires certain conditions to be 
borne in mind. These are as follows : 


• y • 2 

(i) We usually wish to make not exactly -, but somewhat smaller, say, 

t 3 

= 0*65, or 0*64 (see under Fissures, p. 384). 


For a similar reason —, should be about 0*34, 01*0*35 ; though this is less 

essential, and ^ = o’3o to 0*32, is not necessarily a bad design. 

(ii) The resultant R, should make an angle with the vertical not much in 
excess of 35 degrees. This is usually secured by the above rules. 

(iii) The discussion of Atcherley’s theory and Wilson and Gore's experi¬ 
ments suggests (see Sketch No. 106) certain additions to the section as 
theoretically determined. 

In the final calculations, therefore, we usually find that a certain economy 
can be secured by beginning to batter the water face outwards at about one- 
third of the total height of the dam above its base, even if the calculations do 
not indicate any theoretical necessity for this. 

As an example, let us suppose that at : 


Xn—i — 4 5 feet, with p = 2*28. From the preliminary design we find that, 
t n -\ = 30-00 feet. A n _x = 668. N b -i = 6695. Therefore a n _ 1 = 10*02 feet; 


and y n -\ — io‘o2 + 


—^12S — io , o2 + q , q8 = 2o‘oo feet. 

1523 


Thus ,/ = 



30 1 


I V 




=0*203 units=i2*7 lbs. per square foot. 


Thus, the conditions are satisfied, and : 

q =ioi*5 units = 6340 lbs. per square foot. 

101*3 units = 633o lbs. per square foot. 

Thus, the stresses are well within the permissible limits. When x n — 50 feet, 
t n is about 33*20 feet, according to the preliminary equation. 

Assuming that r n — o , we at once find that : 

A n =A„_ 1 + ' 63*20 = 826 


N n =M«=M*i 1 + | (63*20 x 3° + 33‘2o 2 ) = 9i93 

Therefore, a n - in3 feet=tf„, since r»=o. 

jj/ n = 11-13 + ^^=11*13+11 *07 = 22*20 feet. 


24 












37 ° 


CONTROL OF WATER 


Thus, /, is negative, and although the value is small, 4 > must be slightly 
increased unless a batter be given. 

Putting 4 = 33-30 feet will probably make/, positive. 

The values of M„, and A n , corresponding to 4=33*30 are : 


A„=826-25 Mn = 9201. Thus, 11*14,.yn=22*19 feet. 

and/, is now positive. 

Let us now investigate the batter required to make a n — -\ in which case 

. # 3 

4 could obviously be diminished to 3x11*06 = 33-18 without causing /, to 
become negative. 

Equation page 366 (given for obtaining the batter) is obviously too coarse for 
work where the quantities involved are approximately 0-05 foot, and we must 
use a more exact equation. 

Taking moments about the water face end of 4 , we get in the general 
case : 

h 

N n — A. n -i (fin -1 + fix) +g{ 4 -i( 4 -i + 2 r n ) +4(4-1 4 - 4 +?»)} 

is equal to A n —, if the middle third is selected, or to A re 4, if the centre of 
3 

pressure is to lie at a distance k n , from the water face when the reservoir 
is empty. 

—. _ _ 2 A W 4 6M W 

’ 11 6 A„_! + ( 24 _i + t n )h 

where M n , is the value previously calculated, when r n — o , for the moment 
round the water face end of 4 - 1} of A n . 

In this particular case, we have, when 4=33-18 feet, 


r n — 


2 x 825-9 x 33-18—6x9190 


343 


6x668 + 2x30x5 + 33-15x5 4474 

which might also have been obtained from the equation : 


— o - o8 foot, 


u n — 



since u n , 


is about o*i2 foot. 


Thus, the correct adjustment requires an overhang, and, as a general 

principle, it is impossible to make a n =~, without an overhang, if once a n , 

3 


becomes greater than and the divergence once started increases as the 


depth below the top of the dam increases. 

Thus, in large dams, either the slight overhang indicated as occurring at 
the second section must be put in, or a certain small excess in the dam section 
must be allowed to occur throughout. 

The example (which is taken from a carefully worked design) shows the 


trend of affairs. At 45 feet the ^divergence, a n — ~, is 0*02 feet, increasing to 


0*04 feet at 50 feet, and to 0*06 feet at 55 feet. So that 4, is increased by 
o’o6, o'i2, and o’18 feet at these depths. 

The increase in bulk of the masonry thus produced is not very great, and it 
is doubtful whether it is really required. In fact, the real justification for 





PERMISSIBLE PRESSURES 


37i 


making ^50 = 33*45, which was the value actually adopted, was that/, is thus 
increased to 0*55 unit, or 35 lbs. compression per square foot which affords a 
•safeguard against cracks (see p. 387). 

For this reason, parabolic topped dams must be considered as leading to a 
"better design when practical conditions permit their construction. 

High Dams. —When checked by the exact method this preliminary process 
suffices for a design of a dam, so long as the height does not exceed a certain 
quantity. We have very approximately : 

, 2p A . , . r rr xt 

q=pt- —- — px ,—since A, is not far off —. 


Hence, the maximum vertical pressure is about 2^25 x the hydrostatic 
pressure; and, as later indicated, the maximum pressure according to the 

theory of elasticity is px sec 2 6 , and tan 6 = - = -j-z approximately. So that 

x v p 

.the maximum pressure is close to : 



or, 203.1: lbs. per square foot, where x, is in feet, and q , the vertical pressure is 
i4o.r lbs. per square foot, approximately. 

The limits are usually specified in terms of the vertical pressure. 

For example, Rankine gives, ^ = 15,625 lbs. per square foot, orx=m feet, 
on the downstream face, and / e = 20,000 lbs. per square foot, or x= 143 feet, on 
the upstream face. 

Since the upstream face is nearly vertical, we see that Rankine’s rules 
secure that the maximum pressure does not exceed 22,500 lbs. per square foot 
approximately. 

Other rules for vertical pressure are those of: 


Helocre . 
Furens Dam . 
Fernay Dam . 
Ban Dam 


. . 12,300 lbs. per square feet, or x= 88 feet approx. 

.(1860)13,280 „ „ x= 95 feet approx. 

.(1873)14,320 „ „ x= 102 feet approx. 

.(1870)16,360 „ „ x= 115 feet approx. 


Even if we allow for an increase of 44 per cent., these are all well below the 
permissible working stresses of first class masonry in compression. 

The real determining factor is not resistance to pressure, but resistance to 
shear. The ordinary theory gives the maximum intensity of shear as inclined 
at 45 degrees to the maximum intensity of pressure, and one half that maximum. 
That is to say, the maximum shear is equal to 101*5^ lbs. per square foot 

approximately, and accurately to : ~(i + tan 3 6 ). 

This last formula agrees very fairly well with the experiments of Wilson and 
Gore ( P.LC.E ., vol. 172, p. 128), except that they state that 6 — angle between 
the resultant of the forces V and H, and the vertical. The difference may be 
of importance in the upper portions of the dam, but where the condition of 
limiting pressure is the determining factor of the design, the resultant and the 
downstream face of the dam face are practically parallel, so that theory and 
experiment agree. 

Now, according to Bauschinger, the shearing strength of stone is about ^th 




372 CONTROL OF WATER 

of its compressive strength, and for cement mortar the ratio is about gth. The 
actual figures are : 

Concrete (i Portland cement, 2 sand, 2 gravel) well rammed, shearing 
strength 70,700 lbs. per square foot. 

Granite, shearing strength 92,250 lbs. per square foot. 

Old Masonry, shearing strength 94,000 lbs. per square foot. 

Allowing for the fact that the shear is about 072 of the vertical pressure, the 
above figures do not provide much over 7, to 9, as factors of safety. 

The highest stresses actually existing in a dam appear to be those in the 
old Almanza Dam, with a vertical, and likewise maximum pressure of 28,660 lbs. 
per square foot. 

The following are examples of maximum pressures actually existing (not 
vertical): 

Lbs. per 
Square Inch. 


• 

Alicante 

. 23,080' 




Fernay 

. 21,500 

All calculated by scaling the 


Ban 

, 28,600 

sections in order to 

obtain d, 


Furens 

. 24,600 

and therefore liable 

to some 


Echapre 

. 23,000 

degree of error. 



Komotau . 

. 24,500 j 




We may therefore consider that a maximum pressure of 25,000 lbs. per 
square foot can hardly be exceeded, and that the factor of safety against shear 
is then about 6 to 8. 

As a confirmation, it may be noted that the well designed Habra Dam 
(see Wegmann, Desig?i and Construction of Danis') failed under a maximum 
pressure only slightly in excess of 26,600 lbs. per square foot, although Bouvier 
states that 29,460 lbs. per square foot maximum pressure is safe for hydraulic 
lime concrete, when not also exposed to shearing stresses. 

In actual work the rules given by Rankine or Wegmann for vertical 
pressures may be followed, the latter gives : 

16,380 lbs. per square foot on downsteam face, x = 115 feet. 

20,408 lbs. per square foot on upstream face, x = 146 feet. 

The value, maximum pressure = 29,700 lbs. per square foot, occurs in the 
proposed Quaker Bridge Dam (see Wegmann, nt supra , Plate 77), and if all 
earth pressures are neglected, 35,000 lbs. per square foot in the dam as 
constructed. 

The assumptions made are unfavourable, so that such a stress is probably 
not actually sustained. 

Very High Dams. —In dams where the above pressures are reached, the 
intensity of pressures becomes the limiting factor in the lower portions. 

The design of the lower portions of such dams is in an unsatisfactory state, 
and most engineers would wish to have some further experimental evidence, 
such as the processes of Messrs. Wilson and Gore have given for the ordinary 
low dam, before erection. 

The best method appears to be as follows : 

Put q 0 , as the limiting vertical pressure, either assumed to be constant as 
when Rankine’s or Wegmann’s rules are followed, or calculated from : 

q 0 = (Maximum permissible pressure) cos 2 6 






VERY HIGH DAMS 


373 


where 6 is the angle which the downstream face makes with the vertical as 
measured from the design of the upper portion. 


Then 


_ 2 Ap . • , . dA 

— — £ -, approximately. And t = —r ^. 


Therefore, 


d A = 

A q 0 


Integrating, and remembering that when x = .xi , the area is A/, where xi is 
the depth where q first exceeds q 0 . 


9 n 




Therefore, A = A ie ° 




and, , dA . 2p 

t ~ .j- = A^ 'T 

and the profile of the dam can be set out from the logarithmic curve. 

The profile should be checked at each step (say h = 5 feet) and a n made 

equal to — by first adjusting the water face batter r n , by the equation : 

3 

„ _ 2 A n t n 6 M n _ 2 A M —j(/)i — 1) Mi—1 2 


bA,!-!+^( 2 /,!-!+4) 6A/1-X +//(24-i + 4) 

-v- 3 

and then determining,^ = and calculating both q and p e . 

opJ\ n 

It is also evident that if the value of 6 has markedly changed at any step, 
it will be advisable to calculate a new value of q 0j and to use this to determine 
the succeeding thickness. 

The work is laborious, and needs constant checking. The process can be 
continued until p e , exceeds its limiting value. 

No approximate equation can now be given, and we must proceed in the 
manner indicated by Wegmann (lit supra). 

Measure the angles of inclination of both faces, and thence determine the 
permissible vertical pressures p 0 and^ 0 . 

The approximate length of the next section is given by : 


t 2 

I'll 




X r, 


and the batter by : 


A,1—1(44 6 a n — 1) *T tn-\h(t n 4 — 1) T 4 “ ^ h ■ ^ 


r n = 


6A n -! + h(q2.t n —1 + 4 ) 


These equations are cumbrous, and the face slopes vary rapidly, so that 
q 0 , and/ 0 , must be calculated afresh at each step. 

I am not aware that these equations have ever been applied in practice, 
and as the result of actual experiment I am inclined to believe that a return to 
first principles and trial and error is probably more rapid. The equations, 
nevertheless, form a very valuable check. 

Further Theory of Masonry Dams. —The preceding methods permit 
a dam to be designed, which is safe against failure by vertical stresses acting 
across horizontal sections, (either tensile, or of undue magnitude if compres- 











374 CONTROL OF WATER 

sive). A little consideration, however, will show that failure can conceivably 
occur : 

(а) By the dam shearing off horizontally. 

(б) By horizontal stresses acting across vertical sections. 

(e) By shear along vertical sections. 

The following discussion is mainly concerned with case (b), but formulae 
which permit cases {a) and (c) to be investigated are developed. I hese two 
cases are not considered in detail, as experimental evidence exists which shows 
that the really weak points of a dam are not accurately indicated by any theory 
at present existing, although, fortunately, a dam designed according to the 
present theories requires very little modification in order to make it safe 
against failure in the manner indicated by the experiments. 

Atcherley's Theory. —Until 1904 the theory of masonry dams was 
considered to be in a very satisfactory state, and the relation between practice 
and theory was far closer than is usually the case in engineering. 

The conditions laid down concerned horizontal sections of the dam only, 
and were as follows : 

(i) The resultant of the water pressure on the dam above each horizontal 

section, and of the downward forces due to the weight of the dam 
above this section, should cut this section inside its middle third, 
thus securing that no vertical tension existed in the masonry. 

(ii) This resultant should, at each section, make an angle not exceeding 

35 degrees with the vertical, thus securing that the dam has no ten¬ 
dency to slide as a whole against the friction between horizontal layers. 

(iii) The maximum pressure per square foot should not exceed about 

one-tenth of the crushing stress of the masonry employed. 

Where the water face of the dam was inclined, it was usual to neglect the 
vertical component of the water pressure thus brought into play. In condition 
(iii) engineers generally considered only the maximum vertical pressure, 
ignoring the fact that the laws of elasticity rendered it perfectly clear that 
close to either face the maximum pressure is parallel to this face, and is equal 
to the vertical pressure multiplied by sec 2 0 , where 6 is the inclination of the 
face to the vertical. 

The matter does not seem of much importance. Those engineers who 
considered the point usually employed a higher working stress, and it was 
only in the case of very high dams that the condition became worth 
consideration. 

In 1904 Messrs. Pearson and Atcherley re-opened the whole question, and 
showed that, under the assumption that the theory leading to condition (i) was 
rigidly true, the vertical sections on the downstream side of dams designed 
according to these rules were under horizontal tension {Some Disregarded Points 
i?i the Stability of Masonry Dams). 

Their paper is somewhat mathematical in form, and the following resume is 
given on my own responsibility, but I believe that it is correct as to facts, 
although the objection may be raised that it is an incomplete presentation of 
the investigations of these gentlemen. 

Let us first consider a dam designed to satisfy condition (i). Let us assume, 
for the sake of simplicity, that the water face is vertical. Then, any piece of 
the dam above a horizontal section is subject to the following applied forces : 


ATCHERLE Y’S THEORY 375 

Water pressure on the face AB, represented by the triangular stress diagram 
A£B. 

The weight of the piece of the dam is represented in the same manner by 
the section ABCD. It will be noticed that if the actual dam section is taken as 

the stress diagram, the line bB is —, where p is the specific gravity of the 

masonry (Sketch No. 105). 

These are equilibrated by : 

(a) The vertical upward pressures on the base BC, which, according to the 
usual theory, are always positive, when condition (i) is satisfied, and when the 
resultant of the first two forces just lies within the middle third, are represented 
by the triangle B^C, the area of which is equal to that of the dam section ADCB, 
and in the general case by a trapezoidal diagram of the same area. 

(b) There is also a set of horizontal forces termed shears, with a resultant 
equivalent in magnitude to the water pressure. As indicated by the usual 
theories of elasticity, if the vertical pressures are distributed according to a 
triangular (or trapezoidal) stress diagram B^C, these shears must be distributed 
according to the parabolic diagram B/'C, where the area B/'C is equal to the 
area of the triangle A^B, representing the water pressure. 

It must be noted that this theory is known to be only approximate, and, 
since shears and pressures bear a differential relation to each other, it is quite 
possible to draw a curve of pressures which will generally have the same look 
and aspect as a triangular one, but which (having a different slope at each point) 
will produce a very different set of shears. Thus, an experimental proof that 
the measured pressures do not materially depart from those given by theory, 
is no assurance that the shears may not greatly depart from the theoretical 
value. It must also be noted that in every proof of the pressure law that has been 
attempted, points in the section close to either face are carefully excluded from 
the theoretical proof, so that we have no mathematical evidence that the shears 
follow a parabolic law near the faces of the dam. In fact, I believe that I am 
justified in saying that the theoretical proofs existing are, if anything, adverse 
to such an assumption, even Pearson’s attempt (Experimental Study of the 
Stresses i?i Masonry Dajns ) being inconclusive when carefully investigated. 

Let us now consider the equilibrium of a portion of the dam cut off by a 
vertical section, say EFC, where, for simplicity, (and as is almost invariably the 
case in critical sections) EC, is a straight line. 

The stress diagrams of the applied forces are as sketched (see Sketch No. 
105), and consist of: 

The triangular weight diagram EFC. 

The trapezoidal pressure diagram YfcC. 

The parabolic shear diagram F Cf'. 

Let us now combine the first two, and for the sake of clearness, twist the 
whole round 90 degress. We then get a quasi dam, subjected to a quasi pres¬ 
sure on the face CF, represented by C^F, where any line Kk = Kk—Kh' i and 
and to a quasi weight force represented by a parabolic shear diagram Cf' F, and 
these are equilibrated by pressures and shears on EF, of the same nature as 
those on BC, in the original section. Messrs. Pearson and Atcherley show that 
the resultant of the EF face forces falls outside the middle third, and that 
therefore, if we calculate the pressures on the vertical face EF, according to the 


CONTROL OF WATER 


376 

theory employed when considering the horizontal sections, the face EF, is 
frequently exposed to horizontal tension near F. 

In Atcherley’s example, this tension is large, and very few existing dams 
(if they have been designed according to the old horizontal section theory) are 
found to be entirely free from tension when the stresses on vertical sections are 
investigated in this manner. The few exceptions occur when the dam itself 
forms a spillway, and is consequently far thicker than conditions of equilibrium 
alone require. 

So far, I believe that I am in exact agreement with Messrs. Pearson and 
Atcherley, although my methods differ materially. While they express their 
doubts as to the absolute accuracy of the parabolic law for shears, it would 
appear that in many dams (although not all that I have investigated), the 
assumption of a uniform shear over the horizontal section (which is a far more 
favourable case than any that theory suggests to be likely to occur) still leads to 
horizontal tensions over vertical sections. In fact, were not their results con¬ 
tradicted by careful experiment, I should be very diffident in making any criticisms. 

I venture to put forward the following :—Firstly, the law of the distribution 
of the weight forces as represented by ABCD, not only as a sum, but as in¬ 
dividual forces, is very doubtful. This may materially alter the quasi pressure 
diagram CcgF ; and, similarly, while the shears represented by C/ r F, have been 
regarded as playing the role of the weight of the masonry, their points of 
application are not in the centre of each small section K/i (as would be the 
case with weights), but at the face K. 

This, of course, has been allowed for in Messrs. Pearson and Atcherley’s 
investigations, but it is quite evident that the conditions necessary to cause the 
ordinary theory to be approximately correct for centrally applied weight forces, 
may be quite inadequate to make the theory hold good for these face forces. In 
fact, I believe that actual dams are sufficiently rigid to cause the usual theory 
to hold good, but are saved from the stresses indicated by this very same theory 
(as applied by Messrs. Pearson and Atcherley) through insufficient rigidity. 

I would point out that Mr. Deacon (with the instinct of an engineer) had, 
long before the publication of this theory, advocated hydraulic mortar for dams, 
in place of cement, on the ground of less rigidity. 

The theory of Messrs. Pearson and Atcherley did not pass unchallenged. 
Many engineers relied upon the fact that of all the dams (now amounting to 
several hundred in number) designed according to the old theory, not one had 
failed or even shown signs of failure, in the manner indicated. 

I consider that the question has been settled, from a practical point of view, 
by the labours of Messrs. Wilson and Gore, and that their results are in a large 
measure confirmed by the less accurate, but more easily copied work of Messrs. 
Otley and Brightmore. My one stricture on the work of these gentlemen is 
perhaps hypercritical. They were forced to work with markedly non-rigid 
materials in order to get measurable deformations from which the stresses 
could be deduced. 

A very full description and discussion of these experiments is given in 
vol. 172 of PJ.C.E ., and should be read by everyone interested in the matter. 

The experimental results show that the ordinary theory gives a very fair 
general idea of the stresses in a dam, at points far removed from the foundations, 
or faces, and that the stresses calculated by this theory are not likely to be 
exceeded in any portion of the dam. 


EXPERIMENTAL INVESTIGATIONS 


377 

In fact, the old theory is shown to be a good working guide, but it is useless 
to refine it more than engineers have been accustomed to. 

Several interesting points appear in detail, and I believe that the following 
deductions are worthy of careful consideration in future design. 

There appears to be a possibility of horizontal tensions existing near the 



Sketch No. 105. —Diagram showing Forces acting on a Vertical Section of a Dam. 

Fig. 1 shows the ordinary forces acting on a dam, and except in the fact that the shears 
shown by the parabola Ck'fB, act along the line CB, needs no explanation. 

Fig. 2 shows the portion of these shears Cf'F, which act on the base of the portion 
CEP', acting as quasi weight forces along the line CF, while the pressure forces obtained 
by the ordinary theory act as quasi “ water ” pressures, and are diminished by the forces 
produced by the weight of the portion CEF, of the dam. 

Thus, the elementary forces acting at, say K, are quasi weight forces, represented by 

KV = shear acting at K, 
and quasi pressure forces, represented by 

Kh~Kk-hk — Wc-Kh', i.e. base pressure at K, less weight of dam above K. 




























378 CONTROL OF WATER 

water face toe of the dam ; not so much in the dam itself, as in the foundation 
vertically below the toe. This suggests the advisability of making the water 
face vertical, or slightly sloping outwards, and any overhang is quite unper¬ 
missive, even though this rule may cause the line ol pressure (when the 
reservoir is empty) to pass slightly outside the middle third. 

The construction of the corner formed by the water face of the dam and the 
foundations needs careful thought. The masonry, or concrete, near to this 
point should be composed of as large blocks of stone as possible, and if the 
upstream face of the dam is curved, the faces of the blocks should be shaped 



Rock 


Sketch No. 106. —Modifications of the Theoretical Section of a Dam suggested 
by Atcherley and Wilson and Gore’s Investigations. 

to the correct curve, so as to avoid joints. A layer of asphalt, puddle, or 
other elastic impermeable material should be placed over the corner, so as 
to prevent percolation of water into the crack. 

The experiments indicate that the crack will probably extend in a vertical 
direction into the foundation, rather than into the dam. The results obtained 
when investigating the stresses produced by fissures in the dam show that a 
vertical crack is less dangerous than a horizontal one. 

Both Atcherley’s theory, and the results of the experiments, indicate that 
the rock just beneath the base of the dam is more severely stressed than the 
dam itselfi Thus,, all available information is decidedly adverse to dams 













SHEARING STRESSES 


379 


founded on any but the best and strongest rock. Such designs as masonry 
dams founded on piles driven into a clay stratum have failed too frequently 
to be good practice, quite apart from any experimental results. 

The horizontal shears found by the experimenters appear to be distributed 
according to an irregular law, and the maximum shear occurs near the down 
stream face ; so that the distribution is not even approximately parabolic or 
uniform. But, as the tension found by Atcherley does not manifest itself until 
long after failure by tension at the water face toe has occurred, the matter is of 
academic rather than practical interest. 

The water face toe tension appears to be the cause determining the failure 
of model dams, and its magnitude is by no means inappreciable, being, in 
models, about i-£ times {i.e. 3*9 tons per square foot for 125 feet depth of 
water) the hydrostatic pressure when the toe joins the foundation in a sharp 
angle, and about ^th of this value if the junction is a curve of about 15 feet 
radius in the full size dam. 

It would therefore appear that the form of junction of the water face and 
the foundation should be a curve of large radius, and that the construction 
about this point should be of the very best quality. Subject to this condition 
the following are safe rules for dam design: 

(a) Adhere rigidly to the middle third law for the condition of reservoir full. 

(b) The middle third law is of less importance when the reservoir is empty, 
and any overhang of the upstream face is unadvisable. A coating of imper¬ 
meable material should be put over the water face junction of the dam and 
its foundation ; and a system of drains should be formed in the dam itself to 
carry off the water that may percolate through a possible crack. 

( c ) The stability of each section should be investigated with respect to 
condition (ii), i.e. for resistance against sliding. 

( d ) The maximum vertical pressures given by the trapezoidal law should be 
multiplied by sec 2 d where 6 is the angle of inclination of the face of the dam, 
and the values thus obtained should show a factor of safety of at least 10, with 
regard to the crushing strength of the rock. The values adopted in practice 
are given on page 371. 

(e) The vertical sections near the downstream tail of the dam should be 
investigated to ascertain the mean values of the shearing stresses produced by 
the resultant of the upward pressures found in (d), and the weight of the 
masonry cut off by the vertical section. This will usually produce a thickening 
of the tail of the dam of the character investigated on page 382, but if the dam 
is partly buried in earth, the original design may amply suffice. 

I consider that such a dam (when founded on a good rock foundation) will 
be as safe a structure as any that are made. 

As regards practical details, I believe that the real result of the controversy 
started by Messrs. Pearson and Atcherley is that a dam in hydraulic lime mortar 
is likely to possess certain advantages over one constructed with cement. 

It is also clear that the Cyclopean method of construction in blocks of stone 
as large as can be handled, and set in good mortar, has many advantages over 
smaller stones or cut masonry. It appears quite unnecessary to spend any extra 
money on specially cut stones or thinner joints for the face work. Such outward 
show is liable to induce unknown stresses, is costly, and (I consider) even aestheti¬ 
cally, is an error. A good dam is independent of any outside prettiness.. 


CONTROL OF WATER 


38° 


I would also note (although personally adverse to the principle) that bonding 
between the dam and its foundation, by iron rails, has been employed. It has 
also been proposed to keep the dam face unwetted by water, by means of a 
series of slabs of reinforced concrete supported from the dam, leaving a vacant 
space between the dam and the slabs, so that they and the dam face may be 
inspected. 

The question of the general determination of the stresses across the vertical 
sections of a dam is best investigated algebraically. 

Consider OA, a horizontal section, of length /, at a depth z/, below the top of 
the dam. 

Take the horizontal and vertical lines through the downstream end of this 
section as axes of co-ordinates. 

Let y—tnx+c be the equation of the line BC, the downstream flank of the 
dam. As a rule c— o, but it will be found that the results obtained indicate that 

d 

c should be about — i.e. that the “tail of the dam ” should be thickened. 


Draft 7 Channel through Masonry to connect 

roun/iAhnn firkin with Pram zap Turnip! In flam 



Sketch No. 107.— Cyclopean Masonry and Drainage of a Dam (after Deacon). 

Using the notation for forces and pressures employed when investigating the 
stresses on horizontal sections of the dam, we find that : 

The horizontal shear at any point P, in OA, where OP=ur, is given by the 
equation : 



if the distribution of the shear is parabolic 


Thus, the resultant of the shears or quasi weight forces acting on the 
length OE, where OE = «, is : 



So also, the vertical pressure at P, is given by the equation, r^q — ^q—p) T. 

The weight of the dam above P, partially counteracts this force, and the 
nett vertical force acting at P, is : 































TAIL THICKENING 

The resultant of these quasi pressure forces acting on the length OE is: 

(q—pc)a—(^—^+mp^ ~=K say. 

This acts at F, where OF =x and : 

_ (q-?c) \~{ ? ~r+P m ) a 7 

x = -—-- J 


K 


_ a 2 \3(q-pc)-a(j—^+pm)} 

Thus, EF — a—x — -A_i_— 

’ 6K 

The resultant of K, and W, is therefore a force acting along the line FG, 
and cuts the vertical section ED, at G, and 

EG =j' = (a — x) 


W 


6(3/—2 a)H 




Sketch No. 108.— Investigation of Atcherley’s Theory. 


The modifications necessary when the flank of the dam is curved, so that y is 
not equal to ?nx+c , are obvious. 

The horizontal pressures and vertical shears acting at any point in the 
vertical section ED, can now be written down. It is unnecessary to go through 
the work. In a dam designed according to the usual rules, i.e. where horizontal 
sections are alone considered, c=o, and with very close approximation : 


q = pd 

Vp 

H = — 

2 


ft = 0 
m = V p 


Substituting these values we get: 


-_pd p (3 t—2ci ) d 3 __d 
y ~ 3d 2 (3t-2aj pdo~3 










































3 82 


CONTROL OF WATER 


to 

A 


Thus, all vertical sections between the tail and the point a= —are exposed 

2 \ p 

horizontal tensions at and close to their lower edge. 

If the circumstances of an actual dam, where q, is slightly less than pd, where 


is a little greater than o, and /, is a little less than 



be investigated, it 


will be found that the locus of G, is no longer a straight line, but a very flat 
hyperbola scarcely distinguishable from a straight line. 

Since the theory employed is known to be somewhat inaccurate, the actual 
calculations need not be performed. The general results are unaltered. 

The case when c, is not equal to nothing can be similarly treated, and we 
then obtain the following : 



Putting <2 = 0, we find that: 



Sketch No. 106 shows a dam designed on these lines. 


It will be obvious 


tnat ;/z, is now somewhat less than Vp, and that if t= —=, the section will require 

v p 

further modification in order to fulfil the conditions obtained by considering 
horizontal sections. 

The final results of investigations conducted on these lines indicate that a 
dam could be made “ safe ” (when Atcherley’s theory is taken as correct) by a 
tail thickening amounting to approximately 15 or 20 per cent, of the volume of 
the dam. Most dams are thickened at the tail; but, as a rule, not sufficiently 
to confirm to Atcherley’s theory. 

The above investigation therefore leads to the following conclusions: 

Atcherley’s theory is probably erroneous, otherwise dams which are known to 
be satisfactory would fail. On the other hand, some thickening near the tail is 
desirable, and a shearing area sufficient to support the stress K, should be 
provided (see p. 372 for Shearing Stresses). 

It will also be plain that the distribution of shears near the downstream face 
of the dam is of importance, and that the place where the tensions are indicated 
is doubtless in the dam, but close to its foundation. The circumstances are 
consequently hardly analogous to those in which tensions exist in a dam at an 


unsupported face. 

The whole evidence indicates that tensions may exist, but their existence 
depends on a theory which is approximate, and large tensile stresses only occur 
just where this theory is well known to be doubtful ; and, in fact, may almost be 
said not to hold. 


The tensions revealed by this somewhat doubtful theory exist at points 
where the dam is well supported by the solid rock of its foundations. 

I therefore consider that the question is one in which theory alone has no 
real weight, and believe that the evidence afforded both by the experiments of 
Messrs. Wilson and Gore, combined with the satisfactory results of general 
engineering practice, are quite conclusive proof against the theory. 

I think that engineers must be grateful to Mr. Atcherley for raising the 






FISSURES IN DAMS 


3 8 3 


question, as the result Jias been to disclose the unsuspected weakness existing 
at the water face toe of a dam. It will be quite evident that the foundations of 
a masonry dam must be solid rock, and that any fissures running parallel to 
the length of the dam (especially near either toe) must be carefully examined, 
and, unless capable of being properly filled, may necessitate the site of the dam 
being shifted. 

So far we have implicitly assumed that the only horizontal pressures acting 
on the dam are those produced by the water. Rock of a quality suitable for 
the foundation of a masonry dam very rarely occurs at the natural surface of the 
ground. Thus, the lower portions of nearly all existing dams are buried in 
earth. The earth, in view of its situation under water, or at the best in a very 
moist state, may be regarded as equivalent to a fluid weighing about 120 lbs. 
to the cube foot. When the pressures of the earth both up and downstream of 
the dam are taken into account it is usually found that the final section is 
approximately triangular down to the level of the top of the earth, and approxim¬ 
ately rectangular below this level down to the rock foundation. Under these 
circumstances, the necessary tail thickening is not very great, but the shearing 
stresses near the downstream face of the dam, at and about the level of the top 
of the earth, must be investigated. 

Fissures in Dams. —It is well known that good masonry, such as is found in 
a well constructed dam, can resist a certain, and by no means negligible, 
tension. 

Nevertheless, we have already seen that the whole design of dams (other 
than such unusually high examples as are subjected in their lower portions to 
the maximum permissible compression stress) is mainly determined by the 
condition,—that no tension shall (in theory) exist in any portion of the dam. 
This appears to be somewhat uneconomical, but the following investigation will 
show that it is absolutely necessary. 

Let us now consider a section of a dam, and assume that, owing either to 
tension in the masonry, or to faulty workmanship, a horizontal crack exists in 
the water face, and that this crack is of such a width as to allow water under a 
pressure s, to penetrate to a depth 2-, as shown. 

Consequently, we have, in addition to the forces formerly considered, an 
upward pressure j, acting uniformly over the length z, i.e. the resultant upward 

z 

force is sz, acting at a point distant - from the water face of the section. 

Applying equations Nos. 1 and 2 we get for the tensions produced by this 
force : t 



where /, is the horizontal thickness of the dam. 

Hence, the total pressures existing in the dam, due to the combination of 
the ordinary forces and this uplifting pressure, are (Fig. II.) : 


p —p'=~^V^2 — S2 ( 2 ~ 2^)} at ^ ie water f ace - 

and, q — q = — | V 1^ — sz \j~j ~ 1 )] at ^ ie downstream face. 


CONTROL OF WATER 


3 8 4 

Therefore, no tensile stress exists in the dam if: 

V ^2 — — sz ( 2 ~ is positive ; and, in the upper portion of the 

dam, where the resultant of the ordinary pressures lies well inside the middle 
third, we can (in any given case) calculate the pressures produced by the 
ordinary force's, and the extra uplifting pressure due to water in the crack. 


Thus, if we put — =X we find that p—p' — o, when : 
t 




z 4 - 3 * 


P 

A(4 - 3X) 



I ( * l 


which, when s is given, enables us to find the length of the crack that will just 
produce tension in the dam, and if, as is the case in most dams, P = o, s— o, 
or A = o, so that any crack, however small, causes some tension to arise. 

It is also evident that absolute safety against any possible crack can be 
produced by designing the dam so that p—p'= o, when z = t, for then the dam 
would be stable, with a horizontal crack extending right across it. 

Putting z = t, we then get; 

v (> - 

and if r for the sake of simplicity, we assume a triangular dam, and that s is due 





























































CRACKS IN WEAK MASONRY 385 

to a water pressure equal to x, the height of the dam above the section con¬ 
sidered, we have : 

V = Py = p-f* so that, p^2 —■ ^ 1=0; 

or ^ ==/ ( :1 ^p) 5 =0*52/if p = 2-25. 

Now, for a triangular section, with vertical water face, we have ; 

y=(+ x P = / +£l 

3 3V 33 pf 

Hence, for a triangular dam, safe against all cracks, we have : 

or ,/ 2 = _£!_ 

3 3 pt 3P p- 1 * 


Whereas, for an ordinary triangular dam, complyimg with the middle 
third law : 


t 2 = 


x 2 


So that, in order to secure absolute safety against horizontal cracks, we 

must increase the thickness of the dam in the ration/ —or, for p — 2*25, 

v p- 1 

about 34 per cent. 

But, since q, is now 0*56 xp, in place of xp, it is plain that the limiting depth 
before the maximum permissible pressures are exceeded is increased in the 

ratio -i-g or, say 1 ’80, so that in high dams of weak material, a design of this 

character deserves consideration. 

Such a section would be expensive in the usual case of low dams, and 
consequently a design such that p — o, or a small quantity, is adopted. 
Hence, p—p' is negative, or tension may occur across the beginning of the 
crack. 

Now, unless we assume the crack to be of limited extension in the direction 
of the length of the dam, we cannot expect the cracked portion of the masonry 
to support any tension. 

We thus have three further cases to consider: 


(i) 


¥=p-p'~o ={v(*-f)-»(*-g)}* • • • Fig. III. 


That is to say, the stress diagram is as sketched, and no portion of the 
masonry is in tension ; and if we put : 


V = P x lz= i'i2xt, and 2 —we get: 
2 't 1 ’ 0 


z / nx 

^ = o- 666 + y o‘444-2-24— 


2 5 









386 CONTROL OF WATER 

The negative sign alone gives a physically existing value, and we have, 

X 

when - —i : 


n —0 

-y=o*666 

z 

t ~° 

n = 0-033 

| = o -633 

y = o-o6 

^ = o‘o66 

Z =0 -6 

t 

Z 

- =0*12 
/ 

n — o'166 

y 

T=°' 5 

Z 

t = °' 4 ° 

72 = 0-198 

y 

r°: 47 

z , 

— = 0*67 


(ii) The stress diagram is as sketched in Fig. Ill#, and k , the distance to 
the point where the stress is o, is less than z. Therefore, putting Q, for q — q\ 
we have : 


hQV-t)(X) =Vj, -T 


Hence, 


|Q(/— k) = V — sz 

_ V(6y-4t)+sz(4 t -3 z) 
2 (V—sz) 


and O - 4 (Vsz) 2 

y ~ 6V (t—y) — yz( 2 t—z) 

The crack does not tend to increase in depth, unless tension exists at its 
end. The condition for this is obtained by putting k = z. 

Or, since V = V12xt, simplifying the equation, we find as the equation for 
z s 
? or x: 

X 2 —X^4 —2-24’i^ + 672y =0 


which permits us to determine X, when «, and -, are given ; 


x . . 

e.g. - = 1, n = o 033 ; gives X = o'14. 


When z = k, we have, Q = 


2(V — sz) 
t-z ’ 


V = 


V(4 t—6y + 2z) 
(4 t—z)z 


and when z, is given, k = z, when : 

/(i+ —) 

V yi) 


X( 4 -X) 


(iii) The dam is so badly cracked that the inner end of the crack is exposed 
to tension. (Fig. 11 H.) 

Here we merely have to substitute as follows in Equation page 383 : 

Z Z 

t—z , in place of /, y—z t in place of y, and —> in place of when 
z, is a co-ordinate, but not in the expression sz. 








We thus get: 


STRAINS NEAR A CRACK 


3 8 7 


or : 


P = 




3 Z \\ 

2 {t — z)'S 


V> — 2 ( SZ / ^ 

r — (/_ 2’) 2 \V( 2 ^“3j+2') — y \ 4 ^~ ; where P, is a pressure 

when positive. 

Q = (^j2{ V (3t / -/-2S') + ' y | (*+2/)} 

It should be noticed that the upward force sz, now increases the compression 
at, and near, the downstream face. 

As before, put V = i• 1 2xt --Z— n - = \ 

3 t t 

We get: 

=^|ri2(3»+X)-^X(4-X)} 

—— = x{ 1*12 (i — 3^ — 2\)+ — X( 2 + X)| 

2 ^ 2X J 


It will be plain that if X, be assumed at each joint (not necessarily as 
constant, but rather as a variable value corresponding to a fixed length of 
crack), since n, is known from the original design, Section No. (ii) permits 
us to determine whether the end of the crack is exposed to tensile stresses, and 
these last equations enable us to determine whether the assumed crack is 
likely to spread. 

We may therefore consider that a complete design for a dam will not only 
include a table of the values of p and q , but also a table of the “ permissible 
length of crack,” calculated from Equation page 384, or a table of the stresses 
existing at the end of a crack of definite length, calculated from the appropriate 
equation. 

The importance of such work cannot be measured solely by the values of 
the stresses as calculated, for their numerical values alone do not fully disclose 
the strains that may be induced in the masonry. The stresses occur at a re¬ 
entering angle. We have no exact theory of the effect of stresses near the end 
of a crack, such as are now considered, but there is little doubt that this is a 
more unfavourable case than that of a spherical flaw in a cylinder under 
torsion. In the latter we have sound theoretical justification for the statement 
that the strains may rise to twice the value calculated from the average stress 
according to the usual rules. 

Thus the stresses obtained above are not only high, but act on a weak spot, 
and are therefore likely to be very effective in extending the fissure. 

As examples of the application of the above equations, let us assume the 


following : 

(i) A dam designed to satisfy the middle third law exactly. 
n — o, and 


Then, —=—, or 
t 3 


P(l 2 X) l = ,r{ri2A~A(4-A)}. 











3 88 


CONTROL OF WATER 


Or, assuming successively that: 



X = 0-05 „ 


X = 0-03 „ 


X = o‘io 




Hence, if s = x, as will be the case if the crack is of measurable width, even 
the smallest crack (if horizontally directed) produces a tension at and around 
its end. 

Now, assume the workmanship to be such that an open crack i foot long 
may possibly occur. 

When x = 15 feet, / = 10 feet approx. 

Thus, for a 1 foot crack we have X — o*io, and the tension when s = x, is 
o'2o;r = 190 lbs. per square foot, and qua causing an increase in the crack we 
may consider the tension as being about 380 to 400 lbs. per square foot, which 
is not likely to break good masonry. 

Next, when,r = 75 feet, t = 50 feet approx., and for a 1 foot crack, X = 0’02, so 
that when s = x, the tension is o'026jt = 120 lbs. per square foot, which is 
also safe. 

Thus, we may conclude that a 1 foot crack, although undesirable, is not 
necessarily fatal. 

If, however, we assume that a 3 foot crack can exist, we get, when x = s = 
75 feet, X = o*o6, the tension is o‘ii6ar = 547 lbs. per square foot, which is 
probably unsafe, since it is in reality equivalent to 1000 to 1100 lbs. per 
square foot. 

We may therefore conclude that the determining factor is the workmanship, 
in which must be included the methods employed to counteract the changes of 
temperature which occur. 

(ii) It will also be evident without detailed calculation that if we design the 

y 

dam so that^ = 0*63, or n — 0*036, X = 0*15, or the crack must be at least 0*15/ 

long when s = x, before tension occurs at its end. Although only 5 to 6 
per cent, thicker than the theoretical minimum, the dam is practically 
safe against cracks such as are likely to occur even with unusually bad 
workmanship. 

The assumptions are, of course, somewhat unfavourable. At 75 feet depth 
the dam is about 50 feet thick, and a continuous horizontal crack extending 
7‘5 feet into, and with some extension along the dam, (I find roughly that there 
is an appreciable beam action unless the extension in this direction exceeds 
30 feet) must be considered as indicating very careless workmanship ; but is 
not impossible in a concrete dam built up in horizontal layers. Also, the 
assumption of uniform, pressure over the whole depth of the crack, is a very big 
one, for if the crack is narrow, leakage and the surface tension of the water in 


FAIL URES OF DAMS 


3 8 9 


contact with the masonry will prevent the full pressure being carried over 
the whole depth. 

It is difficult to avoid the conclusion that a dam, as ordinarily designed, 
is liable to fail, unless of first class construction, through the gradual opening of 
a horizontal crack starting at the water face. 

It therefore seems advisable not only for this reason, but also on the ground 
of the tensile stresses experimentally shown as likely to exist near the junction 
of the water face and the foundation of the dam, to consider the water face as 
the portion of the dam requiring the most careful inspection and workmanship. 
The question of preventing infiltration will be discussed later. 

Failures of Masonry Dams.—Owing probably to the fact that masonry 
dams are rarely constructed without careful technical consideration, actual 
failures are but few. 

Nearly every long masonry dam, which is straight in plan, has cracked, 
and it may be laid down as a general rule that for this reason, if for no other, 
the plan of a dam should be slightly curved. 

Of actual failures, the most instructive are the Puentes in Spain, the Bouzey 
in France, and the Austin dam in Texas. 

Puentes Dam Failure. —The failure of the Puentes dam is more 
interesting from the point of view of the properties of permeable strata, than 
from that of actual dam design. The description and following quotation are 
taken from Aynard’s Irrigatio?i du Midi de PEspagne. 

Sketch No. iio shows the dam to be of unscientific design, which is not 
surprising in view of the fact that it was constructed in 1785-1791. The design, 
nevertheless, is a safe one, since no tension occurs, and the maximum com¬ 
pression is 16,250 lbs. per square foot. 

The dam is founded on piles 22 feet long, driven into a bed of sand, and 
gravel, at least 25 feet deep. The original design contemplated reaching solid 
rock, but this was found to be impossible. 

The piling, and the slab of masonry 7*4 feet in thickness, were continued for 
131 feet (40 metres) below the dam, thus securing an impermeable coating 
283 feet in breadth. 

For 11 years the water never rose more than 82 feet above the top of 
this apron, and the dam showed no signs of failure, the apron evidently being 
sufficiently broad to prevent deleterious percolation under this pressure. 

In 1802, however, the water rose to 154 feet above the level 164*2 (i.e. to 
the full supply level), and, as stated by an eye-witness: 

“ On the downstream side of the dam towards the apron, water of an 

exceedingly red colour was boiling up in great quantities.” 

“ Half an hour later, this boiling up had increased to an enormous mass 

of water,” 

and a definite passage was formed. 

The dam still remains (1864) like a bridge, the opening being about 56 feet 
broad, by 108 feet high. 

I think that it is impossible to describe a failure due to percolation more 
clearly. The only doubt is as to whether the apron, shown as 131 feet broad, 
was blown up, or whether there was some portion of the sandy pocket which 
was not covered by the apron. 

In any case, it appears that the dam failed owing to the percolation being 


39 o CONTROL OF WATER 

so excessive as to actually lift up the sand. The example is unusually interest¬ 
ing, because, so far as I am aware, most percolation failures can be tiaced to 
the foundations being too narrow. Whereas in this case, the foundations were 
evidently too shallow. Their effective depth, according to my rules, being 
about 23 feet, under the assumption that the impermeable core wall is 7 feet 
deep at 131 feet from the centre of the combined dam and apron (see p. 297). 

As no engineer is likely to be so reckless as to construct a stone dam on 
permeable foundations, any further comment is needless. 



Bouzey Dam Failure. —The Bouzey failure presents several interesting 
features. The detailed section taken from Langlois’ Rupture du Barrage de 
Bouzey , is as per Sketch No. in. So far as can be gathered from the figure 
and reports, the law of the middle third was unknown to the designer, who 
appears to have been satisfied, provided that the line of the resultant pressure 
fell within the section of the dam, and that the maximum pressure did not 
exceed the working compressive stress of the masonry. Consequently, the 
masonry seems to have been considered as capable of resisting tension, and 
certain limiting values, both for the tensile and the compressive stresses, 
appear to have been laid down. From certain statements, these seem to have 
been 3075 lbs. per square foot (1*5 kilogram per square centimetre) in tension, 




























































































39 1 


BO UZE V FAIL URE 

and 20,500 lbs. per square foot (10 kilos, per square centimetre) in compression. 
At any rate, some limits were assigned, and were evidently determined by 
experiment previous to construction. The tensile stress assumed to be per¬ 
missible appears very great, but there is no doubt that the dam did actually 
sustain tensions exceeding 2000 lbs. per square foot. 

The dam was founded on a layer of micaceous sandstone, traversed by 
seams and fissures of clay. The guard wall AB was intended to be carried 
down thiough this fissured rock into a compact and impermeable stratum. So 
far as can be ascertained, this was not effected in many places, owing to lack 
of pumping power, and in certain spots where an impermeable stratum was 



Sketch No. hi. —Bouzey Dam, original section and repairs. 


reached this was only a layer, and permeable rock was known to exist at a still 
greater depth. 

Under such circumstances, it is not surprising that in 1884 (when the water 
level reached the line 368'8o) the dam cracked, moving bodily forward in 
places. Later, the reservoir was emptied, and it was found that the dam had 
separated from the guard wall, over a length of 453 feet, and had moved 
backwards as much as 14 inches at certain points. 

The gravity of the situation does not appear to have been fully realised. 
The cracks were closed with grout, and the repairs, as sketched in dotted lines, 
were carried out. These can hardly be supposed to have checked percolation 
along the crack in the guard wall and the consequent uplifting pressure. 

The reservoir was again filled, and all seems to have gone well, except for 








































39 2 


CONTROL OF WATER 


certain leaks, until 1895. Then, the water level rose to the originally designed 
full supply level 371*5? and the dam cracked horizontally at the levels 361*5 and 
358, and failed through the upper portion being swept away over a length of 
600 feet. This length was quite distinct from the 345 feet that had previously 
failed. 

The stresses in the original dam appear to have been as high as 11,480 lbs. 
per square foot (5*6 kilos, per square centimetre) compression, on the downstream 
side, and to have reached a tension of 3,075 lbs. per square foot (1*5 kilos, per 
square centimetre) at the level 358 metres on the upstream side. These 
values are obtained under the assumption that the masonry can resist tension. 

Langlois calculates the stresses at the level 349*40 under the assumption 
that the masonry cannot resist tension, and gets (14*13 kilos, per square 
centimetre) 28,800 lbs. per square foot compression. As he believes that the 
masonry could stand (30 kilos, per square centimetre) 61,500 lbs. per square 
foot compression and (3*5 kilos, per square centimetre) 7,175 lbs. per square 
foot tension, he considers that the dam might have been safe, were it not 
for the uplifting pressure on its base, due to infiltration of water. His 
calculations regarding infiltration pressures seem to be affected by an error in 
measurement, so I do not quote them. 

Those referring to the level 361*5 metres (where the final failure occurred), 
are useful. We have, taking p = 2, and working with metric units : 


V = 2 x 46*1 =92-2 


H 


10- 


= 5o 


M = 97*4 
a — 2'\2 metres 


y — 2*12+— — = 2*12 + r81 =3*93 metres 
Thus, 3 

p — 2X ~~^2— - ^.q^ 3 ) = *“ 11 *44— — 2 345 lbs. per square foot 

^ = 2 x 1 ) = 47 * 67 = +9772 lbs. per square foot 

since these units are thousands of kilos, per square metre (205 lbs. per square 
foot), and are converted into kilos, per square centimetre by dividing by 10. 
Thus, there is a tension in the upstream face, so that the failure is quite 
explicable. 

Consider also the case of a horizontal crack 1 metre deep, with a water 
pressure of 10 metres acting on it, or a total upward force of 10 units. Then, 
remembering that in this case no support from the sides of the crack can be 
relied upon, we must put t~ 2-= 5-09— 1, and we get: 


P-2X 92 ' 2 ( 2 -3X2- 93 y 

20 / 

2 + 3X °' 5 )- 

— 18*35 

4*o9\ 4*09 / 

4‘°9 

v 4*09 / 



= — 3762 lbs. 

per square foot. 

Q = 2 x 9 2 ^^ 3 X 2 ^ 3 _ i ^ 

+ 2 °.| 

r 3 xo-5 + ,\ 

4-58*53 

4*09 \ 4’o9 / 

4’°9 

V 4-09 / 


= + 12,000 lbs. per square foot. 

M. Langlois also discusses the effect of temperature stresses on the dam, 
which was not curved in plan, and endeavours to show that the repairs 
(especially the grouting), really tended to weaken the structure. 











A US TIN FAIL URE 


393 


I agree with the conclusions of M. Langlois, and would particularly 
remark that his resume of the advantages of curving a dam in plan is most 
excellent; but it appears unnecessary to go beyond the above figures for an 
explanation of the failure. 

As is invariably the case when a failure is investigated, the materials appear 
to have been of second-rate quality. The stone was fissured, and clayey, and 
the sand very fine, so that the masonry was neither as dense nor as strong 
as the designer assumed. I do not consider that such statements throw any 
real light on the laws of dam design. Practical engineers are well aware that 
not one work in ten is really perfect in construction, and that the other nine, 
if well designed, are saved from failure by the factors of safety adopted in 
their calculation. 

It may, I think, be taken as a ruling principle that no work fails except 
when it combines bad design and imperfect workmanship ; the amount of 
imperfection necessary to secure failure depending on the inferiority of the design. 

The Bouzey design was radically bad, and therefore a very small imperfec¬ 
tion in construction caused failure to take place. 

Nevertheless, these facts create a feeling not so much of astonishment at 
the disaster, as of confidence in a well designed dam. We have a dam 
violating in every possible manner all the present-day principles of sound 
construction. The foundation is bad, and the dam is not carried down far 
enough ; yet, it only partially fails. Later, when the dam,—due to this 
particular defect,—was exposed to upward water pressure, it did not fail until 
at least 16 lbs., and probably (owing to upward pressure) 30 lbs., per square 
inch tension had been induced. 

It would therefore appear that a dam designed with but one half the factor 
of safety usually existing, only fails when, besides heavy tensile stresses, 
percolation occurs. It seems unnecessary to add that both the stone employed, 
and the mortar used, are stated to have possessed only about two-thirds of the 
usual strength. 

Austin Dam Failure. —This failure is discussed by Gillette (. Engineer¬ 
ing News , May 30, 1901). 

The dam was founded on weak limestone, stratified in nearly horizontal 
layers. This was known to be leaky, and water under pressure was found by 
boring into the foundations during construction. 

The leaks which developed after construction were stanched by careful 
treatment with clay, and, in view of the large quantity of silt deposited in the 
reservoir, during its seven years of life, there is little doubt that the leakage and 
the permeable strata that probably existed beneath the foundation of the dam 
had little influence on the ultimate failure; although, no doubt, they were 
hardly conducive to sound sleep on the part of the responsible engineer. 

The circumstances existing at the time of the failure are shown in Sketch 
No. 112, (except for the unknown depth of the silt deposit upstream of 
the dam). 

The horizontal pressure of the water on the upstream face of the dam was 
equal to 181,500 lbs. per lineal foot of the dam. The back pressure of 37 feet 
depth of water below the dam is equivalent to 42,800 lbs. per lineal foot; so 
that the nett force producing sliding is 138,700 lbs. per lineal foot. 

Assuming 145 lbs. per cube foot as the weight of the masonry, the weight 
of the dam was 320,000 lbs. per lineal foot. 


394 CONTROL OF WATER 

Weight of water, n feetx 18 feet, on the crest of dam=i300 lbs. pei lineal 
foot. 

Weight of water, n feetx40 feet, on slope of dam = 27oo lbs. per lineal foot. 

Weight of water, 20 feetx 30 feet, on curved toe = 37,000 lbs. per lineal foot. 

Total, 360,000 lbs. per lineal foot. 

Thus even with this (in my opinion), large over-estimate of the watei loads 
on the dam, we obtain the ratio against sliding as 0*38, and if we allow for 
a back pressure of only 26 feet depth of tail water, the ratio is C44. 

Now, we know that there was a fault in the strata under the base of the 
dam, so that it can hardly be supposed that the limestone rock had any cohesive 
strength near this fault; and, even if not faulted, such a rock has little cohesive 
strength along its bedding planes. 


Flood Hi. 



Morin gives the coefficient of friction for limestone on limestone as 0*38, and 
for stone on wet clay as 0*33, so that it must be acknowledged that there was 
very little, if any, margin against sliding, unless the limestone had some cohesion. 

The reports on the failure of the dam, (which was seen and photographed 
in a very complete manner), seem to show that a length of about 500 feet did 
actually break away, and move bodily downstream. 

Abnormal Loads on Dams. —Abnormal loads are principally produced by 
ice, and shocks from floating bodies. 

The thrust exerted by the expansion of a sheet of ice 1 foot thick can 
theoretically amount to as much as 34,000 lbs. per linear foot of the dam. In 
America {Trans. Am. Soc. of C.E ., vol. 53, p. 89), a thrust of 29,000 lbs. 
appears to have been observed, but the thickness of the ice is not recorded. 

In the Quaker Bridge Dam, a value of 43,000 lbs. was assumed, and at the 
Columbus Dam, 22,670 lbs. per lineal foot, each including an allowance for 
shocks from floating blocks of ice. 














395 


LIME VERSUS CEMENT 

No lule can be given for shocks from floating bodies, and local circumstances 
alone can indicate if any allowance should be made ; and if so, its exact 
magnitude. 

Practical Construction of Dams. —The discussion of Messrs. 
Pearson and Atcherley’s theory, and the investigation of the effect of horizontal 
fissures, will have shown the points where weakness is most to be apprehended. 

Consequently, the ruling factors are to prevent horizontal cracks at all costs ; 
and to ensure water-tightness, in particular, at and near the junction of the 
water face of the dam and its foundation. 

The first condition excludes any construction such as brickwork, where 
horizontal joints run through the dam. Modern practice appears to be trending 



Sketch No. 113.—Remschied Dam (after Intze). 


towards the adoption of mass concrete, with large blocks embedded at random 
in the concrete, rather than rubble masonry. In view of the fact that well made 
concrete apparently possesses greater shearing strength than the best masonry, 
this practice appears to be logical. 

The question of hydraulic lime versus Portland cement as the binding 
material of the concrete or masonry, is a debatable one. Cement is the 
stronger of the two materials, but the slow setting of the lime allows initial 
strains to adjust themselves. 

Water-tightness is best secured by a correct proportioning of the concrete, 
and by good workmanship. The designs of Intze (see Sketch No. 113) are 
costly, but afford a very perfect shield for the junction of the dam and its 
foundation. In the case of the Remschied Dam, the water face was plastered 

































































CONTROL OF WATER 


396 

with cement, and this was covered with asphalt, which was again covered with a 
wall of brickwork from 1 foot to 2 feet thick. It may be parenthetically remarked 
that plastering the face with cement appears to be universal in German practice. 

The old and leaky Mouche Dam was rendered water-tight by a covering of 
concrete, about 7 feet thick, in which drains were formed at intervals of about 
3*5 feet (vide A.P.C., 1907, vol. 5, p. 136). 

Kreuter {Beitrage zur Berechnung der Staumauren ) recommends that the 
whole water face of the dam be covered with jack arches ; and that the spaces 
between these arches and the dam face be kept free from water by means of drains. 

In British work, water-tightness is usually secured by a skin of slightly 
richer concrete on the water face. The method is open to objection, but has 
proved successful in cases where the range in temperature is no greater than in 
England or Germany. 

In hotter and drier climates (possibly owing to unequal contraction) such 
skins are found to crack during the setting of the cement. 

Where frost does not occur, Wade ( P.I.C.E. , vol. 178, p. 7) states that 
water-tightness can be secured by the concrete being placed very dry (where a 
rich skin is required, the concrete must be laid wet), and coating the green 
concrete, as soon as the shuttering is removed, with two layers of neat cement 
laid in with a brush. 

Such painting with neat cement can always be advantageously applied ; 
although, when exposed to frost, its durability is open to doubt. Very good 
results are also secured in masonry by pointing the face joints with pure cement 
mortar of a very stiff consistency. 

Personally, I am strongly adverse to the insertion of plums in anything but 
wet concrete ; although it must be acknowledged that Deacon at the Vyrnwy 
Dam, and Wade ( ut supra) secured excellent results with mortar and concrete 
respectively, of a “ putty ” consistency. 

According to Rafter’s experiments ( P.I.C.E ., vol. 178, p. 90), a certain amount 
of strength is gained by using dry concrete. The figures for 12-inch cubes, at 
18 to 24 months, are : 

Dry concrete ..... 355,700 lbs. per square foot. 

Plastic concrete.330,200 lbs. per square foot. 

Wet concrete ..... 313,900 lbs. per square foot. 

These results are relatively better than usual. 

Wade’s figures for dry concrete with a sandstone aggregate are : 

1 : r66 : 3*33 concrete . 270,000 lbs. per square foot at 90 days. 

1 : 2*5 : 4'4 concrete . 248,100 lbs. per square foot at 90 days. 

Mortar ..... 230,000 lbs. per square foot at 90 days. 

While Bruce obtains with : 

1 : 2\ : 4, and an unsatisfactory aggregate, figures ranging from 282,000 to 
335,000 lbs. per square foot at 6 months. 

The worst figure reported for concrete of modern Portland cement appears 
to be 215,000 lbs. per square foot, for a 1i| : 6b mixture at 30 days, rising 
to 327,000 lbs. per square foot at 90 days. 

Deacon ( P.I.CE ., vol. 126, p. 68) states that hydraulic lime mortar mixed 
as jb : 1 can be made (if precautions are taken) to stand 340,000 to 450,000 
per square foot in compression, and 200 to 300 lbs. per square inch in tension. 


RESISTANCE TO SHEARING 397 

Hill (. P.I.C.E ., vol. 126, p. 109) finds that 1 to 3, or 1 to 4, lias lime concrete, 
8 feet thick, is quite water-tight in puddle trenches under 150 foot head of 
water. 

The above figures show that failure by crushing is unlikely, even with weak 
concrete. It has, however, been shown that when strength becomes a 
determining factor in design, the shearing strength, rather than the crushing 
strength, should be considered. It is probable that all the test pieces, the 
strengths of which are recorded above, really failed by shear. Nevertheless, in 
designing a dam it would appear desirable to test the samples of the proposed 



Sketch No. 114. —Typical Algerian Dam, showing Draw-off Arrangements. 


materials in “shear” rather than in “compression” in the sense used by 
testers. Some results thus obtained are recorded on page 372. 

Similarly, the design of the joints in the dam should be conditioned by 
the shear, rather than by the pressure. Thus, the common practice of laying- 
masonry or plum concrete with the joints of the masonry or the longer dimen¬ 
sions of the plums normal to the flanks and faces of the dam, may be a mistake. 

The correct disposition of the material is that in which the direction best 
fitted to resist shear is at 45 degrees to the faces or flanks. Thus, in a rock 
with beds along which shear easily occurs, these beds should lie either parallel 
or perpendicular to the dam faces in all stones close to the faces. The rule 
usually leads to the disposition above referred to ; but, in some varieties of 
granite, blocks laid normal to the faces would be in the worst possible position 






























































CONTROL OF WATER 


39 8 

to resist shear. Similarly, it will be plain that the relative shearing strengths 
of the mortar and of the individual stones should be considered before the 
method of arranging the materials is determined. 

Temperature Stresses in Dams.—The question of the influence of temper¬ 
ature on the stability of a dam is puzzling. We have the following figures: 

The coefficient of expansion of concrete is about 0*0000076 per i degree Fahr., 
while the value of Young’s modulus ranges between 1,400,000 and 2,800,000 lbs. 
per square inch. Thus, a fall of 20 degrees Fahr. below the temperature at 
which the concrete was deposited, should theoretically produce tensile stresses 
ranging from 210 to 420 lbs. per square inch. Consequently, variations of tem¬ 
perature occurring in any but the most equable climate (if they really penetrate 
into the.substance of the dam) should cause cracks of an appreciable width ( e.g. 

inch wide for each 100 feet length of the dam, if a fall of 20 degrees Fahr. 
occurs and causes rupture). 

So far as is recorded, the Mouche Dam (see P.I.C.E ., vol. 115, p. 157) is the 
only case where cracks of a width equal to that indicated by the above calcula¬ 
tion have actually been observed. 

The facts may be explained as follows. The interior body of the dam pro¬ 
bably does not experience an alteration of more than 20 degrees in temperature 
during the whole of its existence. The outer portions, especially those near the 
downstream face, which experience greater ranges of temperature and are 
therefore called upon to sustain severer stresses, are prevented from cracking 
noticeably by the support of the main body. 

Consequently, the shortening produced by the change in temperature is 
largely absorbed in producing a slight flattening of the curve of the dam ; and 
the cracks are probably due more to differences in the expansion and contraction 
of the various portions of the dam, than to a more or less uniform contraction 
of the whole length of the dam. It should be remarked that the Mouche Dam 
is straight in plan. 

If the above reasoning is correct, w^e may deduce the two following prin¬ 
ciples : 

(i) Dams must be curved in plan. 

(ii) Arch and buttress dams, although theoretically economical, must be 
regarded as more liable to temperature cracks than the usual type ; and arming 
at the haunches of the arches with rods, or beams, should be held to be essential. 

All the measurements of temperature deflections w T hich have been made 
appear to confirm this statement, although it is incorrect to consider the de¬ 
flections produced by bending loads (such as the w f ater pressure) as absolutely 
comparable with those resulting from extensions or compressions arising from 
changes in the temperature. 

As examples, De Burgh (P.I.C.E., vol. 178, p. 64) reports that in the very 
thin Barren Jack Dam, a change in the temperature from 57 degrees to 100 
degrees Fahr. produced an inward deflection of 0*14 inch (the reservoir being 
empty). The water load is stated to have produced an outward deflection of 
0*47 inch. 

So also, in the case of the far thicker Vyrnwy Dam (P.I.C.E., vol. 115, p. 117), 
the deflection due to temperature does not exceed 0*366 rnm. ; and that caused 
by the load produced by the upper 13 feet of water retained, is not more than 
0*868 mm. 

In the Remschied Dam (Sketch No. 113) Intze reports (Ztschr. D.I.V ., 


TEMPERATURE STRESSES 


399 

June i, 1895) temperature deflections of £ inch, and load deflections equal 
to i inch. 

The data collected by Gower (Trans. Am. Soc. of C.E., vol. 61, p. 399) and 
others, on the effect of temperature changes in American dams, are very com¬ 
plete. Nevertheless, they cannot be considered as universally applicable, since 
the climate of the United States is such that the difference between the tem¬ 
perature during the period of the deposition of the concrete, or masonry (i.e. May 
to November), and the lowest temperature ever experienced, is far greater than 
that which occurs in other localities, even when the same annual range of temper¬ 
ature is experienced. In most of these localities the working season is usually 
the colder portion of the year ; whereas, in America it is the hotter portion. 
Thus, American circumstances are unusually favourable to the production of 
contraction cracks in masonry or concrete. 

The general results are as follows : 

(i) The actual expansion on the surface of the concrete or masonry is about 
o*6 of that calculated from the range of temperature experienced, and from the 
coefficient of expansion of similar concrete or masonry in small specimens. 

These values are: 

For concrete, 0*0000054 to 0*0000081. 

For concrete exposed to alterations in humidity also, 0*0000044. 

For masonry, 0*0000050 to 0*0000060. 

The coefficients of expansion actually observed by Gower in thick granite 
masonry ranged from0*000003 5 2 to 0*00000264, with a mean value of 0*00000307 per 
degree Fahr., and Dana finds that for granite the coefficient of expansion ranges 
from 0*00000440 to 0*00000480 per degree Fahr. The differences are possibly 
largely explained by alterations in the humidity of the masonry. 

(ii) The actual visible cracks which occur, rarely account for more than 
0*6 of the theoretical contraction. (In the Assouan Dam the ratio is only 0*2, 
and it is highly probable that tensile stresses of 300, to 400 lbs. per square inch 
exist on cold days.) 

(iii) Actual temperature measurements in the interior of the Boonton Dam 
indicate that the annual variation of temperature at a distance D, feet from the 
face of the dam, is represented by: 

R 

x— „ _ 

3 VD 

where R, is the annual variation in the surface temperature of the dam. 

It would also appear that unless x, exceeds 60 degrees Fahr., cracks either 
do not occur, or are not sufficiently wide to permit water to pass through them. 

Cardew ( P.I.C.E ., vol. 152, p. 239) attempted to provide for temperature 
stresses in the Burraga Dam, by burying iron rails in the top. The principle 
appears to be correct, as the rusting of the iron cannot influence the stability of 
the dam as a whole. If cracks are prevented in the thin top, where temperature 
changes are most marked, there is little likelihood of their starting in the interior 
of the dam. 

Form of the Downstream Face of Overflow Dams— The upper 
portion (if not the whole), of the overflow face of a dam is usually a parabola. 
Muller (Engineering Record , October 24, 1908), has suggested that since the 
ordinary parabolic form does not follow the curve which the under surface of 



400 


CONTROL OF WATER 


the nappe would assume if left to itself, a certain vacuum will exist between the 
nappe and the dam. If the dam is high, and the head of water passing over 
it is large, this is undesirable. Certain dams seem to have been exposed to 
some such action. Muller consequently designed the top of the dam so as 
to lie inside the nappe boundaries, as obtained by Bazin (.Ecoulement en 
deversoir). 

The errors in detail are plain. Bazin’s curves refer to sharp-edged notches, 
under heads not exceeding 17 foot; and Muller applies them to thick notches, 
under heads of 5, or 10 feet. The principle is a good one, and the process 
leads to a nice curve. 


Idesl TJV.L. 



Sketch No. 115. —Muller’s Diagram for Face of a Overflow Dam, 

and Flexible Flashboards. 

The nappe boundaries can be plotted from the following tables : 
Lower Boundary — 


X 

D 

= 0*0 

0*05 

0*10 

o*i 5 

0*20 

0*25 

0*30 

°’35 

y 

D 

= O'O 

0-059 

0*085 

0*101 

0*109 

0*1 12 

0*1 I I 

0*106 

X 

D 

= 0*40 

0-45 

0*50 

0*55 

o*6o 

0*65 

0*70 


y 

D 

= 0*097 

0*085 

0*071 

0*054 

0*035 

0*013 

0*009 



Upper Boundary — 


X 

D ~ 

- 3 *o - 

■1*0 

0 

0*1 

0*2 

o *3 

y 

D 

0*997 

0*963 

0*851 

0*826 

0*795 

076 

X 

D “ 

0*4 

0*5 

o*6 

0*7 



y _ 

D 

0*724 

o*68o 

0*627 

0*569 































O VERFL OW CUR VES 


401 


where D, is the depth of water over the theoretical weir crest, as observed by 
Bazin’s methods; and x, andj, represent the co-ordinates of the nappe curves 
referred to the water face of the dam as vertical axis, and a line through the 
top corner of the water face as horizontal axis. 

Thus, it will be plain that the process amounts to assuming that a Bazin 
notch exists at the water face of the dam, and making the downstream face 
conform to the theoretical nappe curve. Thus, the highest point in the dam 
is situated o’2$D, downstream of the water face, and is o‘H2D, above the 
level at which the sill of the theoretical notch is assumed to lie. 

The depth of moving water above this point is only 0*650, but it is assumed 
that the design of the dam secures a discharge equal to that calculated for a 
head D, from Bazin’s weir formulae (see p. 109). 

The tables suffice to determine the dam face for a distance 07D, from the 
water face of the dam. 

The mean velocity at this point and its direction can be calculated from the 
cross-section of the nappe, and the direction of the tangent to the dam face. 

It may be assumed that the curve of the dam face should be continued so 
as to conform to the path of a particle falling under gravity, with an initial 
velocity equal in magnitude and direction to the calculated mean velocity. 

Muller thus finds that the equation : 

x 2 = 2‘3D y 

fairly represents the lower portion of the dam face, when referred to horizontal 
and vertical axes through A, the highest point of the dam. 

Muller continues this curve until the tail of the dam is reached (see Sketch 
No. 115), but an extension much beyond 2D, or 3D, below the crest seems 
unnecessary. 

The real objection to the process seems to lie in the fact that D, is assumed 
to be constant, and is actually variable. For instance, let us assume that 
D = 5 feet. No discharge occurs until the water surface in the reservoir is 
at least 0-56 foot above the level from which D, is measured. A certain small 
discharge then occurs, but it can hardly be assumed that Bazin’s formula is 
applicable until the water has risen some 1*5 to 2 feet higher. Thus, the dam 
is really only discharging water properly when the water surface is 2 feet or 
more above the level from which D, is measured, and in the earlier stages 
it may be doubted (see Horton’s Weir Experiments , pages 106 et seq.) 
whether it is safe to assume any greater discharge than that given by the 
equation : 

Q = 3'3°L(D—o’56) 15 

until D, is 2*5 or 3 feet. 

Thus, the conditions assumed but rarely occur in practice, unless the 
water level is systematically kept well above the crest of the dam by flash 
boards, or shutters. 

Flashboards. —The use of flashboards, or temporary retaining walls, in 
order to block the waste weirs of dams is more common in India or America 
than in Europe. From this it cannot be inferred that the practice is a bad 
one. Absence of flashboards in European countries is mainly attributable to 
the fact that the climates are usually too changeable and erratic to enable a 
flood to be predicted sufficiently in advance to ensure absolute certainty in the 
removal of the flashboards. 

26 


402 


CONTROL OF WATER 


The difficulty of removing the dashboards is to a large extent overcome by 
adopting the following designs. 

(a) The dashboards are supported by iron pins, sunk into holes on the weir 
crest. The pins are calculated so as to bend when the dashboards are 
materially overtopped. 

The following analysis is due to Muller (. Engineering Record , August 22, 
1908): 

Let the pins be d, inches in diameter, and spaced s, feet apart. 

Let h, be the height of a dashboard, and x, the height of the water over 
the weir crest when the pins are required to bend, both in feet. 

Put x l =x—h. 

The bending moment on a pin is : 

125 sh 2 (yi' x -\-h) .... [inch-lbs.] 

The moment of resistance of the pin is 0*098 fd 3 , where f is the stress 
which produces bending. This Muller gives as 70,000 lbs. per square inch. 

. , , m f)') 9 ' » • IJJ Oil- ) .* \ • 1 '' . * • ' ‘ > 1 ' J 1 J -*•'' i J 

Thus : i 2 $/ds( 2 >x 1 + /i) = 686od s 

d 3 

3 * 1 +A = 3 *-- 2 A = 54 * 9 ^ 

i8*3^ 3 , 2 h r _7 • • 1 i 

or, X ~h 2 s - -^-3" • id, in inches] 

Also the pins should not be unduly strained when the water level reaches 
the top of the dashboards. Thus, taking a (high) working stress of 25,000 lbs. 
per square inch, we dnd that : 

d= 'dlb . [d, in inches] 

2 7 

(1 b ) Sketch No. 229 shows the dashboards used at Tajewala to control a branch 
of the river Jumna. Here, it will be plain that the boards will fall as soon as 
the water rises to 3 inches below their top. In practice it is found that small 
gravel and horse dung (used for dusting the boards in order to render them 
water-tight), accumulates at the bottom of the boards, and, in consequence, the 
falling is somewhat irregular. No board ever stood with much more than 
6 inches of water above its top. The proportion of boards that fell according 
to design was quite sufficient to remove all apprehension as to the failure of the 
system, and in actual tests a man was able rapidly and easily to throw down 
the boards when nearly overtopped. 

The system is reliable, provided that a variation of 3 inches above the 
designed level of falling can be permitted. It is probable that the iron pin 
dashboards will fluctuate to an equal extent. This is not a defect, as a flash- 
board system that was considered automatic in its action would never receive 
sufficient inspection, and consequently, sooner or later, would fail and cause a 
bad disaster. A less reliable system which would necessarily be carefully 
watched would probably be assisted in its fall at the critical moment. 

The Tajewala system appears to be better adapted than Muller’s type for 
re-erection before the water has ceased flowing over the weir. 

For more elaborate methods the sections on Shutters and Gates should 
be consulted. 




ARCH DAMS 


403 


SYMBOLS CONNECTED WITH CURVED DAMS. 

a, is the vertical height, in feet, of the horizontal arches into which the dam is divided 
for purposes of calculation. 

A„, is the area of the cross-section of any one of these arches. A n = at n approx. 

D n (see p. 405). 

d, is always used for the sign of differentiation. 

E, is the modulus of elasticity of the masonry, in tons per square foot, probably 
E= 100,000 to 120,000, but a knowledge of the precise value is unnecessary. 

I ,is the moment of inertia of the section of the dam, about a horizontal axis through its 
mass centre in (feet) 4 . 

L (see p. 406). 

M, is a bending moment (see p. 406) expressed in feet-tons. 

vi, and 71, are used as numbers to indicate the various sections typified by A. 

P, is the pressure in tons per square foot; but P m , or P, with a suffix is the total water 
pressure, in tons, on the water face of the area A m . 
q, and r (see pp. 406 and 407). 

r d , and r u , are the radii of the dam, in feet, measured to the downstream and upstream 
faces. 

R, is the radius measured to the mass centre of the section of the dam, but Wade 

(see p. 404) puts R = r M . 

S, is the working compressive stress of the masonry in tons per square foot. 

S x , and AS (see pp. 404 and 405). 

t, is the horizontal thickness of the dam, in feet. 

X m , is the portion of Pm, which is carried by the dam as a gravity dam. 
a (see p. 406). 

/ 3 , 7, A (see p. 407). 

fj., is the reciprocal of Poisson’s ratio (see p. 405). 

. , . . . , Weight of a cube foot in lbs. 

p, is the density of the masonry =- 2 ----——• 


SUMMARY OF FORMULA 7 .. 


Thickness of the dam 


/= ™ 

s 

Correction for thickness of the dam 


S 1 = S- 

r u + r d 

Correction for slope of the faces in Wade’s type (see p. 405): 

AS= -J- 

The deflection formulae are not summarised. 


(1 + - r “ V 

V r u + r d J 


[Tons] 


[Tons] 


[Tons] 


Theory of Curved Dams.— [In this section the loads are expressed 

in Tons.]—I propose to briefly investigate the theory of dams which are 
so markedly curved in plan, and are so well supported by the sides of the 
valley which they cross, that they may be considered as acting partly as 
arches. 

Such dams are usually calculated as arches only, and the following very 
simple formula is used : 

_ ■ • • • • • • • 


[Tons] 





CONTROL OF WATER 


404 


Where /, is the thickness at any level, in feet. 

R, is the radius in feet. 

P, is the water pressure at that level, in tons per square foot. 

S, is the permissible compressive stress in tons per square foot. 


Plainly 


Depth in feet below top water level 
36 


The section of a dam designed by this formula is plainly triangular. 

The best practical discussion of this type of dam is given by Wade ( P.I.C.E ., 
vol. 178, p. 1), and is founded on his experience of thirteen such dams. Wade 
adopts a section with a vertical upstream face, and battered downstream face 
(Sketch No. 116, Fig. 1) ; as, after trial, this has been found to be more satisfactory 
than sections with both faces battered, or with a vertical downstream face. 
The top width is always made 3 feet 6 inches, in place of zero, as indicated by 
the formula. Water 2 feet deep has passed over dams of this width without 
causing damage. 

The values of S, depend on the rock used in the dam, and on the character 
of the foundations. For quartzite and sandstone, S, ranges from 10 to 12, or 
even 15 tons per square foot. For conglomerate, altered slate, or granite, 
S, is equal to 20 tons per square foot; and for special granite and diorite S, 
is equal to 24 or 25 tons per square foot, although this last value is not at 
present employed by Wade. 

The dams are made of Portland cement concrete, in the proportion of 
1 : 2\ : 5, with large plums of rock inserted ; usually from 25 to 30 per. cent, of 
the volume of the dam being plums. 

The concrete being laid very dry, these plums are laid in mortar and “ wriggled” 
into the mass by handspikes, in place of the usual ramming with mauls. 

The value of S, is determined by allowing a factor of safety of 5, on the 
crushing tests of unsupported 6-inch cubes of the concrete ; and this probably 
gives 7| on the crushing stress of a large mass of similar concrete. 

R, is measured to the vertical face of the wall, which increases the factor 
of safety. 

When a dam is designed by these rules, it is found that when S = 20 tons 
per square foot, and R, is 500 feet, the section obtained is practically as large 
as that of a similar dam designed so as to resist the water pressure by gravity 
only. 

Thus bearing in mind the extra length entailed by a curved plan, no 
advantage is gained unless the radius is somewhat less than 500 feet. 

The maximum radius of any curved dam yet constructed by Wade is 
300 feet. 

The most economical curve for a given span of the dam is one with a 
central angle of about 100 degrees. 

The formula is theoretically correct only for a dam battered on both faces, 
and may be corrected as follows, where : 


r u , is the radius to the upstream face. 
r d , is the radius to the downstream face. 


(a) Correction for thickness of the dam : 



2 r u 

r u +r d 


where S, is the stress obtained 


-by the original formula. 




PRELIMINAR V FORMULAE 


405 


{b) Correction for vertical pressures due to the weight of the dam. The 
above value is increased by AS, where : 

For a vertical downstream face, and a battered upstream face (Sketch No. 
116, Fig. 2) : 


AS 




For Wade’s type (vertical upstream, battered downstream), Fig. 1 : 


AS 


__ P_ 
3H- 


(1+*-§-) 

' r u +r d / 


where , is Poisson’s ratio, and is o‘i6 to 0*22 for concrete, i.e. in the mean say 

fi 


/x = 5, see Bellet (.Barrages en Maqonnerie ). 

These corrections are incomplete, but may be used in order to obtain a 
preliminary section for treatment by the more complete method now developed. 
This will be applied in an approximate manner so as to illustrate the method of 
testing a preliminary design. 



Sketch No. 116.—Curved Dams. 


The principles are complete ; and, after a dam has been proportioned by 
the present theory, it is quite possible to select more accurate formulae for 
determining the arch deflections, and more closely spaced horizontal sections 
for determining the cantilever deflections. 

The theory is simple. Assume that the dam at its highest point is com¬ 
posed of m (say 5, or 10) horizontal arches, each a, feet high, so that the 
total height of the dam is via. Let the total water pressure over one of these, 
the centre of which is {in — n + i)a, above the base of the dam, be P„, per foot 
length of the arch. Calculate D n the deflection in this arch, which is of known 
radius, and length (measured from the plan of the dam) under a uniform radial 
load P w — X„. This gives us an equation as follows : 

■p. _ (P n X n )R n Lft COt (In 

Un ~ 2EA„ 

Where R n , is the radius of curvature of the dam, at the level considered, 
measured to the upstream side. 


































CONTROL OF WATER 


406 


L n , is the length of the centre line of the arch ring, and varies for each arch 
according to the cross-section of the gorge across which the dam is built. 

a n , is one-quarter of the angle the arch subtends at the centre from which 
R„, is measured : 

• L n 

l.C. Q-n ^-p) 

4 K n 

A n , is the area of the arch ring. 

A n , is best calculated for the preliminary work either from the corrected 
formulae already given, or by a consideration of the shear produced at the 
abutments of the arch by the resultant of the radial forces P n , acting over its 
whole length L n . 

Now, consider a vertical section of the dam, at its highest point, under the 
action of a series of m, concentrated leads, X 1} X 2 , . . . X,«, acting at 

distances ma y {iu — i)a, . . . a, from the base of the dam. 

Taking the beam thus obtained as 1 foot wide, we have as an equation for 
the deflection under these loads : 

d 2 y _ M 
dx l ET 


where M, is the bending moment of these concentrated loads at any point, the 
co-ordinate of which is x; and I, is the moment of inertia of the section at this 

point, or I = —, where i, is the thickness of the dam, which can be scaled from the 

drawing. 

The section of the dam is assumed to be made up of a series of trapezoids, 
and the angles in the faces of the dam occur at the points of application of the 
forces X m , X m _ l5 etc. X l5 as shown in Sketch No. 116, Fig. 3. 

Consider any horizontal section in the lowest trapezoid ABCD. Let x y be 
measured from O, the point of intersection of AB, and CD produced. Let the 
vertical distance of O, from the base of the dam be ra. 

Then, t=b m x y and: 


M = X m {x — ra+a) + X m -i(x — ra + 2 a) + etc. + -- ra -f ma) 

Therefore ^ = 2X m -„ tl (i -^ ) 

Integrating, ^ ± =SX „,.„ +1 (-]+£=?«) + C 

Now, ~ = o when x = ra. 
ax 


Therefore, 


C 


— 2X, n — n+ j 


2 r~a 


Integrating again, = 2X,„_ +] (-log.ar-~a) + Car+C, 

and_y = o, when x — ra. 

Therefore, Cj = -raC + 2X w _„ +1 (lo gera+~F-^ 

Thus, by putting = r—ia, we can calculate A wl , the beam deflection at the 
point of application of X m , and tan / 3 m , the tangent of the angle of inclination of 
the central line of the beam at this point. 












407 


ACCURATE CALCULATION 


Plainly A m = value ofy, when x—{r— i)a, 

and tan / 3 , u = value of ^ when x=(r— i)a. 

ax ' 

Next, consider any horizontal section in the second trapezoid BDEF. 

Take O', the point of intersection of the lines BF, and DE, as the new origin 
for x. 

We have:_ t=b mm . 1 . r, where b m - x is the new value of b m , and 

M — X m -.i(x q— ia) -f- etc. q—m-j-ia) where qa , is the vertical height 
of O , above BD, and X m , no longer contributes to the moment. 

These equations can be treated in precisely the same manner, the conditions 

now being that y=o, and^ = o, when x — qa, and we obtain, by calculating the 


values of^, and ~ when x—(q—i)a, § m -i and tan y m -i, the deflection and the 

angle of inclination of the centre line of the dam at the point of application of 
relative to the section BD. 

Thus, the absolute deflection and angle of inclination measured from the 
foundation are: 


Am—i §m_]. ~t “a tan / 3 Hl and tan / 3 m—i — tan / 3 Wi ,-j-tan y-m— i* 

Similarly we can calculate : 

Am—2 Am—i "P §m—2 ~h ^ tan / 3 m—i and tan / 3 m—2 — tan / 3 m—1T tan y r a— 2. 

In this manner all the deflections A m . ... A x can be expressed as linear 
functions of X m .... Xp 

Now, in accordance with the usual methods of treating statically indeter¬ 
minate structures, put: 

A n — D?j 

We thus obtain m linear equations connecting: 

X H1 .... Xj and .... Pi 

Solving these equations, we obtain X m .... X 1} in terms of the water 
pressures. And thus the dam sustains the X loads as a gravity dam, and the 
(P —X) loads as an arch. 

The method is laborious, and could be improved at the cost of some extra 
liability to error by assuming the points of application of X m , X m -i, etc. as 

being -, —, etc. above the base of the dam, and the changes in slope of the 
2 2 

faces as occurring at a, 2a, etc 

I may refer to a paper by Messrs. Harrison and Woodward on the Lake 
Cheesman Dam ( T}-ans. Am. Soc. of C.E., vol. 53, p. 89), for two very 
able discussions of similar methods by the authors, and Mr. Shirreff. I have 
combined the two methods, as I felt that in order to obtain any accuracy in 
such calculations it was imperative to use formulae which are comparatively 
simple, and are logically deduced. If theoretical advantages alone are con¬ 
sidered, a really skilled computer might with advantage follow Mr. ShirrefFs 
method entirely. 

Vischer and Wagoner {Trans, of Technical Society of Pacific Coast , 1888) 
have endeavoured to investigate the question in a general fashion. They find 




4 o8 CONTROL OF WATER 


that for a triangular dam (top width = o) spanning a gorge with vertical sides 
( i.e • L — constant): 

P-X_ 2X 2 
P “R 2 + 2;r 2 

where x, is the height above ground level. 

According to Duryea (ut supra , p. 180), in a dam 126 feet high, with R, 
averaging 180 feet, and L, varying from 300 feet at the top, to 25 feet at the 
X 

bottom, p varies from 0^84 at the top, to 0^95 midway down, and is 0*99 at the 
bottom. 

In the Lake Cheesman Dam, which is very close to a gravity section: 


—=o - 54 0*90 0-94 0*98 
at points ^ ^ T % {ij 


1*00 

the height of the dam, 


and the radius is 400 feet, with L, varying from 580 feet downwards. 

The object of the above theory is to provide a method that will permit some 
result not too wide of the truth being obtained for preliminary designs, within 
a reasonable time. This having been done, the design can later be refined on 
as much as is deemed wise, by assuming more numerous sections. In this 
connection I would remark that the real assumptions are that the dam is 
sliced horizontally when the arches are considered, and vertically when the 
cantilever is considered. This really means that shear is partially neglected 

X 

in each case. Thus, we may assume that the ratio is liable (how¬ 


ever fully this theory is developed), to an error of at least 5 per cent, of 
its own value (more probably 10 per cent., that being equal to about 
, modulus shear \ . r 

^ modulus of elasticity / Consequently, refinements of greater apparent 

accuracy in calculations based on this theory need experimental justification. 

I believe that the theory is fairly accurate, as any treatment following the 
ordinary principles of elasticity seems to produce approximately the same 

X 

values of the ratio —. 

Jr 


As an actual example, it may be stated that in the Bear Valley Dam the 
maximum stresses are: 


, 

(i) As a pure arch, 40 tons per square foot. 

(ii) By the above method, with 5 loads, 33*5 tons per square foot. 

(iii) Ditto, 10 loads, 33*1 tons per square foot. 

(iv) By correction by the approximate formula already given, 327 tons 

per square foot. 

We are consequently justified in assuming that the actual pressures do not 
materially exceed 33 tons per square foot, and that the shear is therefore about 
36,000 lbs. per square foot; which, although high, need not necessarily produce 
failure. 

X 

It is perhaps advisable to state that the value of the ratio —, is to a certain 

extent under the control of the designer. 

Such dams as Wade’s, which are primarily designed as arches, will be 






RATIO OF ARCH TO GRAVITY LOAFS 


409 


found to have small values of -p. Similarly, if a curved dam be designed as 
a gravity dam, but with a somewhat higher stress than usual ; and the section 
thus obtained is then investigated as above, the values of —, will be found to be 



Radii of Centre 
Lines of Dam 

R.L. 

Radius 

90 ' 

50 

87 

52 

809 

54-2 

71 

55A5 

63 

53-50 

55 

57-50 

57 

57-63 

39 

58-00 

31 

58-00 

85 

57-57 


Sketch No. 117.—Proposed Domed Dam at Ithaca. 


I 































4 io 


CONTROL OF WATER 


large. The relative increase in p, as we proceed towards the foundation will 

be found to occur in all cases. The dome shaped arch section adopted by 
Williams at Ithaca, N.Y. ( Trans. Am. Soc. of C.E., vol. 53 j P* * s 

X 

singularly bold, and has apparently been designed so as to keep —, fairly 

constant all over the dam. Such designs seem to be well adapted for closing 
gorges with nearly vertical walls of firm rock. They are, however, not likely 
to meet with the approval of unskilled engineers ; indeed, the design has not 
been carried out in its entirety, and it is fairly evident that the real reason was 
that the Committee which investigated its safety, although capable of testing 
the calculations, did not fully rely on the results obtained. This, I consider 
creditable conservative practice, but in the light of Wade’s experience there is 
little doubt that the Ithaca design is safe, provided that the precautions against 
under-mining at the base of the dam are sufficient. Personally, I would con¬ 
sider these insufficient unless the rock were perfectly flawless. 

Arch and Buttress Dams. —These dams are composed of a succession 
of arched dams, bearing against piers or buttresses, which are sufficiently wide 
to carry the stresses produced by the water pressure on the halves of the two 
arches which abut against them. 

The calculation of the arches may be effected by the methods already given, 
and the buttresses are determined by the rules used for gravity dams. 

It is stated that a certain economy in material (when compared with a pure 
gravity dam) may be secured by the adoption of this type. But when the unit 
costs of cut stone masonry, or of thin concrete with complicated shutterings, 
are respectively compared with those of rubble masonry or mass concrete, it 
becomes extremely doubtful whether any economy in the total cost can be 
secured except under very peculiar circumstances. 

From a theoretical point of view, the arch and buttress dam combines the 
disadvantages of both types of dam. The stresses in the arches are in¬ 
determinate*-to the same degree as those in a curved dam. All the objections 
raised by Atcherley to gravity dams, as at present designed, can be urged 
against the buttresses. The type therefore appears unlikely to be adopted, and 
will not be further discussed. 

Reference may be made to : 

(a) The description of the Meer Alum Dam, Hydrabad (India), in 
Engineering News of the 18th June 1906. 

( \b ) A very excellent paper by Garrett, “ Theory of Arched Masonry Dams ” 
(Government of India Technical Publications'). 

Design of Reinforced Concrete Dams. —Reinforced concrete dams 
are as yet mainly confined to America. Possessed of many theoretical 
advantages, it is probable that the few failures on record are principally due to 
over confidence placed in the principles of their design, and insufficient care 
given to workmanship and good foundations. 

When properly constructed, there is little doubt that, as a type, reinforced 
concrete dams are by far the most satisfactory form of dam. r But it is 
evidently quite useless to construct a dam which is satisfactory in itself, if the 
foundations are insecure, and many of the earlier dams possess foundations 
evidently designed in accordance with sound rules for houses, or bridge piers, 
but which are quite useless when applied to dams. 


REINFORCED CONCRETE SLABS 


411 


It therefore appears that success will be attained by utilising American 
experience for that portion of the dam above ground level, and (like the newer 
American designs) following the methods adopted in dams of other types as 
regards design of foundations. 

Above ground, the dam consists of a series of buttresses of triangular 
section, carrying a flat slab of reinforced concrete on their upper face. 

The dam may be designed as an overflow dam, or may be provided with a 
separate waste weir, as circumstances require. 

I propose to consider the design of an overflow dam, and the modifications 
necessary when there is a separate spillway will be evident. 

Let the horizontal distance between the centres of the buttresses be l feet. 

Let the length of the slope of the upstream face of the dam be s times 
its height. Then, at any depth //, below the high flood level of the water 
passing over the spillway (which, as a first approximation, we can assume as 
5 feet above the crest of the dam), the pressure per square foot of the slab face 
is 62*5/2! lbs. 

Thus, the bending moment per foot width of slab at the centre of the slab, 
assumed as non-continuous, is : 


^ foot-lbs., or say equal to ~ . 
8 8 


If the slab is continuous over several buttresses, theoretically the bending 
moments in each span vary according to the total number of spans. The 
variation is of importance only when there are less than seven spans. Owing 
to the fact that long lengths of concrete are liable to crack by expansion, it is 
doubtful whether continuous slabs are advisable. If, however, the slabs are 

built continuous it is safe to provide for a bending moment of —, at the centre 

of each span, producing tensile stresses on the downstream side of the slab, 


and a bending moment of —, at each support, producing compressive stresses 

20 

on the downstream side. For the two end slabs, close to the point where the 

dam is joined with the hillside, the theoretical bending moments largely depend 

on the exact manner (freely supported or built-in) in which the end buttresses 

and slabs are connected to the hillside. In good construction it is probable 

that the connection is so complete as to justify the assumption that the slabs 

K K 

are built in, but it is safer to provide for ~, over the two end buttresses and -g, 

at the centre of each of the two end slabs. So also, theory shows that the 
pressures on each buttress are not exactly those given by the rules for non- 
continuous beams, being roughly 1*01x62*5^/, and 0*99x62*5^/, alternately. 
Such differences are negligible, except in the case of the first buttress at 


each end of the dam, where ^x62*5 hi (exactly 1*134 for 9 spans) should be 

8 

provided for per foot width of the slab. 

Many theories exist concerning the proportions of reinforced concrete 
beams and slabs. 

The following rules are principally based on the methods adopted by 
Marsh (Reinforced Concrete ). Considerations of space prevent a full discussion 
of the matter, and a design obtained by these rules should always be carefully 
checked for shearing and adhesion stresses before being finally passed as 



412 


CONTROL OF WATER 


correct. In my own practice, however, I have invariably found that the rules 
are sufficient, and believe that in hydraulic work generally the beams and 
slabs are too thick (owing to the necessity for preventing percolation) to permit 
the above stresses ever becoming unduly intense. Marsh’s treatise, and the 
Reinforced Concrete Pocket Book , by Messrs. Marsh and Dunn, are, however, 
indispensable, and even in preliminary designs their tables and diagrams save 
much time and labour. 

Let b , represent the breadth of a beam, or slab, in inches. 

Let d represent the depth of the beam or slab from the compression face to 
the mass centre of the reinforcement on the tension side. 

Then, if M, be the bending moment in inch-pounds which the beam has to 
sustain : 

M = ju6o obd 2 (M in inch-pounds) . . . [Inches] 

M = n$obd 2 (M in foot-pounds) .... [Inches] 

The analogy with the ordinary formulas for timber beams is obvious. Just 
as in the case of timber beams the coefficient of bending strength depends on 
the species of timber, so in reinforced concrete beams the coefficient /x depends 
on the ratio of the area of steel to the area bd , the effective area of the concrete. 

[. Note .—The tensile reinforcements being buried from to 2 inches in the 
beam, the gross area of the concrete is at least (d -\-1 \)b square inches.] 

Put cot — the area of the steel reinforcement which is on the tension side of 
the beam. 

Put oi c — the area of the steel reinforcement which is on the compression 
side of the beam. 

Then Marsh and Dunn give as follows : 


VALUES OF fji 





W c 

, ! 



bd 

0 

0 ' 2 CJ t 

0 * 4 (J« 

o' 6 u)( 

o‘ 8 w t 


0*005 

0*14 

0-15 

0-15 

o'i6 

0*17 

0*17 

0*0075 

o*i6 

0-17 

o*i8 

0*19 

0*20 

0'2 I 

O'OIO 

0-18 

0-19 

0*20 

O'2 2 

0-2 3 

0*24 

0-015 

0*20 

0*22 

0*24 

0-26 

0-28 

0-30 

0*020 

0*22 

0-24 

0*27 

0-30 

0-32 

°' 3 S 

0*02 5 

0-23 

0*26 

0-30 

°*33 

o *37 

O-4O 

0-030 

0*24 

0-28 

0-32 

0-36 

0-40 

o *45 


The required cross-section can therefore be obtained by trial and error. 
The original diagrams give three significant figures, and enable the required 
section to be selected at once. 

In the case of continuous slabs co t denotes : 

(a) At the centre of a slab, the steel on the downstream side. 

(b) Over a support, the steel on the water-face side. 

Accurate testing of the design for stresses induced by shear and cohesion 
requires tables, or lengthy calculations. In preliminary designs let F, denote 

































STRESSES ON A BUTTRESS 


4 i 3 


the greatest shear in pounds. Then, if F, be less than 50A/, the design is 
usually quite safe, and can certainly be rendered absolutely safe by inclining 
the steel rods, or turning up their ends, without increasing the weight of steel. 
The patented methods are not considered, as each patentee has his own 
rules. 

In the case of the slabs facing the dam we have to consider a width of one 

K 62*1 ‘Jit 1 

foot. Thus, <£=12, and M = g-—^— foot-lbs. per foot width. 

Thus, i2cp . [d, in inches] 

hi 2 

or, d 2 =— . . . 17/ inchesl for a non-continuous slab. 

77/x 

We can thus determine the thickness of the slabs at every point. 

Now, it is plain that percolation must be carefully guarded against. This 
is easily effected in a non-continuous slab, as all the reinforcement lies on the 
downstream face of the slab. In a continuous slab, however, the water face is 
in tension over the supports, and some steel must be placed near the water 
face. Thus, it is probable that the extra thickness of concrete necessary to 
protect this steel from action by water will counterbalance any decrease in 
thickness, or percentage of steel, that might theoretically be obtained by 
continuity. 

It also seems probable that future experience will show that a layer of 
waterproof material at, or near to, the water face of the slabs is advisable, 
although, so far as I am aware, no such construction has yet been adopted. 

We can now proceed to proportion the buttresses. Theoretically, the 
work is carried out just as for a solid dam, the buttresses having to support 
water pressures indicated by 62*5 /ils, lbs. at each foot of height, and their own 
weight. 

In actual practice, the dam is not usually founded on hard rock, and its base 
is therefore about one and a half times'to twice its height. In such cases tension 
in the buttresses does not occur, as can be seen by merely inspecting the 
annexed sketch (No. 118). 

It will be found by actual trial that the easiest method of design is to 
proportion the buttresses so as to produce a safe intensity of pressure on the 
foundation, and to make them of triangular section from this level upwards. 
It will then be found that such buttresses are of ample strength when tested on 
any other section ; and, as a matter of fact, in actual dams, passage ways and 
arched openings are frequently made in the buttresses, either to save material 
or to provide a means of communication along the dam. 

Let us therefore assume the following : 

The thickness of a buttress at its top is /, feet (usually about o*8 to 1 foot). 
At the base, or at the level at which it is proposed to investigate the stresses, 
let the thickness be represented by d, feet. 

Let H l5 be the height, and L l5 the base length of a buttress ; each measured 
at the level where the stresses are to be investigated. 

Then its thickness at any height x, above this level, is represented by 





CONTROL OF WATER 


414 

Thus, the volume of a buttress is : 

I^Hj 

T" 3 

and its centre of gravity lies in the median line of the buttress at a height: 

t-\-ci 
2 t + 2d 

So also, the volume of the upstream slab is represented by : 

2 

where t x , and d x , are top and bottom thickness of the slab, and 4, is the 
distance between the nearer faces of two adjacent buttresses, and m = H x s is 



Sketch No. 118. —Diagram of Forces acting on a Reinforced Concrete Dam. 


the slant length. The centre of gravity lies very approximately in its face at 
a distance : 


m 2t l J r d l 
3 t 1 + d 1 


from the bottom, measured along the slope of the slab. 


It is plain that the variation in l x ( = l— t at top of dam, and /— d, at the 
bottom of the dam) has been neglected. In preliminary calculations the error 
is inappreciable. If it is desired to use the accurate formulae they are : 

Volume of slab : 



Q- d) (d x - t x ) - d x (d - t) _ (d x -t x ){d - /)) 
2 3 / 


Distance of mass centre along median line of slab : 



(/ - d)d x _ (/ - d) {d x - t x ) - d x (d — t) _ (d x — (d - t) 
2 _ 3 _ 4 

^^ ^ C d) (d x ^1) d x (d /) (d x /j) {d t) 


We have also the top of the dam to consider ; the thickness of this depends 
on whether we use it as a bridge, or fix dashboards on it, or merely shape it as 
a parabola to secure the best discharge. 









































DIAGRAM OF STRESSES 


4i5 

In this particular case, I take it as 4/^ cube feet, i.e. 3 feetx 1 foot 4 inches, 
in section, and assume that the mass centre is immediately over the apex of 
the buttress. 

The downstream face of the dam is (in a spillway type at any rate) covered 
with slabs. The thickness of these cannot be determined by any ordinary rule. 
If we regard the depth of water flowing over the dam as the determining factor, 
we find a pressure of at most 312 lbs. per square foot, assuming a depth over 
the dam of 5 feet and taking no account of the velocity of the flowing water, 
which would tend to diminish the pressure. 

As a matter of practice, we find in spillway dams, that such damage as 
occurs is apparently due to a partial vacuum induced by the flowing water ; and 
the form of crest that theoretically, at any rate, prevents the formation of this 
vacuum is discussed on page 400. 

In a hollow dam, such as we are now considering, it is plain that a few 
holes in the slabs, should prevent any vacuum. I find that the best practice 
in America usually makes the thickness of the slabs about two-thirds / l5 say 
12 inches. 

The volume is plainly /;z, where «, is the length of the downstream face, 

3 

and the mass centre lies in the middle of the length of the slab. 

We have thus estimated all the weights, and can combine them into one 
resultant, which is best done graphically, as shown in the sketch. 

We have now to estimate the water pressure. This is as shown by the 
trapezoidal stress diagram. Its magnitude in the present units, i.e. the weight 
of 1 cube foot of reinforced concrete is : 

I . . r - • , ' » 4* , j | ! , f r \ M 

hn Ht+2 h x 

7 2 

where h x , is the overflow depth ; and for a first approximation we can take p = 2. 
Its line of action is normal to the upstream slab, and cuts it at a distance ; 

m . 

— X * J r 1 from the base, measured along the slab. 

3 Hj + 2 h x 

Sketch No. 118, which is purely diagrammatic, and does not indicate good 
proportions, shows a case : 

L/=45 feet ^ = 30 feet ^ = 5 feet i= 1 foot d = 2 feet 
l —15 feet A=°'5 foot ^i = r 5 foot ^ = 3 6 ‘° feet n = 3°‘5 feet 

and the forces expressed in units of 125 lbs. = weight of 1 cube foot of concrete, 
as ascertained and laid off from the above formulae. 

The total vertical pressure produced by the weights and water pressures is 
4451 units = 556,000 lbs. Allowing for the eccentricity of the resultant the 
maximum pressure is, 

2 x 6i8o( ^ x _ j j — 7622 lbs. per square foot, 

V 45 / 

and the minimum pressure is : 

2 x 6 i 8 o( 2 - 3 X 2 -^| 5 )= 473 8 lbs - P er square foot. 






4 i6 CONTROL OF WATER 

These are pressures of a magnitude such that they can be resisted by even 
the weakest rock. 

The total horizontal shear produced by the water pressure is 3945 units, or 
493,000 lbs. Thus, the average shear is 5480 lbs. per square foot, which is a 
greater intensity than most of the weaker rocks can be expected to sustain, 
especially if fissured. Thus, as already indicated, the foundations of a rein¬ 
forced concrete dam form its weak point. 

The work now proceeds exactly as for a masonry dam, and the pressures and 
shears can be laid down as in the example worked out. 

It should also be noted that the section of the dam should be tested at several 
points above the base. 

In American practice, tensions are permitted in the upper portions of the 
buttresses. In view of the fact that we are dealing with reinforced concrete 
this appears allowable, and if the experimental results found by Wilson and 
Gore, and others, for solid masonry dams, are considered as applying to the 
buttressed type, it is advisable to reinforce the buttress near the angle A. No 
rules can be given for this reinforcement. 

Similarly, while the horizontal slab reinforcement is easily calculated from the 
stresses, some vertical reinforcement is needed in the face slabs. So far as can 
be judged experimentally, temperature cracks are possible, unless the area of 
steel in the vertical reinforcing bars exceeds o'3 per cent, of the area of the 
concrete in the slabs. No dam that I am aware of has so large a percen¬ 
tage of vertical reinforcement, but it must be remembered that reinforced 
concrete dams are new, and few of the older examples greatly exceed 30 to 
40 feet in height. If a smaller percentage of reinforcement be adopted, the 
designer can at anyrate console himself with the consideration that such cracks 
as do occur can be repaired without necessarily causing a disaster. 

I also notice that some dams are so proportioned as to be in tension, not 
only in the upper portions of the buttresses, but also at the base. This, I 
consider, is a departure from good practice, and I believe that such dams are 
unsafe. 

Foundations. —The design of foundations depends on the character of the 
material on which the dam rests. 

In really solid rock, a shallow seepage trench is perhaps all that]is necessary ; 
but, in gravel, or fissured rock, it appears to me that the only safe rule is to 
follow the practice evolved for earth dams. We have one great advantage,— 
our impermeable wall being of concrete, cannot be injured by burrowing 
animals, and we can therefore put it right in front of the dam. 

I prefer the following design : 

A concrete core wall carried down either to an impermeable stratum, or to 
such depth as investigation of the material, conducted on the lines discussed 
under earth dams, shows to be necessary. Behind the core wall is a small 
stone drain, as discussed under earth dams, which should be connected with 
one or more vent pipes. 

The whole floor of the dam is covered with a layer of concrete, the thickness 
of which need only be 4 inches for good foundations, and, in the case of bad 
soil, may be reinforced so as to spread the pressure of the buttresses, if any 
doubt exists as to their foundations being of sufficient width. 

At the tail of the dam is another core wall, the depth of which is fixed by 
the scour produced below the dam by the overflowing water. The sections on 


RETAINING WALLS 


4i7 

Falls, and Weirs may be consulted when determining the site and thickness 
of this tail wall. 

It may also be pointed out that lines of steel, or cast-iron sheet piling, may 
be substituted for the core wall or walls, but such work, unless carefully executed, 
is liable to prove faulty : and I doubt whether it will be as satisfactory even from 
the point of view of cost ; since each core wall should probably be replaced by 
a double line of piles. 

Some dams exist which depend on several shallow core walls in place of 
two deep ones. Personally, I doubt whether such foundations are trustworthy, 
but they appear to be satisfactory for heads up to 30 or 40 feet. 

In such cases, a very wide foundation similar to that of an Indian weir is 
necessary. It therefore seems doubtful whether expense is saved, more especi¬ 
ally as in any soil fit for a dam foundation it is usually possible to sink a deep 
trench and fill in with concrete. 


ML fl£0d_696 _ 



Concrete wall carried down 
to below rock lore I 


In Clay, concrete wall goes to day 
k base of Oam is floored with it' 
concrete with drain holes 5 ‘c. toe. 
Buttresses are provided with tontines. 


auxiliary Oam U'hioti needed 
unless foundation is hard rock. 


Sketch No. 119. —Design for a Reinforced Concrete Dam. 


Earth Pressures on Retaining Walls. —The pressure of earth or 
similar materials, differs front that of water in one very marked respect. The 
pressure is not necessarily normal to the surface across which it acts. If this 
were the only difference, it would not be difficult to obtain an accurate theory, 
but all earthy substances also possess a certain amount of cohesion, and there¬ 
fore neither the magnitude nor the direction of the pressure at any given point 
can be calculated. Dry sand may be considered as possessing very little, and 
hard clay, or earth rammed in horizontal layers, a great deal of cohesion. 
Since the effect of cohesion depends very largely on the state of the earth, and 
probably varies greatly from time to time, in the same piece of earth, and can 
certainly be considerably affected by the manner in which the earth is treated, 
it seems useless to endeavour to define it exactly,—and, consequently, no 
mathematical method of estimating its effects exists. 

The method now put forward neglects the effect of cohesion entirely, and 
therefore considers earth as differing from water only by the existence of 
27 







































4r8 


CONTROL OF WATER 


oblique pressures. Thus, the theory is extremely defective, but it errs on the 
side of safety, and walls which, when treated by this theory are only just stable, 
may be assumed to actually possess a factor of safety which varies from J g °- in 
the case of artificially dried sand (which possesses no cohesion) to 5, or more, 
in the case of hard clay not exposed to the weather, where the cohesion is so 
great that the pressures might be entirely neglected. The theory is believed 
to be applicable only to earth that has been disturbed ; and at great depths in 
undisturbed earth, such as must be considered when designing timbering of 
deep trenches, it is absolutely misleading, and as a rule greatly over-estimates 
the pressure. 

In practice, the rules obtained by following this theory lead, in ordinary 



Sketch No. 120.— Earth Pressures on Retaining Walls. 


Brunei 's Section 


cases, to retaining walls of safe, but not unduly extravagant sections, and may 
therefore be considered as guides for design. It must, however, be remembered 
that the theory assumes a state of things which we know but rarely occurs, and 
which, when it does occur, usually causes the wall to crack. 

As in Sketch No. 120, let CA, be the inner face of the wall, and HCS be the 
angle of repose of the earth, so that CS, would be the face of the earth if there 
were no wall. 

Let AX, be the terrain line, or top of the earth which rests against the 
wall. 

Now, draw any line CX l5 and let us assume that the earth is about to slip 
down this plane CX 1} and cause the wall to overturn. 

Then, the forces acting on the wedge of earth ACX 1? are as follows : 











WEIGHT OF EARTH 


419 

(i) W l5 its weight, which, considering a length of 1 foot of the wedge or 
wall, is given by: 

Wj = p x area of triangle ACXj 

where p is the weight of a cube foot of the earth. 

(ii) R l5 the pressure of the wall on the wedge. 

(iii) Qx, the reaction of the undisturbed earth acting across the face CXx. 

Now, since it is assumed that the wedge is just about to slip the ordinary 

rules of statical friction hold. Thus R 1} makes an angle x with the normal to 
the face CA, of the wall, and Q 1} makes an angle (f) with the normal to CX 1} 
and since these forces resist the downward motion of the wedge they are both 
directed upwards. The problem is therefore reduced to the statical problem of 
determining the magnitude of two forces, acting in given directions, when the 
magnitude and direction of their resultant (W l5 in this particular case) are 
known. 

The solution is therefore easily obtained as follows : 

Let a and 0 1 be the respective angles between the directions of R x and Qx 
and the vertical. Draw TA, making an angle a with XjA, and from X x , draw 
PxXx making an angle $x with AX, and cutting AT, in Pi. Then plainly AXj, 
is proportional to the weight of the wedge ACXx, and can therefore be taken 
as representing Wj, in magnitude, and, on the same scale, the lines APx, and 
P1X1, represent the forces Rx, and Q x . 

Thus, APx, represents the pressure of the wall on the wedge on the wall 
when CXx, is taken as the boundary of the wedge. A similar construction can 
now be effected when any other line CX 2 , is taken as the wedge boundary. 
The only differences are that since Wj, is not equal to W 2 , AX 2 , is not equal to 
AXj, and the angle 0 2 = P 2 X 2 A is not equal to the angle #i = PiXiA. Hence, 
we get a new value for the pressure of the wall on the wedge, AP 2 = R 2 say. 
Now, by trial and error the position of the line CX, say CX m = CX 2 in Sketch 
No. 120, which gives the largest value of AP m (= AP 2 ) can be selected. Let 
this be denoted by R w . 

This theory is almost entirely a pure assumption. All that can be said is 
that when AX, is horizontal it leads to a position CX m , which agrees very well 
with experiment, but when AX, is either sloping in the same direction as CS, or 
is oppositely directed, Darwin’s experiments on sand (. P.I.C.E ., vol. 71, p. 350) 
seem to indicate that results agreeing more closely with experiment are obtained 
by assuming that X, H C bisects the angle ACS. 

The difference, however, is not very great, and the construction given above 
seems safer. 

Now, let us consider the forces acting on the wall. 

These are R m , which we know, both as regards magnitude and direction, and 
which we assume (both on experimental evidence and on the analogy of water 
pressure) to act one-third of the way up CA, the weight of the wall, and the 
pressures and shears on its base. 

The distribution of the stresses on, say, the cross-section CK of the wall can 
therefore be calculated by the rules already given under Dams. 

We may assume that </> is about 30 degrees, and that x is about 20 degrees. 
These assumptions are probably somewhat unfavourable. Earth weighs from 
112 pounds per cube foot, which is probably a slightly low estimate, up to 125, 
pounds per cube foot, if heavy clay is considered. Thus*p= r8 to 2’o. 


420 


CONTROL OF WATER 


The resultant of R m , and Y, the weight of the wall, should fall slightly inside 

CK 

the base CK, say at M, where MK = -g-* 

Engineers are usually satisfied with testing the stability of the full height of 
the wall, but the method is plainly applicable to any portion of its height. 

Bligh has carefully investigated type sections of walls by this method 
( The Practical Design of Irrigation Works'), and deduces that: 


“ The back face of a wall should be vertical, or inclined towards the 
earth, any batter required being given to the front face of the wall.” 

This is somewhat opposed to ordinary practice, but the reasons are obvious. 
If the front face of a wall is inclined, either specially cut bricks or stones are 
required, or the beds of the masonry cannot be set horizontal, and thus provide 
a possible channel for entry of rain water into the wall. 





Sections shown arc for H=25'. Density of Earth H2-5 lbs. here. ft. Masonry 151-3 tbs.perc.ft. 
Sketch No. 121.—Typical Sections of Retaining Walls. 


Nevertheless, the economy obtained by walls with face batters is so con¬ 
siderable that the extra expense of cut stones or bricks is justifiable wherever 
the walls considerably exceed 20 feet in height. 

For example, let us take the sectional area of a wall 25 feet in height, as 
proportioned by Bligh:— 


Face Batter. 

Vertical. 

0 

I in 10. 

i in 8 . 

1 in 6 . 

1 in 4. 

General ex¬ 
pression for 
bottom width 

o- 4 H 

M 

1 

b 

o' 4 H-i‘ 5 ft. 

o- 4 H-2*5 ft- 

o’ 4 H- 4 ft. 

Area of cross- 
section for 
25 ft. height, 
and 2 ft. top 
width . 

4 

7 37'5 

K3 1 

119 

100 



















































RETAINING WALL SECTLONS 


421 


Sketch No. 121 shows typical designs of walls. Bligh’s rules agree very 
well with the practice adopted in Indian irrigation, and it is believed that the 
proportions given will suffice to secure safety under unfavourable circumstances. 
It may indeed be said that were it not for the fact that the top width of a wall 
is not always 2 feet, and that the terrain line is not always horizontal, the above 
sketch would provide all that is required in practice. The theory will be found 
of the greatest utility not in proportioning the cross-sections of walls, but in 
selecting the design which is best adapted to local conditions, from among a 
series which has already been determined by eye or by experience. This view 
is admirably illustrated by Brunei’s section, Sketch No. 120. This section is at 
first sight very thin, and “ looks weak.” When tested by the above theory it 
will be found amply stable, and in practice it produces very satisfactory results. 
In all cases it is as well to remember that a cracked retaining wall is not a 
disaster, and that a section which will not crack under any imaginable circum¬ 
stances is an impossibly extravagant ideal. 

Practical Details of Construction .—The function of a retaining wall is pro¬ 
bably far more that of protecting the cohesion of the earth from being destroyed 
by the action of the weather, than of actually retaining the earth in the sense 
that a dam retains water. 

The necessary construction therefore is as follows: 

(a) Keep the water, as far as possible, away from the back of the wall, 
but give it a free vent through the wall by means of weep holes. 

(f) If the foundation of the wall becomes saturated, it is only a question 
of time when the wall will slip. 


* 


CHAPTER VIII 
PIPES 

General Considerations concerning the Motion of Water in A Pipe. 

Entrance Head. —Practical Rules. 

Formula for the Discharge of Pipes. 

General Formulae. — Tutton’s formula — Skin-friction equation — Logarithmic 
formulae—Rough rules. 

More Exact Formulae for Existing Mains. —Experimental results—Extension to 
large pipes. 

Measurement of the Discharge of a Pipe. —Use of colouring matter—Practical 
details. 

Effect of age on pipes. —Limpets—Protective coatings—Calcium carbonate incrusta¬ 
tions—Slime—Silty, or nodular deposits. 

Angus Smith’s Process. —Original process—Newer methods. 

Cleaning and Scraping Pipes. —Torquay records—Melbourne practice—Table of 
discharges before and after scraping. 

Formula expressing the Deterioration of Cast-iron Pipes with Age.— 
Table of values of C, for old cast-iron pipes—Examples of small uncoated pipes— 
Exceptions. 

Darcy’s Formulae. 

Cast-iron pipes. —Thickness of pipe metal—Grashofs value for thickness—Hawksley’s 
and Unwin’s rules—American rules. 

Pipe Joints. —English and American rules. 

Design of Joints in Cast-iron Pipes. —Examples—Summary. 

Pipe La ying. —Specification—Remarks. 

Large Wrought-iron or Steel Riveted Pipes. 

Skin friction coefficients. —Allowances for obstructions by rivet heads and plate edges. 

Distortion of Riveted Pipes. 

Corrosion of Steel Pipes. 

Specification. —Coating—Remarks—Tests for steel. 

Locking Bar Pipe. 

Construction of Steel Pipes. —Rules for riveted joints—Allowance for corrosion— 
Minimum thickness of plates. 

Anchoring Pipes. 

Wood Stave Pipes. —Construction—Calculation—Preliminary experiments. 


SYMBOLS EMPLOYED. 


A, is a coefficient in the equation h = AQ M . 

B, is a coefficient in the equation h = l$Tf n . 

Thus, B=(^)"a 

C, is the skin friction coefficient in the equation v = C Jrs. 
Q, is the friction coefficient in Tutton’s equation : 


v = C 1 


0.67- ft 0 . 54 -fl 
r s 


422 


PIPE FORMULAE 


423 

d, is the diameter of the pipe in feet, and D, is used when inches are employed as the 

unit. 

db, is the diameter of the pipe bands in inches. 

e, is the safe pressure on wood staves in pounds per lineal inch of the band (see p. 466). 
E" (see p. 467). 

f, is the band spacing in inches, f— . 

F, is the safe tensile stress of cast iron = 1850 lbs. per square inch. 

A, is a factor allowing for the reduction in area caused by rivet holes or corrosion. 

h , is the head in feet lost by skin friction in a given length /, of pipe. Thus ~ = s. 

H, is the maximum internal pressure, in feet of water, to which the pipe is exposed. 

kl 

k, is a coefficient such that B = — (see p. 431). 


h kv r ' 


/, is the length of the pipe in feet. 

m, and n, are the indices of d , and v, in the equation-^ — 

N, is the number of bands per 100 feet length of the pipe. N = 


1200 


/ 

/, is the pressure corresponding to H, feet of water, measured in pounds per square inch, 
is the stress in pounds which a band of diameter d ,& inches can safely sustain. 

7 T 7 o 

<7 - uj) s-^, 

4 

Q, is the stress in pounds actually sustained by a pipe band. 

R, is the internal radius of the pipe in inches. R = ^. 

r, = — is the hydraulic mean radius of the pipe in feet. 

4 

dj) 

is the radius of the pipe bands in inches = — • 

.r, is the sine of the slope of the hydraulic gradient of the pipe. s ~~f 

s v is the safe working stress of the metal of the pipe, or of the pipe bands. 

5-3 (see p. 467). 

/, is the thickness of the walls of the pipe, in inches. 
t(h tin (see p. 445). 

T, is the circumferential tension, in pounds per lineal inch, in the walls of the pipe. 
v, is the mean velocity of the water in the pipe, in feet per second. 

W, is the central load in pounds that a pipe can sustain as a beam under a maximum 
stress of 1850 pounds per square inch. 


SUMMARY OF FORMULAE 

Entrance head =— (1 + a ) a = o*20 to o 50 (see p. 426). 
2 £- 

Tutton’s formulae: 

v—Cyr 67 ~^ s °* 5 °^^ (seep. 427). 

U *66 0 «51 j \ 

New r cast-iron pipes, 21=140 r s ' see P- 4 2 9 ;- 

0-66 0.51 

Old cast-iron pipes, 21=105?' ^ (seep. 429). 

Skin friction formulae, v=C sirs 

C = C 1 /’ 17 - For table (see p. 478). 

Logarithmic formulae, h = AQ n =B2? M 

h 7 v n 




424 


CONTROL OF WATER 


. , ,, Discharge when new 

Discharge of a pipe y years old =- 

Cast-iron pipes (see p. 444). 



Grashof, = H 3F + 4/ “ 1 f F = 1850 lbs. per square inch. 

Hawksley,/ H = 0-18^0 ...... 

Unwin, t m = o’ii ^/D + o'io ...'.. 

Steel pipes, t=^~ (see p. 462) ..... 

J\h 

Wood stave pipes, N = (see p. 465) 


[Inches] 

[Inches] 

[Inches] 

[Inches] 

[Inches] 


General Considerations concerning the Motion of Water in a 
Pipe. —Consider the usual case where water is drawn off from a large reservoir 
through a pipe. Assume that the velocity of water in the pipe, when the motion 
is steady, is v feet per second. 

If the loss of head between two points P and Q, in the pipe be observed, it 
will be found that (abnormal irregularities, bends, and other obstructions in 
the pipe being neglected) the loss is proportional to the length of the pipe 
between P and Q. 

The question of the determination of the absolute magnitude of this loss is 
considered in detail later. The general theory, however, shows that if we 
consider the motion from a point R, in the reservoir where the velocity is very 
small, to a point P in the pipe, where the velocity is v ; there must, apart from 


•u* 


all frictional resistances, be a loss of head equal to or rather, a portion of 
the initial pressure energy of the water is transformed into velocity, and the 
pressure consequently diminishes by — feet of water. The term Hydraulic 

—v> 

Gradient is defined on page 471. Sketch No. 122. 

Entrance Head.— We are thus led to consider the “loss of head at 
entry into the pipe.” Reviewing the matter in detail, we find that the total 
localised loss of head which occurs at and near the entrance to the pipe, and 
is independent of the length of the pipe, can be expressed by : 


V 1 


2 & 
<b 


(i+«) 


where a — , represents the resistance of the entrance of the pipe considered as 
an orifice discharging water at a velocity of v feet per second. 

In theory, a — -L — i ? so that a varies from about o’o6 for a pipe with a bell- 

Cd 

mouthed entry, to o'5o for a pipe projecting into the reservoir (see p. 140). 

Actual experimental data are rarely given, and modern experimenters have 
usually found that the flow downstream of the entrance to a smooth pipe does 
not become turbulent for an appreciable distance, roughly 50 to 100 times the 
diameter of the pipe. Thus, it is quite possible that a being masked by the 









HEAD LOST AT ENTRY 


425 

decrease in resistance over the length of pipe in which the flow is not turbulent, 
might be apparently negative. In some experiments of my own on a 12-inch 
pipe, in which theoretically a = o’$o, I found an irregular series of values of 



This sketch is an attempt to show graphically the difficulties attending a correct 
estimation of the “head lost at entry” into a pipe, and is founded on observations made 
on a 12-inch pipe at a mean water velocity of 8 feet per second. The vertical scale of 
the hydraulic gradients has been made five times the horizontal. Five pressure tubes 
were established, 1 foot, 10 feet, 45 feet, 230 feet, and 400 feet from entry. 

The upper (full) line ABC, shows the gradient obtained by the uncorrected theory. 

ip. 

A drop (AB) of — = 1 foot occurs between the entrance and the first tube, and thereafter 

the tops of the water columns lie on a straight line BC, sloping downwards at about 

2 ‘6 feet per 100 feet. This ideal case was very nearly attained when the entry was 

bell-mouthed in the manner indicated in Sketch No. 40. 

The lowest (dotted) line ADE, shows the circumstances that are usually believed to 

. ... . tP 

occur with a cylindrical entry. The initial drop AD, is now about 1*5 — = 1 ‘5 foot, 

and the rest of the hydraulic gradient DE, falls at the same slope as the upper line. 
This case I was never able to observe. The middle (chain dotted) line ADG, shows 
the average of the circumstances actually observed with a cylindrical entrance piece pro¬ 
jecting 6 inches into the reservoir. 

iP 

A drop (AD) at entry occurs, which is certainly greater than —, and is probably less 

2 <^ 

< 2/2 

than 1*5 —. Thereafter for at least as far as the third tube (45 feet from the entrance) 


the water columns pulsated up and down ; but on the average the water levels did not 
lie on a straight line, and the average slope of the curve joining them was less than 
2 '6 feet per 100 feet. 

The columns at 230 feet and 400 feet were, however, steady, and the slope of the 
hydraulic gradient between these points, was 2*6 feet per 100 feet, and (to the accuracy of 
the observations) the same as in the first case. 

If, however, this slope be prolonged backwards, as shown by the full line GH, we 

ip 

find a calculated drop at entry AH, which is usually less than 1*5 —•, and AII, represents 

tP 

the quantity (1 +a) —. 









CONTROL OF WATER 


426 


a ranging from 0H5 to o'6o ; but the possibilities of error were great, and what 
was really observed was «+ all errors in the determination of the friction head 
over 80 feet of pipe, and it was possible to bring all the values of a inside the 
range a = 0*20 to a = 0*30, by assuming errors of a magnitude that could have 
occurred. Similarly, when a whirlpool formed in front of the pipe entrance, 
values of a ranging from 0*90 to no were obtained ; and these were certainly 
more accurate than the earlier set of figures. 

The experimental difficulties are great. It will later be shown that the 
calculated values of friction losses in a pipe are subject to an error of at least 
5 per cent. Thus, unless the length of the pipe is less than 800 times its 

diameter, we may, in preliminary work, neglect the term — (i + a) entirely. 

In dealing with actual observations, I have been accustomed to assume that : 

a = 0*25, and to deduct — (1*25) from the observed frictional loss before plot- 

S 

ing the results. In calculating the large syphons used on the Punjab canals it 

tA 

is usual to assume that the loss at entry is 1*5 —, this is certainly an over- 

estimation, as the water usually approaches the syphon with a velocity which is 
a considerable fraction of v. Even if this correction be applied, the results of 
certain observations show that either a is very small, approximately o'10 to 
0*20, or that the syphons are considerably smoother than the ordinary rules 
would indicate. 

Pasini and Gioppi ( Giornale del Genio Civile , 1893, P- 49 ) experimented on 
three brickwork and concrete syphons, between 4 and 5 feet hydraulic mean 
radius, and respectively 33 feet (10 metres), 581 feet (177*30 metres), and 
861 feet (262*60 metres) in length. The volumes discharged were measured by 

'U 2 

current meters, and apparently with great accuracy, When o'oiZv 1 = 0*55 — 

(v being the mean velocity in meters per second) is allowed for entrance head, 
the whole series of experiments fall into line, and agree very well with : 


v = 112 \' rs 


in English measure as the equation for frictional resistance. 

This value of the frictional resistance also agrees very well with what 
would be predicted for brickwork channels of this size by either Bazin’s or 

Kiitter’s rules. It therefore appears permissible to infer that —^——, is a fair 


allowance not only for the entrance head, as above defined, but also for the 
increase in velocity which occurs as the water quits the earthen canal and 
enters the syphon. 

The matter can be summed up as follows : 

In actual observations, the neighbourhood of the entrance to a pipe should 
be avoided when locating gauges. In preliminary calculations, a can usually 
be neglected. In working up observations, a = o‘2o to 0*30, is a fair assump¬ 
tion. In designing structures, a = 0*50 is amply safe, and probably over¬ 
estimates the loss. 

Formula for the Discharge of Pipes.— It must be confessed that 
the subject of the discharge of pipes is in a very unsatisfactory state, and that 
any definite advance seems to be unlikely. 



TUTTOIV’S FORMULAE 


427 


The two chief difficulties are : 

(i) The usual commercial description of a pipe is not sufficiently exact to fix 
its hydraulic condition, so as to enable the discharge to be predicted with an 
accuracy of even 10 per cent. 

(ii) 1 he flow of water in pipes is affected by accidental irregularities to a 
remarkable degree ; and there are very few, if any, existing experiments which, 
when carefully examined, do not show signs of influence by such conditions. 

The commercial method of describing a pipe is never so precise that those 
experiments only can be selected which were made on pipes of a nature 
similar to that of which it is desired to calculate the discharge. 

Under the above circumstances, therefore, formulae generally applicable to 
all pipes of the same commercial description should be regarded as liable to 
errors of at least 10 per cent, either way. 

Thus in the selection of a working formula, it is permissible to consider 
simplicity in calculation as of primary importance. Agreement with the 
observations used in its deduction may be regarded as indicating the more or 
less unconscious skill displayed in selection, in order to include pipes of the 
same hydraulic character, and reject all cases affected by abnormal disturbances. 
If the formula is a truly practical one, it must be sufficiently wide in range to 
include a large proportion of these unusual cases. 

On the other hand, it appears advisable to give the most definite indications 
possible of the manner in which the discharge of a pipe is influenced by 
alterations of the available head. Consequently, having observed the dis¬ 
charge of an existing pipe under a given head, an engineer can predict its 
probable discharge under another head, with greater accuracy than a general 
formula will permit. 

General Formulae .—The most useful formula seems to be the one 
given by Tutton ( Journ . of Assoc, of E?ig. Societies , vol. 23, 1899), as follows : 


v — Cifyr 2 Vs 

Where : 


v , is the velocity in feet per second. 

r , is the hydraulic mean radius in feet. 

s, is the sine of the angle of inclination of the hydraulic gradient. 

C+ is a coefficient which is approximately constant for pipes of the same 
description. 


This equation does not pretend to any very great accuracy, for the reasons 

given above ; and Tutton’s actual results, as later indicated, give 

0.67-8 0-50 + 8 , 0 

Cj r s where p varies from o’oo to o'ob. 

We have as follows, for diameters up to 4 feet, and probably for greater 
diameters (see table on p. 428). 

This equation can be easily transformed into the form : 


v = Ci^W rs = C V rs 

where C, is the variable coefficient of skin friction for a pipe d — 4r, feet in 

diameter. The values of Cif when C+ = 100 are tabulated on page 47 $- I n 
future we shall usually specify the hydraulic qualities of a pipe by stating that 

C = .... in the equation v = C V rs. 


428 


CONTROL OF WATER 



Description of Pipe. 

• Q. 

Working 
Value 
of Cj. 

» .' . ; c v ' 

Remarks. 

/ 

j L ' 

New cast iron 

Old cast iron, cleaned. 
Cement lined pipes, 
or Angus Smith coat¬ 
ed, or tarred 

126 to 158 

140 

The values of C x 
are very evenly 
distributed irre¬ 
spective of the 
radius. 

II. - 

Cast iron, slightly tuber¬ 
culated, or with mud 
deposits 

87 to 132 

io 5 

The majority clus¬ 
ter round 105. 

III. 

Heavily tuberculated . 

30 to 85 

• • • 

No value can be 
given. 

IV. 

Asphalt coated pipes 
(new) 

140 to 199 

170 

• • « 

V. 

Asphalt coated pipes 
(old) 

140 

140 

• • • 

VI. 

Wood stave pipes 

r 

155 to 129 

140 

The smaller value 
applies to square 
channels. 

VII. 1 

Lap riveted pipes, 
tarred or asphalted, 

New 125 to 
i 35 

130 

• • • 

rivets projecting 

Old 110 to 
114 

I 12 

• • • 

VIII. 

Large brick conduits . 

129 to no 

120 

When obstructed 
by shafts, etc., C x 
may fall to 90. 


In applying formulae No. IV., V., and VII., it should be remembered that 
old pipes of these kinds were rather rare at the date of Tutton’s investigations. 
The coefficients given must be considered as corresponding to a cast-iron pipe 
which is but very slightly tuberculated (say Cj = 120), and a further drop of 
10 to 15 per cent, (corresponding to C x = 105 for cast-iron pipes) may be ex¬ 
pected when pipes such as are now discussed become badly tuberculated. An 
asphalt coated pipe, if successfully coated, takes longer to become incrusted 
than a coated cast-iron pipe, and asphalt coatings being proprietary articles, if 
the coating is unsuccessful any publication of records relating to the discharge 
of an old pipe is unlikely. The fact that the discharge capacity of wood stave 
pipes does not decrease with age appears to be well established. 

With all the accuracy required for practical purposes a yard of pipe D, 

D 2 

inches in diameter holds — imperial gallons. 

Thus, the discharge of a pipe, when the mean velocity of the water is v , feet 


per second, is 

t/D 2 . . 

—— imperial gallons per second 

[Inches.] 

or, 

27/D 2 imperial gallons per minute 

[Inches.] 

























ACCURACY OF FORMULAE 


429 


If U.S. gallons are considered, the figures become : 


tT ) 2 

25 


U.S. gallons per second 


or, 14477T) 2 U.S. gallons per hour . 

'button’s exact formulas are as follows : 


[Inches.] 

[Inches.] 


No. 

I. 

v _ (3 | t' 0-60 y 0>51 

with C x = 

140 say. 

II. 

7 / = Cxr 0 * 66 ^ 0 * 51 

with C x = 

105. 

III. 

V = C 1 ?' 0 * 66 5 ‘ 0 " 51 

with Cx — 

30 to 85. - 

IV. 

v = Cjr 0 * 62 .? 0 * 55 

with Cx = 

170. 

V. 

v = Cir 0 ’ 66 ^ 0 " 51 

with Cx = 

140. 

VI. 

v = C 1 ?' 0 * 59 .y 0 * 58 

with Cx = 

140. 

VII. 

v — C^ 0 * 66 ^ 0 * 61 

with Cx = 

130 or 112. 

VIII. 

v — Cjr 0 * 65 ^ 0 ' 52 

with Cx = 

120. 


These formulae are best adapted to logarithmic computation. In all practical 
examples r, and i 1 , are fractions ; hence, the least liability to error is obtained 
by using the logarithms of ior, and io,oooj, as these quantities are usually 
greater than unity. 

The formulae then become : 


I. New cast-iron pipes, etc. 

log v — o*66 log ior+o’51 log io,ooo.f —0*5539 

II. Slightly tuberculated pipes, etc. 

log v = o*66 log ior+o*5i log 1 o,000 s— 0*6788 

III. Formula is useless. 

IV. New asphalt coated pipes, 

log v = 0*62 log ior+o*55 log 10,000^ — 0*5896 

V. Old asphalt coated pipes, 

log v — o*66 log 1 or+0*51 log 10,000^—0*5539 

VI. Wood stave pipes, 

log v = 0*59 log ior+o*58 log 10,000^-07639 

VII. Lap riveted pipes, 

log v = o*66 log ior+o*5i log 10,00^—0*5861, or 0*6508 

VIII. Brick conduits. 

log v = 0*65 log ior+o*52 log 10,000^—0*6508 

It is believed that the application of these coefficients will permit the dis¬ 
charge to be obtained with an accuracy of about 10 percent., and it is probable 
that the errors will not exceed 5 per cent, either way. It should also be borne in 
mind that a pipe, when carefully laid true to a uniform grade, or with few bends 
either horizontally or vertically, may be expected to have a greater discharging 
capacity than one which is laid with less care, or has many bends and 
sinuosities. In good practice, each individual length of pipe is adjusted with 
extreme care, e.g. is laid by level or boning rod to correct grade. In pipes of 
sufficient diameter to permit a man to get inside them, the spigot end is care- 



430 


CONTROL OF WATER 


fully adjusted to lie centrally in the faucit, so as to present a smooth internal 
surface to the flow of water. Such precautions entail a good deal of extra 
labour, but in return a better discharge may be expected. My own experience 
leads me to believe that this additional discharging capacity remains propor¬ 
tionally constant as the pipe ages, although further studies are greatly to be 
desired. Consideration of such practical matters leads to the following rules for 
cast-iron pipes : 

(i) A pipe laid for temporary purposes may be calculated with : 

C 1 = i3o if badly laid.[Tutton’s formulae] 

C t = 145 if well and carefully laid. 

(ii) A pipe for permanent work should be calculated so as to give the 
required discharge with : 

C x = 90 if badly laid ..... [Tutton’s formulae] 

Ci= 105 if well laid. 

If frequent cleaning is permissible, or if the water is known not to incrust 
the pipes, the coefficient might be increased ; but it is believed that any marked 
increase will usually entail a more frequent cleaning or scraping of the pipes 
than is generally desirable. 

(iii) If the water produces severe incrustation, and cleaning is impossible, 
these values may be reduced to : 

C 1 = 8o, and Cx = 9o . . . ... [Tutton’s formulae] 

but, in such cases, it is advisable to design the pipes so as to discharge the 
required amount for, say the first 10 years, and to provide for laying another 
line as the discharge falls off. 

(iv) Where water is pumped by power, the additional investment entailed 
by a large pipe should be balanced against the extra cost of pumping through 
a smaller pipe when incrusted. In such a case, the rate of interest expected, 
and the cost of a pump horse-power per year, actually determine the size. 

The question is best dealt with experimentally, and one measurement of the 
discharge of a pipe of known age carrying the water which it is proposed to 
deal with is more valuable than several pages of discussion. 

It will also be plain that the allowance for the deterioration in discharging 
power as the pipe ages should be greater the smaller the pipe ; and, if the 
very simple formula v = 100 d rs, be employed, and the diameter thus obtained 
is increased by 1 inch, cleaning is not likely to be necessary for many years, 
indeed if ever. 

Many engineers are accustomed to consider that 7/, should increase as the 
diameter of the pipe increases, and that v = d+2, feet per second (where d, is 
in feet) gives a very fair practical rule. The rule has no theoretical foundation, 
but it expresses, in a practical manner, the least costly size of pipe in cases 
where the available head is not very much more than that which is required to 
transmit the water. 

More exact Formulae for existing Mains. —Let the discharge of a 
pipe d , feet in diameter be observed under the various heads, let the quantities 
discharged be as follows : 

Q 1} under a head h x ) where Q and h are measured in 
Q 2 , under a head h 2 J- any convenient units, preferably 
Q 3 , under a head h 3 J cubic feet per second, and feet; 


LOGARITHMIC FORMULAE 


43 i 


where, in each instance, if necessary, the head has been corrected for the 
loss at entry (see p. 426). Practically speaking, this correction should be 
applied if the length of the pipe is less than 2600 times the diameter in rough 
pipes; or 11,500 times the diameter in very smooth ones. These values give 
the length for which the head consumed at the inlet is approximately 1 per 
cent, of the whole head. 

Plot these values logarithmically. That is to say, plot the points 
(log Q 1? log /zj), (log Q 2 , log h 2 ), etc. 

In ordinary engineering cases, where the water velocity is not so low (less 
than say 6 inches per second, in 6 inch pipes) that critical velocities (see 
p. 19) occur, these points will be found to lie on a straight line. Thus it is 
evident that the relation is : 

log h — n\o>% Q + a constant. 

Thus, h — AQ or, since Q = ?d 2 v, h = Bv n 

4 

where log A, and log B, are best obtained graphically by finding where 
the line passing through the plotted points cuts the lines representing 

Q= 1 ( i.e . log Q = o), and v = \ ( i.e . log Q = log n d 2 ) respectively 

4 


Now, this experimental fact permits us to determine rapidly the discharge 
of a pipe from gauge readings in the reservoirs from which it draws, and into 
which it discharges, when, say, two or three discharges under different heads 
have been measured. 

My own experiments indicate that so long as the pipe does not alter in 
character (due to deposits, or tuberculation) the figures thus obtained agree 
very closely with a series of observations. 

We can, however, go further :—The value of ?z, is connected with the 
character of the pipe. The following rules may be given : 

For a new and smooth pipe, n, lies between 173 and r87, and is probably, 
on the average, smallest for wood stave pipes, and largest for cast iron. 
For all except wooden pipes, n, increases with age, as the interior gets rougher. 
For slightly tuberculated pipes, n , increases about o - 10 on its original value. 
For badly tuberculated examples, such values of n, as 2, or even 2*10 are 
recorded ; although it should be mentioned that the cases where n, exceeds 
2 are few in number, and that the measurements are usually not very 
satisfactory. 

The experimental relation k = Bv n , may be put into the following form : 


h h v 11 D kl 

7 _a 3 => where B= 2 = 


h 


and /, is the total length of the pipe in feet, so that j=s 


The term d m , represents the effect of the diameter of the pipe in 
determining the velocity, and can evidently only be determined by comparing 
the results obtained from observations on other pipes (assumedly of the same 
hydraulic character), and is therefore affected by the uncertainties already 
indicated. 

The following table gives the results obtained by various investigations on 


432 


CONTROL OF WATER 


pipes. The values of will be found useful in checking actual observations. 
Those of in (although less reliable), should be employed when it is required 
to predict the discharge of a pipe from experiments made on one of the same 
construction, but of a different size. 

It is fortunate that the irregularities and abnormalities produced by bad 
adjustment, incrustations, and other less easily recognised factors, do not 
appear to have any great influence on the value of m. Therefore, if k, is 
calculated for the observed pipe, we may, with very fair accuracy, assume that 
the effect of different diameters is sufficiently allowed for by taking as 
equal to 1*25, and assuming that the irregularities influence the value of k , only. 

The following formulae have been proposed : 


Unwin (1886), 

/z_ 0*0004 ^ /1 ‘ 85 

Asphalted cast iron. 

(. Industries ) 

/ d 1*127 



0*0007 v 2 
^ 1.16 

Incrusted cast iron. 

Flamant (1892) 

h h v 

k , for new cast iron, 0*000336. 

(A. P. et C., 

/ d 1 ’ 25 

Do. in service, 0*000417. 

1892, vol. ii.) 


Smooth pipes, lead, glass or 



wrought iron, 0*000236 to 
0*000280. 

Lea (1907) 

(. Hydraulics ) 

|VJ 

II 

' ! * f ; 1 •* t fj f k / ( , 

f f A £ ,, j w 


Description 

Lea’s values of 

Average Values. 

k 

n 

For— 

Clean, cast iron 

k = 0*00029 to 0*00042 11= 1 *84 to 1*97 

0*00036 

1 *93 

j Old, cast iron . 

k = 0*00047 to 0*00069 n ~ 1 *94 to 2*04 

0*00060 

2*0 

New, riveted 
pipes . 

k — 0*00040 to 0*00054 11 — \ *93 to 2 *08 

0*00050 

2*0 

Galvanised 
pipes . 

k = 0*00035 tO 0*00045 72—1 *80 to 1 *96 

0*00040 

i*88 

Sheet iron 
asphalted 

k — 0*00030 to 0*00038 n— 1*76 to 1 *81 

0*00034. 

1 15 

Clean, wooden 
pipes . 

£ = 0*00056 to 0*00063 n — 1 *7 2 to 1 *75 

0*00060 

1 *7 5 

Brass and lead 
pipes . 


0*00030 

i *75 


i 



































SAPH AND SCHRODER'S FORMULAE 


433 


As actual examples, Lea collects for ~ ? v 11 = -Jnr.v* : 

* l l 


Description. 

Diameter 
in inches. 

B k 

l of 1 - 25 

n. 



3-22 

0*00156 

i *97 



5*39 

0*00079 

i *97 



7*44 

0-00062 

1-96 



I 2 "O 

0-000323 

1-78 

New cast iron . 


16-25 

16-5 

0-000214 

i-86 


0-000267 

1 *8o 



19-68 

0*0002 2 

1-84 



3 °*° 

0-00003 

2*0 



36-0 

0-000062 

2*0 



48*0 

O-OOOO57 

1-92 


t 

1*41 

O-OO98 

1 ‘99 



3**3 

0-0035 

i *94 

Cast iron, old 


9-58 

0*0009 

1-98 



36-0 

0-000105 

2*0 



48-0 

0-000083 

2-04 



48*0 

0*000085 

2*00 


r 

i *43 

0'004I 

1-85 

a 


3 *i 5 

O-OOI85 

i *97 

Cast iron cleaned. 


11 *68 

0-000375 

2*0 



48-0 

O-OOO082 

2‘02 



48*0 

O-OOOO59 

i *94 


> 

3 *o 

0-002450 

i-88 



iro 

0-0005I5 

1-81 



n *75 

0-000470 

1 -90 



15-0 

O-OOO27O 

i *94 

Riveted wrought iron 
or steel 


38-0 

0-000099 

2*00 


42*0 

0*000 I I 

i *93 



48*0 

0-000090 

2*0 



72-0 

0*000055 

1 *99 



72 f O 

0-000077 

1-85 



103*0 

0*000036 

2*08 


( 

44 *o 

0*0001254 

1*73 

Wood . 


54 *o 

72-5 

0*0000830 

0*0000610 

1 ‘75 

1-72 



72-5 

0*0000480 

i *93 


Perhaps the most general formula is that given in 1903, by Saph and 
Schroder (Trans. Am. Soc. of C.E., vol. 51, p. 306), which is as follows : 

For ideally smooth pipes, i.e. brass, glass, lead, etc. 


h 

1 


O’000296 

d 1 - 25 


v 


1.75 


with errors of + 7 per cent. 


For commercial pipes of all sorts, including brick and cement lined, the 

28 
































434 


CONTROL OF WATER 


graphic plots of log d, and log k, cover a zone of some breadth, and they get 
as follows: 

ll _ Q OOO296 1-82 to 1-99 


smoothest pipes ,-j = — 




, h 0*000469 

central lme of zone,-j = - ,y 5 - v 1 ' 7 * to 2 ' 00 


. . h 0*000687 

roughest pipes, j = ^ 125 v V82 to 1 


99 


This formula is obviously almost useless for general calculation. It is, 
nevertheless, worth putting on record, since it shows the general laws with some 
accuracy, and thus forms a guide for cases outside ordinary experience. 

Thus, let us assume that we wish to calculate the discharge of a conduit 
about 7 feet in diameter. There are only (to date of 1912) six cases of ex¬ 
periments on pipes over 48 inches in diameter, so that the ordinary rules are 
quite inapplicable. A study of Saph and Schroder’s diagram, however, shows 
fairly clearly that : 

ji 0*0006 

For old, heavily tuberculated, cast iron, a value not far off j = d i^ T v 


,2.05 


is 


h 


ii' O'OOO * 

most likely. For heavily tuberculated, say 4 years old, - = ~ d \Th 2/2 * s most 
likely. 

If we take wood stave pipes, the values are more irregular, but we find that 
7 = v 1 - 75 will be safe ; while for riveted pipes, s' 1 * 90 appears 

to be sound. 

These figures are, of course, only approximate, and 20 per cent, of errors 
are by no means unlikely, but one useful deduction can be made : The law, 
h . 1 

/ VarieS aS ^L25 


appears to be well founded. Thus, we are fairly justified in 


assuming that the discharging power of similarly constructed pipes, under the 
same hydraulic gradient, varies very approximately as: 

to d 2.m 

It will be obvious that Tutton’s formula could be transformed to a form 

similar to the above. When this is done, it will be found that varies as 

1 / 

^29 f° r formulae I, II, III, V, and VII ; and as for formula IV. 

Measurement of the Discharge of a Pipe. —This is generally one of 
the easiest operations in hydraulics, provided that the pipe is so long that the 
water takes more than 200 seconds to pass through it. 

The process consists in discharging a small quantity of some easily recog¬ 
nised colouring matter into the upper end of the pipe, and noting when this 
colouring substance appears at the lower end. The interval of time thus being 
observed, and the length of the pipe being known, the speed with which the 
colouring matter traverses the pipe is easily calculated. As a general principle, 
it can be stated that in smooth channels this speed is the mean velocity of the 
water, provided that the water is moving at a greater rate than Osborne 











COLOUR GAUGING OF PIPES 


435 


Reynolds’ higher critical velocity (see p. 20). This statement is not at first 
sight in accordance with the general ideas as to the distribution of velocities 
over the cross section of a pipe. If, however, the true circumstances ot 
turbulent motion are considered, it will be seen that a particle which at one 
instant is moving forward very rapidly at the centre of the pipe, will a second 
later be, not at the centre, but somewhere else, and travelling less quickly ; and 
that the particle now at the centre will have previously been moving more slowly. 
This continual alteration in speed causes the mean velocity of any individual 
particle during, say, one minute to be very much the same wherever it may 
happen to be situated at the moment of observation. 

The best proof of this statement is the practical one of discharging a 
colouring matter, which is recognisable when greatly diluted, into the pipe, and 
observing the interval between its first definite appearance and cessation at the 
other end. 

The interval of time that elapses will be found to be roughly proportional to 
the length of the pipe, and the length of the coloured streak rarely exceeds 1 per 
cent, of the length of the pipe. Thus, even if the mean velocity be considered 
as uncertain by an amount corresponding to the total length of the streak, it 
can be determined to within 1 per cent. 

In 68 of my own experiments on a 12-inch pipe, 2074 feet long, the greatest 
extension corresponded to a coloured streak 14 feet in length. The colour 
first appeared after 598*2 seconds, and disappeared 4 seconds later. Thus, 
the mean velocity was less than 3*467, and greater than 3*444 feet per second. 

The value 3*456 feet per second is probably far more accurate than could 
be obtained by any other method. 

In 25 other observations, the flow was purposely obstructed by partially 
closing a central valve, and by fixing baulks of timber in the pipe. Obstruction 
was always found to produce an abnormal lengthening of the coloured portion 
of the water. * 

According to my own systematic experiments, this method is applicable to 
pipes up to 18 inches in diameter, and probably to larger ones also. When 
tested against weirs, (as in 28 observations) the differences are within the 
limits of error of the weirs. Benzenberg {Trans. Am. Soc. of C.E., vol. 30, p. 
380) has also used it with success to gauge a brick conduit 12 feet in diameter. 
The method may therefore be considered as universally applicable to smooth 
pipes. Whether it holds in the case of a badly incrusted main cannot as yet 
be definitely stated; but there is no reason to believe that it will not, and the 
results of Benzenberg’s gaugings give : 

Bazin’s y = 0*45, or Kiitter’s zz = 0*014 ( see P- 474 ) which are closer to the 
values for a badly incrusted pipe than for a clean one. 

As practical details of the work, we should consider whether the water is 
intended for human consumption. If so, it is obviously inadvisable to add 
colour to a noticeable degree. The water presumably being fairly clear, any 
marked tinting is unnecessary. 

In such cases I have been accustomed to use bran, or permanganate of 
potash, since either is removed by filtration, and both are harmless in any case. 
Bran is easily strained off by a muslin bag, and permanganate of potash is de¬ 
colourised by the addition of a little ferrous sulphate. 

Where the water is not used for human consumption, such dyes as eosin 
(Benzenberg), or fluorescin (my own standard) are useful. I have even made 


CONTROL OF WATER 


43 6 

very accordant field gaugings with a bottle of red or black ink, the red being 
slightly more easily recognised. 

The conditions for accurate work are obvious : 

(i) The colour must be added in one gulp, (say a pint for a 4 feet pipe) to 
the water, i.e. poured into the entrance of the pipe. 

(ii) The length of the coloured streak increases very rapidly in the first 100 
feet length of the pipe, and is then about four times the diameter of the pipe. 
Thereafter the length increases but slowly, and is never much greater than 1 
per cent, of the length of the pipe. It will, however, be plain that the rapid 
initial increase renders the method comparatively inaccurate if the pipe is con¬ 
siderably less than 400 or 500 feet in length. 

(iii) Usually there is no difficulty in recognising the colour, but a white 
procelain tile laid below the pipe exit is of assistance. 

•(iv) The length of the tinted mass should be estimated, and if it consider¬ 
ably exceeds one per cent, of the length of the pipe, obstructions may be con¬ 
sidered as likely. 

The process is also applicable to smooth, open channels ; but it is very 
rarely that channels of sufficient length to render the method accurate exist. 
Difficulties occur in the case of rough earthen channels, owing to streaks of 
colour being arrested, and delayed by eddies. The quantity of pigment which 
must consequently be added so as to be easily recognisable some 1000 feet 
downstream, is considerable. I have not therefore been able to obtain 
satisfactory results. 

The following will be found an effective method of discharging colouring 
matter into the entrance of a pipe. A glass flask such as the usual thin glass 
long necked flask used in chemistry, is filled with colouring matter so as to 
leave no air bubbles, and corked. The full flask is slung by a string, neck 
downwards, and is lowered until it lies opposite the centre of the pipe, and as 
close in front as possible. The flask is then smashed, preferably with a rod ; 
but if the depth is too great, a lead weight with a hole in it is threaded on the 
suspending string, and dropped. The actual instant of fracture can generally 
be observed, but occasionally the depth is too great. In practice, the small 
degree of uncertainty thus introduced is usually negligible ; but if the pipe is 
a short one, or if extreme accuracy is required, the instant of fracture can 
generally be noted by fixing a bar below the flask, so as to prevent the weight 
being lost, and noting the time at which the jerk thus caused occurs. By using 
piano wire as the suspender, and an 8 lb. weight as traveller, I have been able 
to get accurate results when the pipe mouth was 40 feet below the point of 
observation. The most favourable place for discharging the colour is not at 
the entrance of the pipe, but at a manhole ; the length of wire necessary to 
permit the flask to lie in the centre of the pipe being measured off before 
lowering. I have rarely weighted the flask, although, when the water velocity is 
high, this may be desirable. 

Effect of Age on Pipes.—-With the doubtful exception of wood stave pipes, 
all mains as they grow older discharge less water under similar conditions. 
This decrease is caused by the formation of growths and tuberculations on the 
inside of, or deposits in, the pipes. 

These are due to many causes, and the methods for their removal or pre¬ 
vention are very variable. The classification given by Brown ( P.I.C.E ., vol. 
156, p. 1) seems the most natural, and is as follows : 


DEPOSITS IN OR ON PIPES 437 

I* deposits forming on iron pipes only, wholly or partially consisting of 
the metal, and therefore localised at or near imperfections in their protective 
coating. 

II. Deposits occurring on the inner surface of pipes, culverts, rock tunnels, 
etc., formed from substances existing in the water, and therefore not localised 
by imperfections in the protective coating. 

III. Accumulations of loose debris, either natural to the water, or formed 
from deposits of the first two classes, and therefore accumulated in hollows, 
irregularities, or dead ends of the mains or channels. 

(i) To the first class belong the well-known “ limpet ” formations, occurring 
in iron pipes. These appear to originate in all waters, whether acid, or neutral, 
and are apparently entirely due to pinholes, or flaws in the coating of asphalte, 
or pitch, which is supposed to protect the metal. Limpets may form a con¬ 
tinuous covering over the whole interior surface of pipes which have been badly 
coated, but as each individual incrustation apparently never attains a size greatly 
exceeding that of a hemisphere of 1 to inches diameter, the thickness of the 
coating does not increase indefinitely. Thus, while small pipes may be entirely 
blocked by limpet incrustations, a large main is at the worst rarely choked by 
more than inches of obstruction all round. As will be noticed in the Table 
on page 442, pipes much above 12 inches in diameter are seldom scraped. 

The only preventive is a good coating of bitumen, or pitch, in smooth and 
perfect layers. Brown (nt supra) specifies that the pitch should be free from 
hydrocarbons which volatise, or decompose with long exposure to flowing 
water. 

I give Angus Smith’s original specification, and would remark that the 
results (due to the fact that the coal tar of his period is now largely consumed 
by dyers) are no longer satisfactory. The original process when applied to a 
good mixture of hydrocarbons, yields satisfactory results. 

The first coat should be put on the clean, hot iron, and allowed to cool ; 
then the second should be applied, care being taken that it is not sufficiently 
hot to melt the first. 

Coating should be effected by dipping the pipe into the mixture, and not by 
painting with a brush immersed in the liquid. 

(ii) To the second class belong the more regular, and therefore less detri¬ 
mental incrustations of carbonate of lime, so frequent in mains conveying water 
containing bicarbonates of lime. 

The best preventive is Clark’s water softening process (see p. 591). A 
sufficient interval of time should be allowed before the water enters the mains, 
for the completion of the reaction, especially if magnesia salts are present. 

The most usual method, however, is to scrape the pipes periodically, in the 
manner discussed on page 439. 

(ua) Slime is a deposit of black substance, occurring not only in pipes, but 
also in tunnels, brickwork, and masonry channels. Slime contains iron, and is 
apparently a product of organic life, dependent on the presence of iron in water, 
It is therefore only found in waters which originally contain iron, although 
there is a certain amount of evidence to show that an acid water naturally free 
from iron, can, by contact with uncoated metal pipes, acquire enough iron to 
support the growth of slime. 

The preventives consist in the removal either of the organism, or of its food ; 
protective coatings having no effect on slime deposits. 


CONTROL OF WATER 


438 

The most usual method is to neutralise the acidity which exists in such 
waters by means of lime, or soda. This effectually prevents the growth, prob¬ 
ably more by killing the organism than by removing the iron. 

This neutralisation is effected by filtration through powdered limestone, 
either mixed in the sand of ordinary filters, or in special filter beds, working 
at a high velocity. 

Sometimes, (although not invariably) simple sand filtration is effective, and 
where this is the case, it is unwise to also add limestone, lest the calcium 
carbonate type of deposit be encouraged. 

The older method of straining the water through extremely fine wire gauze, 
is, according to Brown, only effective for a certain period, and sooner or later 
slime will form. (See p. 549). 

It might be gathered from Brown’s paper that slime is a common occurrence 
in pipes and channels, but my own experience is that it is extremely rare, except 
in waters drawn from lakes, or storage reservoirs. No rules can be given for 
predicting its occurrence, but in every instance of which I have heard there is a 
history of peaty deposits in the catchment area of the watershed or brook from 
which the supply is procured; and, as already stated, the water in its natural 
state contains iron, and is acid in reaction. It may also be noticed that slime 
deposits rarely occur beyond the first five miles’ length of a main. 

(iii) These deposits are generally of the nature of silt, either drawn from 
the source of supply, or derived from incrustations of the first, or more usually, 
the second class. 

Certain waters containing manganese, or iron, deposit small nodules 
composed of oxides and carbonates of these metals. As a rule, such waters 
are treated by deferrisation (see p. 584), or demanganisation processes, before 
entering the mains. In certain cases, where the supply pipe is long, the whole 
of the deposit occurs in the main, and the water as delivered does not contain a 
sufficient quantity of the above minerals to give rise to complaint. All such 
loose deposits are very readily brushed out of the pipes by means of the rotary 
brush used by Deacon on the Vyrnwy main, and described in the Proceedings of 
the Institute of Mechanical Engineers , 1899, p. 502. 

The matter is of great importance in a long line of pipes crossing a series 
of valleys, as the nodules accumulate at the bottom of each depression, and if the 
water velocity is not great enough to lift them over the next hill, they form a very 
efficient frictional brake, producing a more and more marked effect as time goes on. 

Angus Smith’s Process. —Information on the exact nature of the process 
formerly applied by Angus Smith is somewhat uncertain, but the following 
details are given by Wood (Rustless Coatings ). 

Coal tar was distilled until the naphtha was removed, and the material was 
deodorised, and had the consistency of melted wax. Five or six, or even 
eight per cent, of linseed oil was then added, and was well stirred in. The 
pipes having been cleaned and freed from all sand, scale, or dirt, and previously 
heated to 500 degrees Fahr., were dipped vertically into the bath, and 
remained there until they had attained a temperature approximately equal to 
that of the bath, i.e. 300 degrees Fahr. 

In actual practice, it appears to have been more satisfactory (owing to ashes 
from the furnace becoming attached to the pipes) to dip the cleaned pipes 
when cold into the bath, and to allow them to attain the temperature of 
300 degrees Fahr. 


CO A TING OF PIPES 


439 


So far as can be judged, the time during which the pipes remained in the 
bath (roughly 30 minutes for 20-inch pipes, and from 15 to 20 minutes for 
4-inch to 12-inch pipes) was the most important factor ; although it was found 
that distillation of the coal tar to a consistency of pitch gave bad results. 

The modern equivalents appear to be compositions of pitch and linseed oil, 
heated to 250 or 300 degrees Fahr. 

Wood states that a mixture of nine parts of pitch, with two parts of boiled 
oil, gives a good coating, and that if the oil is increased to three parts per nine 
parts of pitch, the coating is thicker and requires baking after immersion, in 
order to produce satisfactory results. 

In this case also, the length of the immersion seems to be of vital import¬ 
ance, and failure must usually be attributed to a too hasty removal from 
the bath. 

In modern practice, pipes are usually coated with an asphaltic coating of 
the character specified by Goldmark (see p. 460), or Brown (see p. 437). 

There are also many proprietary articles (usually paints with an inflam¬ 
mable vehicle) which have apparently given satisfaction under very severe 
tests. Care is needed during application owing to the inflammable vapour 
given off by the paint. 

The subject is an important one, and but little is really known about it. 
The actual facts appear to be that any efficient coating is costly, and as the 
difference between efficient and non-efficient coatings only becomes noticeable 
after the lapse of time, experience accumulates but slowly. The one definite 
fact is that “Angus Smith’s” coating, is a polite expression for reliance on the 
maker’s experience. 

If Angus Smith’s coating is specified, the pipes when delivered should be 
covered with a smooth, adherent coating, showing no flaws or pinholes, and 
without brush marks. It is doubtful whether any maker pretends to do more, 
and unless special experiments have been made, it is certainly futile to ask 
for more. 

Cleaning and Scraping Pipes. —The general character of the deposits 
formed has already been discussed, and approximate indications will be given 
of the diminution in discharge thus produced. Such incrustations or growths 
can be removed either manually, or by scrapers ; and reference to the formulae 
for “ cleaned cast-iron ” pipes shows that a discharge equal, or very nearly 
equal, to that obtained in the new pipe, may be expected after thorough cleaning. 

I do not propose to describe the methods used either in manual or 
hydraulic scraping. Hydraulic scraping is far cheaper, and is practicable in 
all pipes exceeding four inches in diameter ; curves and bends of any ordinary 
radius (3 feet in a 6-inch main) do not affect the process, and it will remove 
stones, lead, crowbars, and other abnormal obstructions. When the main has 
been designed for hydraulic scraping, and is properly provided with hatch 
boxes (see Sketch No. 123), the cost is very small in comparison with the 
increased discharge obtained. 

Amongst British Engineers, therefore, it is customary to scrape pipe mains 
whenever the discharge falls off sufficiently to seriously interfere with the 
supply. While it is plain that a Waterworks’ Manager is forced to maintain 
a sufficient supply at all costs, the practice should be entered on with caution. 

As already stated, the limpet form of incrustation may occur at every point 
where there is a flaw in the coating, and once a pipe has been scraped, for all 


440 


CONTROL OF WATER 

practical purposes it must be regarded as no longer coated. Thus, once mains 
conveying water producing the limpet form of incrustation have been sciaped, 
it may be anticipated that a renewal of the process will become necessary at 
.very frequent intervals. 

The water mains supplying Torquay (Devonshire) are a typical example. 
Here, according to Ingham (. Engineering , Nov. 3rd, 1899), a 9-inch and a 
10-inch main laid down in 1859 was first scraped in 1866, and thereafter it was 
found necessary to renew the process yearly. 

The quantities discharged by the main were as follows: 


V •J-.Qlp • 

- » 

Discharge in gallons per minute. 


Before Scraping. 

After Scraping. 

1858 New main 

622 approximate 

• * *5 

1866 .... 

3 T 7 

464 

1867 .... 

Not observed 

564 

1868 .... 

do. 

624 

1869 .... 

423 

659 

1870 .... 

471 

668 

1871 .... 

496 

684 

1872 .... 

499 

5 Sl 

1896 .... 

550 

698 

1897 .... 

600 

693 

1898 .... 

586 

708 


We thus see that in the first eight years the pipe coated with Angus Smith’s 
composition lost 49 per cent, of its discharging capacity. Thereafter, one year 
sufficed to reduce the discharging capacity by at least 20 per cent., and often by 
as much as 30 per cent. 

Ingham also gives figures showing that the effect of these thirty-two years’ 
scraping has been to remove a volume of iron equal to j-inch thickness all round 
the circumference of the pipe. 

This may be regarded as a case of water possessing abnormal incrusting 
qualities. At Melbourne, Victoria, the water has similar, but less marked 
characteristics. Here, it is found necessary to scrape pipes originally properly 
coated, ten or fifteen years after laying, and thereafter every five or seven years 
(Ritchie, P.I.C.E ., vol. 157, p. 315). 

It must also be noted that the Melbourne engineers take extreme care to 
damage the pipe coating as little as possible, and it is fairly evident that, when 
compared with the original process at Torquay, they are tolerably successful. 
There are certain indications that the coating of the Torquay new main was 
but little damaged by its first scraping ; the design of scrapers being now better 
understood. 

We may, nevertheless, consider that in waters of this character scraping is 
a luxury,—and an expensive one,—unless the pressures in the main are such that 






























SCRAPING OF PIPES 441 

a diminution of the pipe thickness by ^ inch can be regarded as immaterial from 
the point of view of strength. On the other hand, where the incrustations are 
derived wholly from the water ( e.g . in the case of carbonate of lime deposits), 
scraping is unlikely to lead to an increased rapidity of incrustation, and may 
therefore be adopted with far less diffidence. It is, however, a rather curious fact 
that scraping has mostly been adopted in pipes carrying limpet incrusting waters, 
and it may be inferred that carbonate deposits are less effective in diminishing 
the discharge. 

It therefore appears that in limpet incrusting waters not only should the pipe 
line be provided with hatch boxes (Sketch No. 123) for inserting the scrapers, 
but wherever the thickness is determined by strength calculations (and not by 
practical conditions of casting) an extra ^ inch to § inch should be allowed, in 
order to provide for the gradual consumption of metal by the “ limpets.” In 




Sketch No. 123.—Scraper Hatch for 4-inch Pipe. 

mains carrying waters which produce incrustations of calcium carbonate, it 
appears preferable to increase the size of the pipe so as to allow for a deposit of 
\ inch in thickness all round, rather than to remove the growth as formed, by 
scraping, because a deposit of calcium carbonate increases but slowly in depth 
after the first j inch has been accumulated, and such deposits are usually not 
rougher (hydraulically) than a cast-iron pipe. 

Few data exist at present for slime deposits. A priori, it appears that scrap¬ 
ing may be undertaken without increasing the rate of incrustation ; but it seems 
more logical to prevent deposit by previous treatment of the water. 

The following table is of value as giving rough indications of the increase in 
discharge secured by scraping ; or, more accurately, of the diminution in dis¬ 
charge which engineers consider sufficiently serious to justify the process. The 
increase is calculated on the discharge before treatment. The small proportion 
of pipes exceeding 12 inches in diameter should be noted. The Bombay 24-inch 
pipe (which, even after scraping, only gave o*8i of its discharge when new) is 
interesting, as indicating the possibilities of incrustation in tropical climates. 














































































442 


CONTROL OF WATER 


Place. 

Diameter of Main 
in Inches. 

Percentage 
of Increase. 

Aberdeen .... 

4 

107 

Oswestry ..... 

6 and 7 

54 

Omagh ..... 

6 

3 °° 

Bridge of Allan 

6 

35 

Thurso ..... 

6 

7 

Cowdenbeath .... 

6 

23 

Cupar, Fife .... 

7 

S 2 

Lanark ..... 

7 

34 

Lancaster .... 

8 

56 

Burntisland .... 

8 

43 

Torquay ..... 

10 to 9 

28 

Whitehaven .... 

13 and 11 

28 

Merthyr Tydvil 

12 

82 

Waterford .... 

13 

40 

Merthyr Tydvil 

14 

3 ° 

Bradford ..... 

18 

5 6 

Bombay ..... 

24 

19 

Boston ..... 

48 

3 ° 


It seems advisable to state that all these waters are, I believe, of the limpet 
incrusting type. Calcium carbonate and similar deposits have been removed by 
scraping at Roublaix, Bath, and Southampton, and probably at other places, 
but figures are not as yet available. 

Formulae Expressing the Deterioration of Cast-Iron Pipes with 
Age. —Weston {Trans. Am. Soc. of C.E., vol. 35, p. 289) gives a formula ex¬ 
pressed in terms of Darcy’s coefficients. When transformed so as to express the 
decrease in discharge, it becomes :— 


Discharge at the age of_y years = 


Discharge when new 



Tutton {ut supra) goes into the matter more in detail, and finds for asphalte 
coated cast-iron pipes :— 


N 6W 

* L ^ V " VV . 

v = 

175 r’ 62 

S .5S 

Slimy, say one year old. 

7/= 

140 r ,C6 

S’51 

Very lightly tuberculated, say four years old . 

V — 

132 r 

s* 1 

Do., say six years old. 

v — 

124 r* 66 

S ’ 61 

Lightly tuberculated, say eight years old 

v= 

116 r’ ,i(i 

S ' 51 

I he average state of distribution mains, say ten years 




old ... 

v = 

108 r * 66 

S ’ 51 

Fourteen years old, varying with the amount of tuber- 




culation. 

V — 

100 r ’ 66 

S-51 

Eighteen years old, varying with the amount of tuber- 




culation. 

v= 

90 r' c,G 

S' 51 

Very heavily tuberculated, twenty-five years old 

v*= 

80 r’ 6G 

S -* 1 


























443 


EFFECT OF AGE 

This set of formulas (although doubtless somewhat complicated), in my 
opinion very accurately represents the actual effects of age. Not only does the 
constant C 1} decrease, but the loss of head varies as a higher power of the 
velocity, as the age of the pipe increases. 

Hill (Proc. of American Assoc, of Waterworks' Engineers , 1907, p. 352) 
gives a table, which, with the addition of five cases given by Bruce for pipes at 

Bombay (. P.I.C.E. , vol. 162, p. 139), and four by Weston {lit supra), is 
as follows : 


Diameter 
of Pipe. 

Coating. 

Age 

in 

Years. 

. ; _: ,, ■ 

Annual Reduction in C. from 
Hill’s Theoretical Value 
when clean. 

Percentage 
of Decrease 
in Discharge 
per Year. 

6 inches 

(?) 

1 3 

3*6 from values of 75 to 82 

4 ’ 2 

10 „ 

(?) 

6 

2 '3 » ii 95 to 101 

2*3 

12 „ 

(?) 

0 

6’8 „ ,, 96 to 103 

6*8 

12 „ 

(?) 

15 

2 '7 >1 „ 96 to 104 

27 

14 „ 

(?) 

18 

I ‘2 ,, ,, IO4 tO I08 

1*2 

16 „ 

Angus Smith 

8-5 

2 *I ,, ,, I l6 

i-8 

16 „ 

Tar 

18 

1*2 „ „ 107 to no 

1 *i 

16 „ 

(?) 

18 

1*0 ,, ,, 107 to 110 

0-9 

20 11 

Tar 

11 

4* 2 „ „ 117 to 123 

37 

20 1, 

Tar 

5 

3'° „ „ 118 

2*3 

2 4 „ 

Tar 

3 

6*7 11 1, 118 to 123 

5*6 

2 4 i> 

Angus Smith 


^ ^ 11 II I 23 

o *9 

2 4 „ 

Angus Smith 

2 4 

r ‘6 ,, „ 123 

i *3 

2 4 n 

Angus Smith 

16 

2 '3 » » 123 

1 ’9 

13 ° 11 

Tar 

9 

7*3 n „ 118 to 123 

6*8 

3 2 „ 

Angus Smith 

42 

1,0 ,, „ 118 to 123 

o-8 

o u >> 

Tar 

7 

9*1 „ „ 124 to 127 

7*3 

48 „ 

Tar 

17 

21 ii 11 J 43 

1 *5 

48 „ 

Angus Smith 

8 

3‘9 11 n 143 

2 ’8 

48 „ 

Angus Smith 

10 1 

r *° 11 n T 43 

07 


The formula here used is the usual one v = C^ rs, and the values of C, given 
are those for a clean pipe. 

Where only a single value of C, is given, it is recorded as the result of 
experiments on a new pipe (not necessarily the same pipe), and some of these 
values appear to me to be abnormal. 

It will be plain that the annual rate of decrease in C, is not constant, but 
falls off as the age increases. 

Hill determines the value of C, for new pipes by a special formula ; which, 
in some cases, gives values differing as much as 5 per cent, from those obtained 
from Tutton’s formulas. In calculating the percentage of decrease most weight 
should therefore be given to figures which agree fairly closely with those stated 
by Tutton. According to Hill, the percentage of decrease in the discharge of a 
pipe is affected by the velocity of the water in the pipes ; but the matter is 
obviously not of great practical importance. 

The experiments recorded by Brackett (Trans. Am. Soc. of C.E., vol. 28, 
p. 269), give the following results : 



























444 


CONTROL OF WATER 


Diameter of Pipes. 

Age. 

C. 

4 Inches . 

65,. 

38 Years 

3 8 » 

12-19 

27-35, rising to 69-82 
after scraping 


The above figures can hardly be considered as normal, as the pipes were 
not coated. As a single example of a pipe apparently unaffected by age, 
Friend’s (. P.T.C.E ., vol. 119, p. 271) value of C=ii4, for a 21-inch pipe, nine 
years old, may be noted. Many others could be collected. 

It must also be borne in mind that the character of the incrustation has far 
more effect on the discharge than the age of the pipe. Limpet incrustations 
present a very irregular surface to the water, and cause humps and blebs on the 
interiors of the pipe. They are therefore far more effective in diminishing the 
discharge than calcium carbonate incrustations, since these are not only 
smooth in themselves, but form an approximately continuous coating all over 
the interior of the pipe. 

Slime deposits seem to act very much in the same manner as weeds in a 
river. The strings of slime wave in the water, and produce a braking action. 

So far as can be traced from the original records, the figures tabulated 
above refer to limpet incrustations. 

Darcy Formula. —The Darcy formula for the discharge of cast-iron pipes 
is both frequently referred to and used by engineers. 

Putting Unwin’s modification (see Encyc. Brit., Article “ Hydromechanics,” 
p. 485) into the form v — C \t rs, we get : 

(a) Clean and uncoated cast-iron pipes : 


C = 


4 


/: 


+ 


1 


8o‘2 


^ ' 12'd 

(b) Slightly incrusted cast-iron pipes : 

C=,-= 

V I + 7 Td 

(c) New cast-iron pipes coated with pitch, no incrustations : 

139*2 




1 + 


12 d 


where d , is expressed in feet. 

The oiiginal experiments do not extend beyond about </= r8 foot. The 
accuiacy of the formula even within these limits is probably not as great as 
Tuttons. It is, however, very greatly in favour with engineers who maintain 
their mains in first-class condition. I believe this is due not so much to the 
fact that the formula applies well to such mains, as that it gives a very excellent 
concealed factor of safety,” especially in the larger sizes. 

Cast-Iron Pipes.—Thickness of Pipe Metal.—The theoretical formula for 
the thickness of a cylinder D, inches in diameter, exposed to an internal 
pressure equal to p, lbs. per square inch, is given by Grashof as : 


ta ~ 2 {\/ _ *} inch es • 


[Inches] 



























THICKNESS OF CAST-IKON FIFES 445 

where F, is the permissible tensile stress on the material of the cylinder in lbs. 
per square inch, and where it is assumed that 7^, is less than f F. 

Now, for cast-iron, Unwin (.Machine Design , 1902, vol. 11, p. 10), puts 
F = 1850, and thus gets : 


p Lbs. per Square Inch. 

p Feet Head of Water. 

! 

•sia 

75 

J 73 

0*021 

io 5 

242 

0*030 

i 35 

311 

0*039 

i6 5 

381 

0*048 

etc. 

etc. 

etc. 


The actual dimensions of cast-iron pipes can rarely be fixed by this rule. 
The static head of water on the pipes seldom, if ever, correctly specifies the 
maximum stress that the mains may be called on to sustain, since the stresses 
due to unequal earth pressure, or water hammer (to mention only two possible 
causes), may largely exceed those calculated by the above equation. We are 
therefore obliged to fall back on practical rules. 

Hawksley, some sixty years ago, gave the following rule : 

/ H =o'i8VD inches. . . . [Inches] 

This may be considered as resulting in but few breaks either from earth or 
water pressure, or from water hammer. For smaller sizes of pipes, it is also 
not very far from the minimum thickness that a founder is willing to cast 
without charging abnormal rates to insure against possible failure. 

This minimum thickness is given by Unwin as : 

t vx —o’\ 1VD -f-o’io inches. . . . [Inches] 

Thus, putting H, for the feet of water that produce a pressure of fi, lbs. per 
square inch, we get : 





t G = t 

when 

w 

D 

tm 

tu 

V 

or H 

Inches. 

Inches. 

Inches. 

lbs. per 
square inch. 

Feet. 

lbs. 

4 

°‘ 3 2 

0*36 

260 

600 

270 

8 

0*41 

0*51 

*75 

400 

1,270 

12 

0*48 

0*62 

138 

315 

3 > 2 5 ° 

16 

o ’54 

0*72 

117 

270 

6,310 

20 

°‘59 

0*80 

!°5 

240 

10,600 

24 

0*64 

o*88 

94 

2I 5 

16,400 

3 ° 

0*70 

0*99 

84 

190 

27,780 

3 6 

0*76 

1*08 

75 

170 

42,740 

42 

o*8i 

1*17 

f Less than 

Less than) 

61,560 

48 

o*86 

1*25 

t 75 

170 J 

84,970 

54 

0*91 

1*32 

J Less than 

Less than) 

113,30° 

60 

°‘95 

1 *40 

1 75 

1 

1 

■^4 

O 

145,ooo 












































CONTROL OF WATER 


446 

Now, if we compare these figures with the theoretical value oi t—to say, 
found by Grashofs equation, it appears that t m -=t G for the values of /?, or H, 
tabulated above. 

With a view to obtaining an insight into the capacity of pipes of a diameter 
D, and thickness t m , to resist unequal earth pressure, I have also tabulated the 
concentrated central load in pounds, which will produce a stress of 1850 lbs. 




Sketch No. 124.—Proportions of British and Standard American Pipe Toints. 


per square inch, in the metal of the pipe, when regarded simply as a supported 
beam of 12 feet span, from the formula : 

^ j X "36 “ 4 ° (D-f2/ ni )- t m approx. . [Inches] 

A consideration of these figures shows that while small pipes of thickness / w , 
have ample strength to resist ordinary internal pressures, they are, relatively 
speaking, more likely to be fractured by straining actions arising from unequal 
earth pressures than the larger sizes. It is fairly evident that Hawksley’s rule 
























































447 


JOINTS OF CAST-IRON PIPES 


gives a pipe which is adequately safe against any ordinary values of water 
pressure, and also against any probable values of beam loading produced by 
unequal support. 

We may therefore regard Hawksley’s rule as a safe standard which may be 
worked from either up or down, according as circumstances are less or more 
favourable. Judging by general practice, the excess of strength given by 
Hawksley’s rule is greatest for diameters between 18 inches and 30 inches. 

The American Waterworks Engineers’ Association recommends the thick¬ 
nesses given in Table, page 448, for pipes under the tabulated pressures. 

The cast iron is specified to bear a central load of 2000 lbs. and to show a 
deflection of not less than 070 inches before breaking, in a bar 26 inches long, 
2 inches X 1 inch, loaded on a 24 inch span, lying on its flat side ; or to show 
20,000 lbs. per square inch in tensile strength. 

The pipes are cast in dry sand moulds, in a vertical position, with faucit end 
downwards. 

Pipe Joints. —The opposite sketch (No. 124) represents an English pipe 
joint, and the American Standard ( Proc. of American Assoc, of Waterworks ’ 
Engineers , 1908, p. 779) : 


[All Quantities in Inches ] 

English (Unwin, ut supra) 

4 = 1*07 inches. 

4 = *o25D+J inches 

to , o 25D + , 6 inches. 

4 — "045D + *08 inches. 
j = *oiD + ’25 inches 

to •01D-P375 inches. 
b\ — ’°75D + 2j inches. 

b'2. ~ 4 

/=’09D + 2| inches 

to *ioD + 3 inches. 


^4 = 'o3D + i inch. 


[. Notation as in Sketches ] 

American (Waterworks Standard) 
(see Table p. 448). 

•57 inches-P02D approx. 

4 = 24= 1*14 inches -K04D approx. 
■40 inches up to D = 14 inches 
•50 inches above. 

370 inches up to D =6 inches 
4’oo inches up to D = 24 inches 
470 inches up to D = 36 inches 
5*oo inches up to D = 48 inches 
5*50 inches above. 

1*5 inches up to D = i4 inches 
175 inches up to D = 2o inches 
2’00 inches up to D = 48 inches 
2*25 inches up to D = 72 inches. 

R= no inches up to D= 14 inches 
1*15 inches up to D = 2o inches. 
k =t 2 +s 

x — \ inches up to D = 6 inches 
1 inch beyond. 

V = inches up to D = 6 inches 
j inch beyond. 


The value for 4, in the American standard, depends somewhat on the 
pressure ; the values being usually increased by 0*05 inch, when the pressures 
exceed 200 feet head. The tabulated value is a mean. 

The dimensions for pipes under pressures greater than 400 feet head require 


448 CONTROL OF WATER 

special calculation by Grashof’s formula. The general effect is most marked in 
the dimensions 1 2 , / 3 , and £ 4 , which should be increased by o'io inches foi each 
extra ioo feet head above 400 feet. The American standards run up to 800 
feet head, but it is doubtful whether cast iron is an economical material for such 
pressures, unless the pipes are either of small diameter, or are exposed to intense 
corrosion. 


D 

Inches. 


Pressure. 


Under 100 Feet 
Head. 

Under 200 
Feet Head. 

Under 300 
Feet Head. 

Under 400 
Feet Head. 

4 

o - 42 

°*45 

0*48 

0-52 

8 

0*46 

°* 5 * 

o‘5 6 

o'6o 

12 

o '54 

0 - 62 

0*68 

075 

16 

o'6o 

070 

o‘8o 

o - 89 

20 

0*67 

o*8o 

o‘92 

1*03 

24 

076 

0*89 

1 ‘04 

1 -16 

30 

o-88 

1*03 

1 ’20 

i*37 

36 . . 

o*99 

i*i5 

1-36 

1-58 

42 

no 

1*28 

i *54 

178 

48 

1 "26 

1*42 

171 

1-96 

54 

i*35 

i*55 

1*90 

2*23 

60 

• 

i*39 

1*67 

2 '00 

2*38 

Up to 20 in. . 

Test Pressure— 
300 lb. per sq. in. 

300 

3°° 

3°° 

Above 20 in.. 

150 lb. per sq. in. 

200 

250 

3°° 


Design of Joints in Cast-Iron Pipes. —Sketches No. 125, No. 126, 
and No. 127 show designs for large pipe joints. 

No. 125 is that adopted at Staines, and may be regarded as the practice of 
the London Water Companies in the year 1898. 

The steel shrunk ring is costly, being practically equivalent to another ton of 
metal ; although, now that the device has ceased to be novel, the expense may 
be reduced by one-half. It has, however, the great advantage of rendering 
breakage almost impossible during laying or transit (I have no record of any 
having occurred). The pipe as a whole is easily cast, and while there is no 
stop to retain the lead jointing, this is not required with skilled workmen. 
Similarly, there is no bead on the spigot end, rendering adjustment of each 
length (so as to secure a continuous inner surface to the pipe), a process 
necessitating some skill. 

The design may be considered as suitable in cases where the labour is 
efficient, and the trenches are kept quite free from water. I am inclined to 
believe that the steel ring was unnecessary in this particular case, since all 
portions of the work were easily accessible. On the other hand, the pipes were 
laid under railways and roads, carrying heavy traffic, and a break in after years 
might have been serious. 




































449 


JOINTS OF CAST-IRON PIPES 

Sketch No. 126 shows the pipe, joint used at Detroit, for 30-inch pipes, with a 
small stop for lead, and a bead on the spigot end. The latter renders good 
adjustment of the pipe lengths more certain ; but, as designed, renders it 
difficult to cast the pipe some 4 inches longer than the working length, in order 
that the accumulated impurities may be removed by cutting off this 4 inches in 
a lathe. The stop is small, and while it may prevent unskilled work in a joint 
run with molten lead coming to grief, it is not sufficiently large to be of real 
assistance in retaining a joint made with lead wool, or leadite, caulked in cold 
(when the trench is not properly freed from water). 

Sketch No. 126 also shows a joint with a deep stop. This is advisable in 
cases where the jointers are unskilled, or where it is expected that cold caulked 
joints will frequently occur. 

Such a pipe would probably be extremely difficult to cast with the spigot 
end upwards, and we can only hope to get rid of impurities by large heads over 
the faucit end, which is obviously a less perfect way than that adopted where 
the spigot end is cast upwards, and an extra 4 inches of the pipe are cut off. 


71 

\ 

F~ 

— J %—• 

■*- /*"— 

+ - Steel Rin^, turned inside ishrunkonhet 

% 

C\ 

) 

■4 

■5s 

1 

i 

V - —’ 

S * 

t t 

( 





J“ 

1 

'---- 



i 

l 


5 " 

«- 5*2" -- 


1 


Staines Reservoirs Pipe Joint 


Sketch No. 125.—Joint used at Staines. 

Modern methods of casting will produce a very satisfactory pipe with head 
removal only. Broadly speaking, this design asks the foundry to do all the 
skilled work, and gives the actual pipe layer every possible assistance. The 
Staines’ design, however, gives the foundry man the easier task, and expects the 
layers and jointers to be first-class workmen, and the trench to be kept very 
free from water. The Detroit design is probably the most equitable. 

Summing up, it would appear that: 

(i) Deep stops and a bead are indicated in cases where the actual laying is 
difficult, and especially where labour is scarce, and water is likely to occur in 
the trench. In pipes less than, say, 24 inches in diameter, a bead is almost a 
necessity, if the pipe line is to be laid with an approximately continuous inner 

surface. 

(ii) A steel, shrunk ring is indicated where the mains are laid in inaccessible 
places {e.g. on a steep hillside, or under rivers), also when laid under roads 
subject to heavy traffic. 

(iii) Deep stops and beads require skilled casting, and therefore good inspec¬ 
tion, before the pipes are accepted. 

A bead can of course be cast say 5 inches long and the top 4 inches rejected 
29 


























45° 


CONTROL OF WATER 


at the cost of some additional lathe work. Similarly, it might be advisable to 
provide pipes with deep specially turned stops for use in river crossings, and 
other localities where water cannot be entirely removed, although it must be 
remembered that cold run joints are undesirable. 

Turned and bored joints were frequently employed with satisfactory results 
in India, when skilled jointers were quite unprocurable. Of late years, how¬ 
ever, the lead joint has almost entirely superseded it. A turned and bored joint 
is quite justifiable where pipe laying is a novelty, but its expense is so great 
that, as soon as large jobs are undertaken, it becomes cheaper to train jointers 
specially for the work. (Sketch No. 138, p. 596.) 



Sketch No. 126. —Joints used at Detroit and British Joint with Deep Stop. 

The design shown in Sketch No. 128 follows Bateman’s practice ( P.I.C.E ., vol. 
126, p. 14). The combination of tubes of uniform thickness and a separate 
joint ring, also of nearly uniform thickness, is obviously well adapted to prevent 
internal stresses caused by unequal shrinkage after casting. The design, how¬ 
ever, has not been widely copied ; and this, I believe, is due both to difficulties 
in laying, and to greater liability to leakage. The Coolgardie pipe joint is of 
this type, and the deeper stops for rings exposed to high pressures show a nice 
graduation in design. (Sketch No. 132.) 

Pipe Laying .—The following specification was employed at Staines by 
Messrs. Hunter & Middleton : 

(a) The pipes are to be cast of best No. 2 pig iron, second melting, cast from 



















































*s PE Cl FI CA TION FOR PIPE LA YING 451 

a cupola, and are to have the bore perfectly straight and cylindrical, and the 
thickness exactly uniform. 

(/>) I hey are to be cast vertically in dry sand, with faucit end downwards, 

and they must all be clean and solid without sand holes, air holes, or any other 
flaw. 

(f) Th e y must be cast with a 6-inch head of metal to secure solidity, and 
this is to be afterwards cut off in a lathe. 

(d) The pipe trench must be taken out to a width of 6 inches greater than 
the outside diameter of the pipes, and a batter of 3 inches per foot of depth 
will be allowed in the sides. 



Note, Hitt) Pipes exceeding /’thick, the spiopkendis bevelled to rthickness 



Sketch No. 127. —Joints used at Manchester and London. 

(e) A faucit hole 3 feet 6 inches long by 9 inches deep, must be excavated 
round each joint, but the body^of the pipe must be bedded solid throughout its 
entire length. 

(/) The pipes are to be jointed with lead and yarn. The joints are to be 
made by having the faucit caulked, with good hemp rope yarn, within 2\ inches 
of the outside, and the space left is to be run full of lead, which must be properly 
staved up with a caulking iron and a 4-pound hammer, so as to be flush with 
the faucit when finished, and perfectly water-tight. The lead used must be 
best soft pig, and a sufficient quantity must be melted at a time to finish each 
joint at one running. 

The following comments may be made: 













































45 2 


CONTROL OF WATER 


Clause (a). The materials and process specified were those generally used 
at the time during which the Staines reservoirs were being constructed. It is 
doubtful whether at present the clause means anything except “ best modern 
practice.” The real security against bad metal lies in clauses (6) and ( c ), and 
the test under pressure, and if the founders can satisfy these, any interference 
with materials or methods seems to be unnecessary. 

Clause (d). This clause merely specifies the quantities of earthwork to be 
paid for. The results are usually somewhat in excess of the quantity actually 
taken out from a timbered trench. Contractors, for some obscure reason, always 
raise the question of “batters on the faucit holes.” 

Clause (e). A very necessary clause indeed, which might be supplemented 



Sketch. No. 128.—Collar used at Manchester. 

by a direction to joint each pipe in place, and adjust true to grade and line by 
“level and theodolite” in cases where the head available is small. 

Clause (/). This clause practically means that the whole length of lead 
joint is to be caulked round twice, and is to be compressed about a quarter of 
an inch in the process. The use of hemp yarn has been objected to, and it is 
now believed to be sometimes detrimental to the quality of the water.’ Jointing 
by lead alone requites more skill. Jointing' with lead wool, or soft wood wedges 
is a makeshift, which is sometimes resorted to when water cannot be kept out 
of the trench so as to enable molten lead to be used. Some of the patented 
lead “ wools ” will produce very good work in the hands of a skilled man. The 
joint, however, must be specially designed if these articles are used. 

Sketch No. 129 shows the details of timbering and the methods of lowering 




































RIVETED STEEL TIRES 


453 

a 48-inch pipe into a deep trench. The timbering is unusually heavy, but even 
so it is plain that the excavation should not be kept open longer than is absol¬ 
utely necessary. It is also plain that a pipe much exceeding 48 inches diameter 
would be very difficult to handle in a timbered trench unless the circumstances 
were very favourable. 

Large Wrought-Iron or Steel Riveted Pipes.— These pipes are 
largely employed in America for water works. Hamilton Smith ( Hydraulics , 
p. 265) states that their discharge (when coated with asphalt) is the same as 
that of well made cast-iron pipes, similarly coated. This we now know to be 
untrue in large sizes. The facts have been collected by Herschel (fig Experi¬ 
ments on ... , large riveted Metal Conduits ), and the following table is a 
resume: 

VALUES OF C IN v=C>jTs FOR NEW RIVETED PIPES. . 


Diameter. 

72 Inches. 

48 Inches. 

42 Inches. 

38 Inches. 

Joints. 

Cylinder. 

Cylinder. 

Taper. 

Taper. 

Cylinder. 

Velocity. 

1 Foot per sec. 

IIO 

IOI 

97 

96 

t 

IOI 

• • • 


I IO 

109 

IOO 

108 

104 

• • • 

3 0 

108 

113 

102 

”3 

106 

115 

4 n >j 

111 

JI 3 

104 

1 13 

108 

109 

5 5 ) )) 

• • • 

112 

io 5 

III 

108 

• • • 

6 » „ 

• • • 

112 

io 5 

IOO 

io8 

• • • 


M. 

B. 

A. 

B. 

A. 

A. 

Thickness of 
plates in inches 

\3 tQ 11 
/ 8 LU 16 

i to t 

- 

1 

i 


i 34% 
A 45 /o 
§1% 

| t t0 is 


Diameter. 

36 Inches. 

16 Inches. 

15 Inches. 

13 Inches. 

ill Inches. 

11 Inches. 

Joints. 

Cylinder. 

Cylinder. 

Taper. 

Taper. 

Screw. 

Taper. 

Velocity, 
i Foot per sec. 

86 


• • • 

• • • 

98 

... 

\p jj )? 

95 

... 

... 

... 

109 

• • • 

3 5 ) 5 ) 

103 

• • • 

• • • 

• • • 

117 

* 

• • • 

4)5 5 ) 

hi 

« • • 

HI 

108 

I 2 I 

• • • 

5 55 1) 

1T 7 

110 

11 3 

HO 

I 24 

108 

6 5 , 

• 

124 

• • • 

116 

V. 

I I 2 

126 

110 

' 


C. 

B. 

B. 

B. 

B. 

B. 

Thicknessl 

i 

1 

1 1 

4 1 

Not 

• 

o'o7 to 

Not 

0*07 to 

ot plates 
in inches; 

recorded 

o’o8 1 

* 

recorded 

o’oS 











































































454 


CONTROL OF WATER 


For similar old conduits we have: 


Diameter. 

103 Inches. 

72 Inches. 

48 Inches. 

48 Inches. 

36 Inches. 

24 Inches. 

Joints. 

Cylinder. 

Cylinder. 

Cylinder. 

Cylinder. 

Cylinder. 

Cylinder. 

Age. 

5 Years. 

2 Years. 

4 Years. 

4 Years. 

4 Years. 

14 Years. 

1 

1 Velocity in feet 
per second. 

1 

2 . 

3 • 

4 • 

5 • 

6 . 

117 

110 

108 

106 

g 2 

98 

102 

104 

10 5 

97 

103 

io 5 

104 

104 

104 

73 

90 

93 

94 

94 

95 

• • • 

• • • 

• • • 

• • • 

106 

• • • 

• • • 

80 

... 

• • • 

• • • 

Thickness 
of plates 
in inches 

B. 

• 

l 1 

2 

4 

M. 

A to TV 

8 LU 1 6 

A. 

1 

4 

A. 

-I-toS 

c. 

1 

4 

B. 

8 

1 « 

1 


fi*6 Temporary Strutwedged) ,-./i 
bepteen Soldiers before removing j j 
Timbering Strut to lower Pitx \ j 


Yialing ^ 

Poling, 

tioards 

lNPacking 
above pages 


l 


X 



12*5 farting 
above Runner 


— Detail of Pdtfino Pieces — 


Double Fhges in lowest Frame 

lowest Frame 5-/’above bottom of trench 
Fora pipe 4-idacross sockets 



i • Fop of Soldiers lit above Fop ofupper 
j i struts For 4? cdernal dia. Pipe 


‘Poling Boards 5'-6‘9'3 
__-Walings ti'\9\5\ 
Struts 7-'6*9*5 __ 
Puncheons 2-S'jf 
s-Lip Pieces /'*£*/' 
N<n 

57*i Poling boards ) 
6 Lip Pieces 
2 Walings 


(per /4'*3'-6" frame 


5 Struts 

6 Puncheons 


noPuneheons 

see detail 

-ttalings 14*9*3’ 
Runners M'*<f*3’ 
■Puncheons 2-7*4* f' 
Att| 7 />s 12*4’2" 
%-PPges 
Struts 6'*H‘f 
orS-/0*ll*4 



Cross Polings ?'-5*6-tfi 
behind struts i puncheons 
inl/eu of runners. 

about t&" 


Elevation- 


IP/eoplDs of Pipe lorFPTTTT 
6 dragged forward, 6 dragged 
backward below lowest Frames 


6*C" Temporary Strutat base 
of Soldiers 

Sketch No. 129.—Timbering of a Pipe Trench and lowering of a 48-inch Pipe 

through same. 


The letters A,B,C,*refer to Herschel’s estimates of the accuracy of the ex¬ 
periment, and M, refers to the results obtained by Marx, Wing, and Hoskin 
( Trans . Am. Soc. of C.E., vol. 44, p. 34). 

It is fairly evident that the experiments can hardly be regarded as 


























































































































































CORRECTION FOR PLATE THICKNESS 


455 


conducted on pipes of the same hydraulic class, even in the very restricted 
sense that all “ new cast-iron ” pipes can be considered as falling under one 
category. 

The question has been dealt with by Kuichling ( Trcins. Am. Soc. ofC.E., 
vol. 40, p. 535), in discussing the results of the new 72-inch pipe (M, of the 
above table). This is made with a cylinder joint, so that the walls of the pipe 
are continuous ; but at each joint four rows of rivet heads project into the pipe, 
and reduce the area. Kuichling considers that the loss of head at such con¬ 
tractions must be allowed for. 

No exception can be taken to the principle, and I give the details of the 
work, although it will be obvious that the coefficients being deduced from 
Weisbach’s experiments on small orifices, cannot pretend to any great degree 
of accuracy. 

We have (see Sketch No. 131, Fig. 1): 

A 1? corresponds to a diameter of 72*22 inches. 

A 2 , is A 1? less the area of the rivet heads, and corresponds to a diameter 
of 71*78 inches. 

- ^=0*98785 = ;;? 

The loss of head (see p. 786) is given by : 



and Kuichling states that when m, lies between o*8 and 1, Weisbach’s results 
correspond to c c = 1 *225-f-i*45;;? 2 —1*675;;?. Thus, for ;;? = o*98785, ^=0*98533, 
and there being 1984 such constrictions, the loss of head thus produced is 
0*34196 feet, when v— 3*846 feet per second. 

When applied to the experimental value, C = 112*6, this correction gives the 
value of C, that includes skin friction losses only, as C = 118*9. 

A more complicated case is that shown in Sketch No. 131, Fig. 2. 

Here we have : 


Ao 

—2 = 0*97629, hence ^ = 0*97177, 

Ai 

and 14143, such constrictions cause a loss of head of 6*880 feet, and 


A • / 

also -A— 0*97204, and the ordinary formula gives a loss of ( 1 — 
A3 v 

or, for 6700 constrictions, the head lost is equal to 0*872 feet. 

So also, Kuichling uses Weisbach’s formula for elbows 

angle 0.* , /2 

4 ,i = ( 0-9457 sin 2 ! + 2 'c >47 sin 4 


MV 

As'2 g* 

of a deflection 


and corrects for stop valves, etc. These last corrections need hardly be applied, 
since we merely wish to cut out those effects which are directly dependent on 
the construction of the pipes. 

The general result appears to be that in pipes of large diameter, and about 
§ths of an inch thick, approximately 10 per cent, of the total head lost can 
usually be explained by resistance due to rivet heads, or discontinuities in the 
inner surface of the pipe, so that the values of C, given above would be increased 
in the case of a smooth pipe by some five or six units. 


CONTROL OF WATER 


45 6 

Le Conte (Trans. Am. Soc. of C.E ., vol. 40, p. 549), has gone so far as to 
tabulate the effect on C, of the thickness of the plates (which influences the 
size of the rivet heads) as follows : 


Plate Thickness in Inches. 


Diameter 
in Inches. 

0*06 

o'oS 

O’lO 

0-13 

0*15 

0*16 

0-18 

0’20 

0.24 

0-25 

0‘28 

§• 

44 • 



• • • 

•120 

1 19 

117 

116 

114 

112 

111 

no 

IOO 

42 . 

• • • 

•. • 

• • • 

116 

1*5 

114 

113 

in 

109 

109 

108 

IOO 

37 i • 

• • • 

116 

114 

112 

hi 

110 

109 

108 

io 5 

104 

104 

95 

30 • 

• • • 

114 

I 12 

110 

109 

108 

106 

io 5 

102 

101 

IOO 

9 1 

24 . 

• • • 

III 

IOO 

107 

106 

104 

103 

101 

98 

97 

97 

87 

12 

TOO 

99 

97 

95 

94 

93 

9 i 

90 

88 

87 

86 

78 


Le Conte’s table gives the plate thickness in “ B.W.G.,” and consequently 
the above thicknesses may err somewhat. It is hardly to be supposed that 



such a discrepancy will materially affect the coefficients, which apply to pipes 
about two years’ old, subject to little tuberculation, and are mostly obtained 
from experiments on taper-jointed pipes. 

The above facts indicate that the discharge of a riveted iron main may be 
considered as greatly affected by the type of joint, thickness of plates, and 
riveting. 

When such a pipe has to be calculated, and the plates are abnormally thick, 
due allowance should be made for the possible diminution in discharge, either 








































































































































CORRECTION FOR RIVET NEATS 


457 


empirically (as by Le Conte), or arithmetically (as by Kuichling) ; and for this 
reason I have, where possible, tabulated the plate thicknesses. 

In new pipes it appears that results not very far from the truth may be 
obtained by assuming a loss of head between 5, and 10 percent, greater than 
that in clean cast-iron mains of the same size, and then allowing for rivet heads, 
and plate thickness (where the-joints are not cylindrical) as above explained. 



Sketch No. 131.— Effect of Rivet Heads and Joints on Discharge of a Steel Pipe. 


This, in the case of ^ths-inch plates, and over, finally produces a total 
increase of lost head equivalent to about 20 per cent., or a decrease in C, of 
approximately 10 per cent. 

Tutton’s value is principally founded upon experiments on pipes with plates 
less than i%ths of an inch thick, so that smaller values of C x or C may be 
expected with heavier plates (page 428). 

In considering the possible decrease in discharge, due to age, we can assume 
that the rivet and joint irregularites are less influential when the remainder of 
the pipe surface becomes incrusted. A badly incrusted riveted main may be 
expected to have the same discharging power as a similarly affected pipe of 
cast iron. Hence, as a value corresponding to Tutton’s 105, for a cast-iron 
































CONTROL OF WATER 


45 8 

pipe with average incrustation, it seems fair to take ioo, corresponding to the io 
per cent, extra loss of head unexplained by Kuichling’s calculations. Tutton’s 
value i io, for steel pipes refers to pipes from 5 to 8 years’ old at the most. 

As practical results, we should bear in mind that riveted pipes were, until 
lately, mostly employed in pioneer work, and that our experience is almost 
entirely derived from such cases. British engineers are now adopting them 
somewhat largely, and, following the usual British principles of design, are 
specifying heavier plates. The maximum thickness of the plates in any of the 
pipes tabulated above, except Marx’s (the engineer actually responsible was 
Goldmark, see Trans. Am. Soc. of C.E., vol. 38, p. 246) 72-inch pipe, was fths 
inch, while the minimum in a pipe of British design may be taken as i 6 $ths inch, 
at least. Thus, it is advisable to make allowance for this fact in estimating the 
probable discharge. There is, however, one circumstance favouring British 
design, namely,—the thinner American pipes are more easily deformed and 
rendered elliptical by earth pressure. The effect of such deformation is not 
calculable, but it evidently tends to decrease the discharge, so that the diminution 
produced by the thicker plates (or rather in the case of cylinder joint pipes by 
the larger rivet heads) may be partly counterbalanced by the more perfect shape 
of the pipe when buried in the earth. 

The adoption of counter-sunk rivets for internal work has obvious advantages, 
and in cases where the size must be kept down, at all costs, the extra expense 
may be justified. 

Distortion of Riveted Pipes.— Clarke {Trans. Am. Soc. of C.E., vol. 38, 
p. 93) gives some experiments which show the following results : 




Compression of Vertical Diameter. 

Pipe 

Diameter 
in Inches. 





Thickness 
in Inches. 

Under Weight 
of Pipe only. 

Extra ditto 
under 54 Feet 
of Sand. 

Extra ditto under a con¬ 
centrated Weight applied at 
Top of Vertical Diameter. 

33 

42 

42 

42 

42 

42 

0'203 

0-238 

0-203 

0-203 

0*203 

0-203 

in. or P 
| in. 

X6 in * t0 1 

Do. 

Do. 

Do. 

1 in. or T V 
t in. or T V 

tf in - t0 A 
Do. 

Do. 

i in. (sand 
saturated 
with water) 

in. under 4,800 lb. 
iyg in. under 17,000 lb. 
4J in. under 36,000 lb. 


Actual measurements in the trench of 42-inch pipes, 0-203 inches thick, 
show compressions of 1^ to inches. It appears that if the earth backfilling 
is not properly tamped round the main, a large thin pipe maybe considerably 
strained, and possibly stressed beyond the elastic limit, thus producing a 
permanent set. If, however, the earth is properly rammed up to the top of the 
pipe, in 6-inch layers, the deformations do not exceed such values as or 
^ inch, and cause no undue stress in the metal. 

Corrosion of Steel Pipes.—O f late years many cases have occurred 




















SPECIFICATION OF STEEL PIPES 459 

(especially in the United States), of marked pitting and corrosion of steel mains. 
The actual facts are hard to arrive at; but it appears that the steel used in con* 
struction was less capable of resisting corrosion than wrought or cast iron, and 
it has been suggested that this is a general property of steel. The evidence 
rather appears to suggest that it is a failing common to cheap steel, as 
delivered by manufacturers who have not been exposed to effective competition. 
The matter is mentioned as indicating the necessity for obtaining the best 
possible chemical advice before accepting a tender which may, in other respects, 
(cost especially) appear to be very satisfactory. 

In all cases (above all, where stray currents from tram, or other electric, 
systems are to be apprehended), the outside of the mains should be carefully 
protected. The problem is more simple than that of the interior coating. The 
pipe when hot from the asphalte or tar dip, is carefully wound round with two 
coatings of burlap, or jute fabric ; and this is again tarred over. This coating 
will generally have to be renewed on the site at each joint, and special pre¬ 
cautions should be taken to ensure a good, adherent coating. 

Specifica tion. —The following is an abstract of Goldmark’s specification 
for a 72-inch riveted steel pipe (Trans. Am. Soc. of C.E., vol. 38, p. 246): 

I. All seams shall be butt seams, with stops exactly fitted to the curvature of the 
main plates. 

II. The round straps uniting adjacent sections shall be placed on the outside of the 
pipe only. The longitudinal seams shall be united by two butt straps, one on the 
inside, and the other on the outside of the pipe. 

III. The longitudinal joints shall in all cases be placed at the top of the pipe, so 
that the straps shall be continuous throughout the entire length of the pipe. 

IV. All butt straps, both longitudinal and circumferential, shall be rolled to the 
correct circular curve necessary to fit the pipe closely. 

V. The edges of the outside straps, both round and longitudinal, shall be planed 
for caulking. 

VI. The inside longitudinal butt straps shall be the same length as the main plates; 
they shall be as straight and true as possible, but shall not be caulked. 

VII. The outside longitudinal straps, where they are built against the edges of the 
round straps, shall be planed down to a feather edge for a short distance, and extended 
under the round straps, the edges of the latter being caulked. 

VIII. The splices in the round straps shall be scarphed joints,extending over three rivets. 

IX. The under strap at the lap must be scarphed, or thinned by machinery, without 
being heated ; the upper strap is to remain of the original thickness for caulking. 

X. The rivet holes shall be punched of iV inch greater diameter than that of the 
cold rivet, except in the case of i-|- inch rivets. In this latter case, the rivet holes shall 
be punched of i-|- inch diameter, on the die side, and reamed to i T 3 g inch. 

XI. All riveting in the shop must be done by machinery, capable of exerting slow 
pressure, sufficient for the formation of perfect rivet heads. 

XII. All burrs caused by punching on the lower side of the plate must be removed 
by countersinking ; all burrs produced by shearing must be removed by filing or chipping. 

XIII. The sheets must be pressed closely together, while the rivets are being 
driven, and until the rivet heads are formed. All rivets which do not properly fill the 
holes, must be cut out and replaced. 

XIV. All riveted seams and joints of every description shall be thoroughly caulked 
on the outside of the pipe in the best and most workmanlike manner usual in first-class 
boiler work. The caulking of all seams made in the shop must be done before the 
coating is applied to the pipe, and every precaution must be taken both in shop and field 
work, to ensure the utmost strength and tightness. 


4 6o CONTROL OF WATER ■ 


XV. All plates and rivets must be free from rust, and kept under cover from the time 
of manufacture of the plates, until the completed pipe is dipped or coated. 

XVI. Any plate that shows anydefect during the process of punching, bending, riveting, 
and in manufacturing into pipes, shall be rejected, notwithstanding that the same may 
previously have been satisfactorily tested. 

A tabulation of the dimensions is as follows : 


Thickness of— 

Diameter 
of Rivets, 
Cold. 

Maximum Stresses in lbs. per Square Inch. 

Plates. 

Inches. 

Straps. 

Inches. 

Plates. 

Rivets. 

Gross 

Section. 

Nett 

Section. 

• 

Shearing. ; Bearing. 

1 ' 

1 i 

16 

1 

2 

1 7 ? 

I 1,000 

12,940 

I J 

5,74° 1 14,600 

5 

8 

1 

2 

i\ 

I 1,200 

13,200 

5,200 ! 14,800 

9 

1 6 

3 

8 

1 

11,400 

13,200 

5,520- j 15,800 

1 

2 

3 

8 

1 

1 r,600 

13,60° 

5,200 i 16,400 

tV 

3 

8 

7 

H 

11,800 

I 3 > 5 °° 

5,020 | 15,200 

3 

8 

1 

7 

8 

12,000 

14,000 

5,300 15,200 1 

. 


Maximum 
Head of 
Water on 
Pipe. 


484 feet 
448 „ 

410 „ 

371 » 
330 » 

288 ,, 


I 


1 


The longitudinal straps were 11 inches wide on the outside, and 16^ inches 
on the inside ; the circumferential straps being 11 inches in width. 

The coating was composed of natural California asphalte, mixed with 
enough liquid asphalte of over 14 degrees Beaume gravity to fill the voids in 
the dry rock. 

The mixture was heated by steam coils, and it was found that a good 
adherent covering was produced on the pipe after one hour’s treatment in 
the bath. 

The details of the process evidently require careful previous study, as the 
time in the bath is longer than is necessary in the case of the typical Angus 
Smith mixture. 

We may further note as follows : 

(i) The design secures only one longitudinal joint, at the cost of a circum¬ 
ferential joint at every 9 feet 2 inches. If two longitudinal joints were used, a 
circumferential joint would occur at every 19 feet : and in view of Kuichling’s 
investigations, the latter seems to be a better system hydraulically. 

(ii) The caulking on the outside is not what would be adopted were water¬ 
tightness the sole object in view, since inside caulking is far more efficient. 
The idea is plainly to avoid damage to the pipe coating, and it is satisfactory 
to know that the main is water-tight. 

(iii) The first part of paragraph X, is not precisely “first-class work,” as 
specified in the second sentence. The whole paragraph, however, shows a 
very nice appreciation of the problem of securing satisfactory work at a cheap 
rate. The “second-class work” is placed where it will do least harm, and 
where impact stresses will be least. The graduation of the stresses shown in 
the table is equally commendable. The pipe line is about 4500 feet long, and 
supplies a power station. Thus, water hammer is possible, and, so far as 
practicable, the design gives the greater margin of strength at the lower end, 
where the shock will be worst. 

























SPECIFICATION OF STEEL 


461 

Goldmark’s specification of the steel is equally complete. Both for acid 
and basic steel he specifies the maximum percentages of sulphur, phosphorus, 
and manganese, and gives the ultimate tensile strength, maximum (65,000 lbs.) 
and minimum (55,000 lbs.) per square inch, elastic limit (as over one-half of the 
ultimate strength), elongation (not less than 24 per cent, in 8 inches) and 
reduction of area (at least 48 per cent.), also character of fracture (as silky) 
and a bending test (free from crystalline appearance), punching test, and a 
drifting test. 

The two last are : 

A row of holes (eight in number), inch in diameter, and if inch between centres, 
shall be punched cold in a plate if inch wide, and 10 inches long, without any cracks. 

Two holes f inch in diameter, 2 inches between centres, shall be punched in a plate 
3x5 inches and then enlarged cold by drifting to if inch diameter, without cracks. 



The undimensioned radii were altered at least once during construction; 
Those shewn ore considered the best: 


iji* • •• $■' 



Sketch No. 132.—Locking Bar and Collars for Locking Bar Pipes. 

The rivets are specified as : 

Ultimate tensile strength between 56,000 and 64,000 lbs. per square inch, elastic 
limit not less than 36,000 lbs., shearing stress not less than 72 per cent, of the ultimate 
tensile stress. 

The chemical details of this part of the specification are, of course, some¬ 
what obsolete at the present day, but the information given is very complete, 
and forms a good model. 

















































CONTROL OF WATER 


462 


Locking Bar Pipe. —This was first introduced by Mephan Ferguson of 
Melbourne, and has been largely used in Australia. 

Several variants have lately been adopted, but none of them appear to 
possess any real superiority. 

Each pipe length is composed of one or two longitudinal plates, bent to 
the correct radius, and connected by locking bars. Sketch No. 132 shows the 
burring of the edges of the plates, and the method in which the locking bar is 
closed, as indicated by Palmer {P.I.C.E., vol. 162, p. 80), and shows the exact 
dimensions of the bar as used for the Coolgardie 30-inch main of 5- inch and 
y^ths inch plates. The design is intended to develop the full strength of the 
plates before failure, and is the fruit of repeated full scale experiments. The 
working stress is 4 \ tons per square inch on the gross area of plates with a 
minimum thickness of ^ inch. 

The tests made by Palmer ( ut sup?-a, p. 88) indicate that: 

C = n5 for new 30-inch pipes, in the equation ^ = C V rs, where no allowance 
is made for irregularities or reduction of area by the locking bar ; and a value 
of 83 appears to be assumed for old pipes. 

Corrosion is reported to have been very active on this particular main. 
The circumstances are unfavourable, since alkaline soils occur ; the external 
coating is in my opinion too soft, and the pipes were not heated in the mixture 
for a sufficiently long period. In any case, there is no evidence to show that 
the locking bar had any material effect in retarding or accelerating the 
corrosion. 

Construction of Steel Pipes.— If R, be the radius of the pipe in 
inches, and /, be the maximum internal water pressure in pounds per square 
inch (which is usually that obtained by considering the lower end of the pipe 
as closed up), the tension in the metal skin is given by : 


T=/R lbs. per lineal inch . 


[Inches] 


Thus /, the thickness of the metal plates is given by the equation : 

T 

. [Inches] 


t= 


/iM. 

Where s 1} is the permissible working stress of the metal in pounds per 
square inch ; and f x is an allowance for the reduction of the effective section 
produced either by rivet holes (where the longitudinal joints are riveted), or 
by corrosion or scraping the pipes if these are considered likely to occur. 

Thus, in lock bar pipes, if the strength of the joint is alone considered f u 
will be found to be equal to 1. Consequently, the portions of the plate at a 
distance from the joint possess no extra strength, and an additional thickness 
of a sixteenth of an inch over and above that calculated for strength is allowed. 
The value of j x , is usually taken as 16,800 lbs. per square inch for mild steel • 
and, in view of the very equable distribution of the stresses at the joints, this 
may be considered as a low rather than a high value. 

For riveted joints put : 


ff=The diameter of the rivet in inches 
/=The pitch of the riveting in inches 
d— U2 to 1*3 V 7 p — to i\d . 


[Special Notation] 


[Inches] 


Then, for single riveted joints, with the rivets in single shear ; 



THICKNESS OF STEEL PIPES 


463 


/i = o , 58 to 077, say 0*50 as a mean ; 

and if two cover plates are used, so that the rivets are in double shear, then : 

71=072 to o*61, say o’6y as a mean. 

For double riveted joints, with the rivets in single shear, it will be found that : 

fi —°*73 to °’57s say o'67 as a mean : 

and if the rivets are in double shear : 

f\ = o' 84 to 071, say 075 as a mean. 

The larger values occur in the thinner plates. 

Thus, except at and near the joints, the plates have a large excess of 
strength, and any allowance for corrosion appears to be unnecessary. 

The final design of the joint of course includes the determination of the 
following stresses (see p. 984): 

(i) The tensile stress in the plate along a line of rivets. 

(ii) The shearing stress on the rivets. 

(iii) The bearing stress on the rivets. 

The values given by Goldmark (see p. 460) are low ; but unless the interior 
of the joints can be caulked, it is inadvisable to reduce the rivet area, as when 
outside caulking alone is possible, leakage is mainly prevented by the grip 
produced by the contraction of the rivets. 

In cases where water hammer is likely to occur, the stress thus produced 
may be estimated ; and, if necessary, the thickness of the plates may be 
increased so as to provide for this. As a rule, it is allowable to assume a 
somewhat higher value of for such stresses, so that an increase in the 
thickness of the plate is not usually required. 

The allowance for corrosion is a matter of experience. Corrosion does not 
usually produce a general and uniform diminution of the plate thickness, but 
occurs in patches, small pin holes being eaten right through the plates long 
before any general decrease in thickness has occurred. 

Consequently, under the above circumstances, British engineers usually 
make a steel plate at least j^ths °f an inch, or §ths of an inch thick, quite 
apart from any stress calculations ; and do not allow any increase above the 
value obtained by stress calculations if the thickness thus obtained exceeds 
§ths of an inch. American engineers use thinner plates, and their practice 
is far more suited to pioneer conditions. The German rule, i.e. : 

Minimum thickness of plates = 0*20 inch. 

may be adopted in favourable circumstances. 

Anchoring Pipes. —Consider a bend or elbow in a pipe. 


Let d, be the diameter of the pipe in feet. 

Let H, be the pressure in feet of water. 

Let </>, be the deflection angle of the bend or elbow. 

Then, an outward pressure equal to 2 627H sin ~ lbs. exists along the 

line bisecting the angle between the initial and final tangents to the bend. 

2/2 

If the velocity be great, H, should be increased by —. 

2 <v 


The stresses thus produced in the pipe metal are not great; and, as a rule, 
even the friction of the ordinary lead joints of a cast-iron pipe is sufficient to 
prevent the bend from being blown out. The stress, however, occurs at a 


4 



CONTROL OF WATER 


464 


point where the joints are difficult to make, and in good practice it is now 
usual to bed the outer curve of the bend against a mass of concrete, of sufficient 
size to prevent motion without producing any stress on the pipe joints. The 
case where trouble is most likely to occur is at the crest of a hill, in a line of 
large, riveted pipes under heavy pressure ; and, under such conditions, saddles 
on the top of the pipes, well bolted down to masses of concrete are sometimes 
required. 

Wood Stave Pipes. —Goldmark {Trans. Am. Soc. of C.E., vol. 38, p. 267) 




W 



p4- 


Section OH. 


n 


n 


-Section CL ■ 


Section 3.8 


Sketch No. 133.— Shoes for Wood Stave Pipes. 


describes the construction of a 72-inch main as follows : The timber used was 
Douglas fir, in place of the usual red wood. I his is far harder and stiffer, and 
tiouble was anticipated in using it for staves, on account of the great amount 
of curvature in the pipe. However, no difficulty was experienced in putting 
the staves together properly, even in curves of 14 degrees. The specification was 
severe, requiring the best class of timber, perfectly free from knots, sap holes, 
season checks, and other flaws. The timber was almost beyond criticism, 














































































WOOD STAVE PIPES 465 


being practically perfect in appearance. It was, as far as possible, thoroughly 
seasoned and dried, and was kept under cover until placed in the trench. 

The pipe was built of 32 staves, the finished articles being 7^ inches on the 
outside, 7^ inches inside, and 2 inches thick. The outside was planed to a circle of 
384 inches radius, and the inside to a circle of 36^ inches radius. The radial sides 
were planes, smoothly finished. No variation of more than inch from the 
theoretical section was permitted. The staves were specified as 16, 18, and 20 
feet long ; but actually the lengths used were from 24 to 26 feet, and over. 
The ends of adjacent staves were at least 12 feet apart; and in all end joints a 
steel tongue, i| inch wide, ^th of an inch thick, and 2\ inches long, was in¬ 
serted into saw cuts in the staves. The tongue thus lay f of an inch in each of 
the staves jointed, and -gth of an inch in each of the adjacent continuous 
staves. 

The pipe was banded with round steel rods, fths of an inch in diameter, 
for pressures of less than 100 feet; and f of an inch for those over 100 feet. 
The unit stress was 14,500 lbs. per square inch ; i.e. 4500 lbs. for a fths inch, 
and 6500 lbs. for a f-inch rod. Thus, for the number of bands per 100 feet 
length of the pipe under a head of H, feet of water we get: 

For ifths of an inch bands, N =- - -= 4* i 6 H. 

8 4500x2 

For | of an inch, . . N = 2*9 H. 

The pipe diameter was assumed to be 6 feet, and the bands are assumed to 
bear the whole tensile stress. 

Sketch No. 133, Fig. I. shows the bands, and steel shoes for their junction. 

The design in Sketch No. 133, Fig. II, indicates a malleable iron shoe for a 
9-inch pipe, in which the forged loop used by Goldmark is replaced by a bolt- 
head bearing on the upper horns, A ; the upset screwed end being placed 
between the lower forks, B. The design is decidedly neat and is due to Fuertes 
( P.I.C.E. , vol. 162, p. 154), who states the following formula : 


33 o_HD 

- 79 • • • 

dtfs 1 

. n rr 1 


[Inches] 


as giving N, for a pipe D, inches in diameter, where each band has a diameter 
of d b , inches, and where j 1? is the permissible working stress Ln pounds per 
square inch. The staves in this case had a small bead on one radial side. 

Latterly, wood stave pipes have been built up with the bands made of 
continuous wire wound round in place, under the calculated tension. This 
appears to be more rational in smaller sizes, although it would be somewhat 
difficult to devise a means for thus handling mains as much as 6 feet in 
diameter. 

Goldmark’s pipe was actually laid with somewhat more than 6 feet vertical 
dimensions, and slightly less than 6 feet (say 5 feet njtjh inch nett) hori¬ 
zontal diameter ; so that deformation under the earth filling may render it ap¬ 
proximately circular in form. The pipe was not subjected to more than 120 
feet head, and was not exposed to great water hammer, the relief arrangements 
being extremely well planned. 

The detailed design of wood stave pipes has been treated by Adams 
{Trans. Am. Soc. of C.E., vol. 41, p. 25, and vol. 58, p. 65), the mathematical 
methods here followed being given by Henny {Trans. Am. Soc. of C.E. , vol. 41, 
p. 71). 


30 





466 


CONTROL OF WATER 


Let: 

R = the internal radius of the pipe, in inches. 

7% = the radius of the band section, in inches. 
t — thickness of stave, in inches. 
f — the spacing between centres of bands, in inches. 

Q = the tensile stress in the band, in pounds. 
q = the safe ditto. 

ft = the water pressure, in pounds per square inch. 

Now, the bands must be initially stressed when the pipe is empty, so as to 
prevent leakage between the staves when the water pressure comes on the main. 
Let this additional stress be represented by X. Then, ? we assume that X = § ftft, 
i.e. X, is 150 per cent, of the pressure of the film of water between two staves. 

When the pipe is under pressure, we have in addition the tensile stress due 
to water pressure. 

Therefore, Q — ftfR-\-% ftp = q, say.. [Inches] 




Sketch No. 134*—Calculation of Bands for Wood Stave Pipes. 


Now, if the tension of the band exceeds (R + />, where e, represents the 
safe pressure on the wood per lineal inch of the band, the timber of the staves 
will be crushed or indented by the band. 

Therefore we get: 

^ ~ ft(R+%t) .[Inches] 

and ft should not exceed : 


(R+^ 

/(R+f *) ’ 

or crushing of the staves may occur. 


[Inches] 


Now, actual experiment appears to indicate that for red wood the per¬ 
missible value of e , is given by e = K r b ; where K, is not far off 660 lbs. per 
square inch (although values as high as 800, 900, and 1100 lbs. occur in 
practice, with satisfactory results), and the width of the portion of the band 
which presses on the timber is taken as equal to the radius of the band. K, 










































INDENTATION OF WOODEN STAVES 467 

however, varies somewhat with the size of the band, becoming less as the 
diameter increases. Thus, Henny tabulates as follows : 


Diameter of Band 
in Inches. 

e, Pounds per Lineal Inch. 

& 

8 

140 

7 

1 6 

153 

1 

2 

165 

5 

8 

200 

1 

232 

7 

8 

262 


and similar values can be obtained for any other wood by experiment. 

The pipe can thus be protected against damage by indentation of the staves 
by the metal bands. Where the water pressure is small, the spacing is large. 
Thus, in cases where crushing is feared, oval bands should be used in order to 
increase the bearing area. 

Adams also states that the bands may be fractured by the expansion of the 
staves on becoming saturated with water. 

The stress thus produced is : 

q 2 =/{( R+fO^ + E'V}.[Inches] 

and Adams takes E"= 100 lbs. per square inch. 

We thus obtain the following conditions, which should be satisfied in a well 
designed pipe : 

(i) Q = j^(R+f/).[Inches] 

and the diameter of the band is given by : 

Q — ^ di?s 1 — q .[Inches] 

where s x , is about 14,000 lbs. per square inch. 

(ii) Calculate q 2 + f*) + E"/} .... [Inches] 

where E", is an experimental coefficient depending on the expansion of the 
wood when wetted. 

7T 

The value of s 2 , given by q 2 — - dtfs 2 .[Inches] 

should not exceed 20,000 lbs. per square inch. 

(iii) Calculate e = .[Inches] 

and ascertain whether the value of the pressure per lineal inch of the bands on 
the timber exceeds the permissible values. 

It will be noticed that very approximately : 

e = = Kr h .[Inches] 

2 

but the variation is sufficient to justify special experiments with bands of 
different diameters. 












CONTROL OF WATER 


468 


# 


It will be evident that these last two conditions are mainly important when/, 
and t , are large when compared with R ; i.e. in big pipes under small pressures, 
or in small pipes under heavy pressures. 

The thickness of the wood staves is apparently fixed more by stock timber 
sizes than by any other requirements. Adams gives : 

For pipes of 10 to 14 ins. diam. the staves are cut from i| by 4 ins. material. 
„ 16 to 48 „ „ „ 2 by 6 „ 

„ 5o to 58 „ „ „ 2£ by 8 

The maximum head of water rarely exceeds 200 feet, and 180 feet is the 
more usual value. 

The durability of wood stave pipes appears to depend mainly on the way 
in which they are treated when in use. Like most timber structures, alternate 
wet and dry conditions are very trying ; and, as a general rule, the pipes should 
always run full, and should only be emptied when absolutely necessary. Under 
such circumstances, the wood appears to outlast the bands, and failure finally 
occurs when the metal is destroyed by rust. It is for this reason that circular, 
or oval bands, are preferable to the hoop iron type. 

There appears to be some difference of opinion as to whether a wooden 
main should be coated, either on the inside, or on the outside. Inside coating 
appears to be unnecessary, and outside treatment is not usually adopted in 
large pipes ; although some of the smaller sizes now manufactured in the 
Western United States as a stock commercial article are (after banding) 
systematically coated with asphalte, rolled in sawdust, and again coated. From 
experience of ordinary wooden structures I am inclined to suggest that if the 
timber is thoroughly seasoned before the pipe is laid, coating is advisable, and 
not otherwise. It must be remembered, however, that Goldmark, whose 
practice must be regarded as most authoritative, and who used wood of a 
quality not easily procurable under present-day conditions, did not coat his 
pipes, and is distinctly adverse to the process. 

In considering the introduction of wood stave pipes of local material into 
countries other than the United States, it should be remembered that the 
timber must be such as is usually considered straight, and long in grain, and 
fairly flexible ; although this requirement is only vital in curved portions of the 
pipe. The engineer will have to obtain values for e and E", by special 
experiments, and he should be entirely guided by local experience regarding 
the durability of the particular timber, and in deciding such questions as 
coating, seasoning, and the amount of tightening to be given to the bands 
before water pressure is put on the pipes. Broadly speaking, the initial band 
stress when empty should be about one-fourth that produced by the water 
pressure. So much depends on the hardness of the timber across the grain 
{i.e. the value of e), and its expansion when wetted {i.e. the value of E"), that 
any general rules are misleading, and more may be learnt from local coopers 
and an experimental length of pipe under pressure, than from any number of 
calculations. 

I have not discussed the question of beading the radial edges of the staves, 
in order to prevent leakage. This practice was adopted in some of the earlier 
wooden mains, but it appears to be now obsolete. Experience in cask making 
is distinctly adverse to the process, quite apart from the question of economy 
in labour and material. 


CHAPTER IX 



OPEN CHANNELS 


Formula for the Discharge of a Channel in Terms of tiie Hydraulic Mean 
Radius and the Slope. 

Definitions.- —Theoretical deduction of formulae is useless—Kiitter’s formula—Table 
of Rutter’s n —Discussion— Manning’s formula. 

Bazin's Formula .— Table of Bazin’s 7 — Classification of channels — Discussion— 
Classes V and VI have probably no physical existence. 

Graphic Solution. —Limits of application of Rutter’s or 
discussion. 

Silt-Bearing Waters. 

Table for Manning’s formula. 

Variable Flow in Open Channels. —General formulae- 

a —Application to a rectangular channel of uniform breadth—Standing wave—Bore. 

Practical Calculation of Backwater Curves. —Corrections for variations in the 
cross section or slope of the channel—Examples—Treatment of the case where a 
standing wave occurs—Drop-down curve. 

Transporting Power of Currents of Water. —Deacon’s experiments—Phases of 
transport—Lechalas’ investigation—Difference between the scouring action of clear 
and silted water—Relation between depth and velocity in a river carrying silt— 
Influence of the absolute quantity of silt carried per foot width of the channel— 
General laws of silt and scour—Comments—Thrupp’s values—Comparison—Physical 

meaning of the equations—Relation between ^ 


Bazin’s formulae—Thrupp’s 


-Possible errors—Values of 


for a river and a canal 


Bed width 

—Results obtained by logarithmic plotting of the mean velocity and the mean depth 
for a river carrying silt—Variation of n in the equation q = kv n for Phases I, II, and 
III—Tabulation of the values of V,. 


NOTATION 

a, is the area of the cross-section of the channel in square feet. 
a 1} and a 2 , are the values of a, at specified points (see p. 481). 
a l2 , (see p. 482). 

b, is the breadth of the channel in feet. _ 

C, is the coefficient in the formula v—C^rs. 

C ]} and Co, (see p. 485). 

Throughout this Chapter d, is employed for the sign of differentiation only. 

/, is the depth in feet of the water in the channel at any point. _ 

F, is the value of f, appropriate to uniform motion, i.e. ^ = C\^D, and bvY = Q<. 

/, is the length of the channel in feet measured along its main stream. 

/ 12 , is the value of /, from the point specified by suffix 1, to the point specified by suffix 2. 
n , is Rutter’s “ coefficient of rugosity” (see p. 47 2 )> an< ^ Manning’s formula. 
p, is the length in feet of the wetted portion of the boundary of the area a. 

Qj, is the total discharge of the channel in cusecs. In the investigation of Variable Flow 
Q, is used for the discharge per foot breadth of the channel. 

r, is the hydraulic mean radius of the channel in feet. r =—. 

r J2 , (see p. 482). 


469 



470 


CONTROL OF WATER 


R, is used for r, when expressed in metric measure. 

s, in open channels is theoretically the sine of the angle of the slope of the water suiface. 
In practice, s, usually refers to the bed slope, and is so used in backwater calcula¬ 
tions. In closed channels s, refers to the slope of the hydraulic gradient. 
v , is the mean velocity of the water in feet per second. 


x, is used for 


L 

F* 


v = - 


Qt 

a 


or v= 


Q 

7 


s 12 , is the fall of the water surface in feet, measured from the point 2, to the point I. 
a is a coefficient (see p. 481), and 
7 is Bazin’s coefficient (see p. 474). 

0 and x are functional symbols (see p. 483). It must be noted that 0 (^r) is tabulated 

under the argument —, and x ( x ) under the argument x, the object being to avoid 

oc 

unduly extensive tables. 


Mean velocity, v — 


a 


SUMMARY OF FORMULA 


Hydraulic mean radius, 


a 

7 


General formula, v= C sirs. 
Kiitter, C = 


„ o'oo 28 i i *8 i i 
41-6 +--— + 


n 


, n f o ‘ oo 28 i 1 

+ V7'l 4r6+ 7 ) 


(see p. 471). 


Manning, v= * \Jr**Js ; C = ( See P- 472 ). 

Bazin, C = “-—- (see p. 474). 


1 + 




Backwater curves, 1 +a=i + ~q 7 ( see P* 4 & 1 ). 


_ 

dl~ 


Qt 2 

s ~ CT/ 3 

1 + ct Qc 

~T W 3 




Note: 0 ^ 7 J ^ is found under the argument]-^. 


(see Table at end). 


Formulae for the Discharge of a Channel in Term of the 
Hydraulic Mean Radius and the Slope. —The mean velocity of water 
in a channel has been defined (p. 44) and is measured in feet per second, and 
denoted by the symbol v. 

Let a, represent the total area of the cross-section of the channel in square 













HYDRA ULIC MEAN RADIUS 471 

feet, and^, be the wetted perimeter in feet, i.e. the total length of that portion 
of the fixed boundary (i.e. air boundaries excluded) of a, which is in contact 
with the fluid. Then 


P 

is defined as the hydraulic mean radius of the channel, and is measured in feet. 

In an open channel the slope of the water surface needs no definition, but it 
is as well to remark that I believe that it cannot be observed. What is usually 
observed, and is almost invariably used in practical applications of the formulas, 
is the bed slope of the channel, which is thus assumed to be of uniform depth. 

In a pipe, or closed channel, we can assume that pressure gauges are erected 
at convenient points, and we may define the slope of the hydraulic gradient as : 


_Th e diff erence of the observed pressures expressed in feet of water__ 

The length between the gauges measured along the axis of the pipe in feet 

The symbol j-, will be used for the slope. 

It is usual in treatises on Hydraulics to give a mathematical investigation 
showing that v — CIrs. 

The principles assumed are that water moves as a solid body, and that the 
laws of friction between this body and the banks and bed of the channel are 
those usually considered as holding for friction between solid bodies. Since 
the assumptions depart hopelessly from the truth, I believe that it is more 
rational to omit the demonstration, and merely to draw attention to its errors. 

The formula is probably quite as far removed from a true representation of 
the facts as its demonstration. Nevertheless, it possesses a certain claim to 
respect owing to its antiquity, and lends itself to easy calculation, so that 
practical advantages justify its adoption as a standard. 

The equation is usually said to apply to rivers flowing in natural beds ; but 
this is merely an instance of the conservatism of engineers. In the days when 
an engineer’s field instruments were limited to a level and theodolite, it is possible 
that the surface slope of a river was really believed to be more easily observed 
than its discharge. 

In the light of the hydraulic knowledge of to-day, it is extremely doubtful 
whether an uncanalised river possesses a surface slope that can be observed ; 
and it is quite certain that the discharge can be obtained with less expenditure 
of time, and greater accuracy. 

The v — CVrs equation is suitable for artificial channels of regular section 
only. When applied to natural channels, it is merely an interpolation formula 
of very limited range. 

I do not propose to discuss any of the earlier equations when C, was 
taken as constant, or as slightly variable ; such formulae served their purpose 
in the past, but are now useless. 

The formula most fashionable amongst British engineers is that of Kiitter 
and Ganguillet. Here, v — CVrs, and C, is determined by the equation : 


41*64 


o'ooiSi . 1 *811 


C=. 


n 


14 


n ( 


6 -j- 


0’0028 1 


) 


where it is as well to state that the somewhat peculiar coefficients, such as 








472 


CONTROL OF WATER 


i *811, etc., arise from a conversion of the round numbers occurring in the formula 
when expressed in metric units : 


C metric : 


0-00155 i 

23 3 - u + - 

° s n 


. n ( . 0-00155\ 

I_p ( 23 -1- ±2 1 

VR V J 7 


R, being the hydraulic mean radius expressed in metres. 

72, is the “coefficient of rugosity,” colloquially termed “ Kiitter’s 72 .” 

The table opposite shows the values specified by Kiitter and Ganguillet, 
and also a selection of those determined by other experimenters. 

It will be noticed that Kiitter himself did not propose to apply his formula 
to pipes. The fact that other engineers have done so is no doubt com¬ 
plimentary ; but I believe that the reason is to be sought not so much in any 
real physical truth underlying the formula, as in the fact that the statement : 
Kiitter’s n= ... . forms a very convenient description. 

The history of this formula is interesting. At the date of its publication 
very few gaugings of large rivers had been undertaken, and modern methods 
were either unknown or in an experimental stage. So far as I am aware, none 
of the large river gaugings accessible to Kiitter and Ganguillet were taken by 
any of the methods which I have discussed ; and those on which they placed 
most reliance (Humphreys & Abbotts’ Mississippi Gaugings) were taken by the 
obsolete double float method, which Bazin ( A.P.C. , 1884, vol. 7) has shown to 
largely over-estimate the velocity in deep streams (see p. 54). 

The terms in the formula depending on 55 were introduced simply to obtain 
agreement with Humphreys & Abbotts’ results, and may therefore be con¬ 
sidered as based on very flimsy evidence. 

Some of the other observations on smaller rivers were more accurate ; and 
as Kiitter and Ganguillet discussed them with great skill, the formula for 
ordinary slopes (i.e. s= o'oi, to s = 0-00003) agrees remarkably well with observa¬ 
tions, more especially when its date is considered. In fact, I regard it as a 
very good example of the possibility of obtaining substantial accuracy by a 
careful discussion of a large number of observations, each individually more or 
less unsatisfactory. 

The continued employment of this formula is therefore not surprising, but 
it is to be hoped that it may be rapidly abandoned. At present, unfortunately, 
“ Kiitter’s 72,” is considered by many engineers as a species of shorthand 
description of a river, and, consequently, familiarity with the formula is 
necessary in order to comprehend the work of any engineer employing it. 

Diagram No. 5 gives C or n with all the accuracy required in practice. 
Bellasis’ Hydraulics contains a very excellent table of C, but since obtaining 
the diagram I have never required it. Most engineers use a table or some 
simplified form of Kutter’s original equation. 

The formula given by Manning (On the Flow of Water iji Channels and 
Pipes) is probably nearly as accurate as that given by Kiitter, and is easily 
calculated and remembered. It is ; 

v — 1 ' 49 ^ 0 . 07 ^ 0.5 

72 

where 72, is the value of Kutter’s 72 , for the class of pipe or channel considered. 

For example, for earth channels in very good condition, where 72 = 0-020, 

v = J4‘6 r°- c,7 s 0 - 5 






"RUTTER'S N ” 


473 


Specification of the Channel. 


Value of 11 . 


Authority. 


Timber, well planed and perfectly 
continuous 

* • 

Planed timber, not perfectly true . 
Glazed and enamelled materials 
with no irregularities, or clean 
coated pipes .... 
Pure cement plaster 
Wood stave pipes .... 
Plaster in cement, one-third sand . 
Pipes of iron, cement, or terra-cotta, 
well jointed, and in best order . 
Timber unplaned and continuous, 
new brickwork .... 
Good brickwork, and ashlar, ordi¬ 
nary iron pipes, unglazed stone¬ 
ware, and earthenware 
Canvas lining on wooden frames . 
Foul and slightly tuberculated iron . 
Rough-faced brickwork . 

Well dressed stonework . 

Wooden troughs with battens inside, 
\ inch apart .... 
Fine gravel, well rammed 
Rubble masonry in cement, in good 

order. 

Tuberculated iron pipes, brickwork 
or stonework in inferior condition 
Earthen channels in faultless con¬ 
dition .... 

Ditto, during heavy silting 
Earthen channels in very good order, 
or heavily silted in the past. 
Coarse gravel, well rammed . 
Wooden troughs with battens inside, 
2 inches apart . 

Large earthen channels maintained 
with care .... 

Small ditto .... 

Channels in average order 
Channels in order, below the average 
Channels in bad order . 

Channels in very bad order . 
Channels of worst possible character, 
with turbulent flow and large 
obstructions .... 


0-009 

o-oio 


o-oio 

o-oio 

o-oio 

o'oio 

o-oi i 

0-012 


0-013 

0-015 

0-015 

0-015 

0-015 

o-oi5 

0-017 

0-017 

0-017 

0-017 

0-017 

o-oi8 

0-020 


0-0225 

0-025 

0-025 

0-0275 

0-030 

o-o 35 


0-040 


Kiitter. 


Kiitter. 

Kiitter. 


Kiitter. 


Kiitter. 


Punjab Irriga¬ 
tion Branch. 
Punjab Irriga¬ 
tion Branch. 
Kiitter. 
Jackson, 
Kiitter. 
Kiitter. 


Jackson. 

































CONTROL OF WATER 


474 


I have been accustomed to use this formula for preliminary calculations, and 
have rarely found that the values obtained by the accurate Kiitter form, or by 
Bazin’s equation, differ to such an extent that appreciable errors are introduced. 

Bazin's Formula. —Experience has led me to use Bazin’s formula of 1897 
exclusively, in accurate calculations. 

Expressed in English units, we have : 

v — C\ f 


where 


C 


_ 1 57*6 
1 + 


V; 


Bazin states that; 

Class I. 7 = 0*109 for smoothed cement, or planed wood. 

Class II. 7=0*290 for planks, bricks, and cut stone. 

Class III. 7 = 0*833 for rubble masonry. 

Class IV. 7=1*54 for earth channels of very regular surface, or 

reveted with stone. 

Class V. 7 = 2*35 for ordinary earth channels. 

Class VI. 7 = 3*17 for exceptionally rough earth channels (bed covered 

with boulders) or weed-grown sides. 

The formula is founded on well-selected modern observations only. Two 
of these, I am aware, were subject to constant errors unknown to M. Bazin, and 
it so happens that these stand out as markedly less accordant with Bazin’s 
results. Such confirmation of my own private knowledge has greatly increased 
my confidence in the formula. 

7 = 0*109, Class I, is founded on 42 observations, with r , varying from 
0*16 foot to 7 feet, and s, from o*oooi to 0*0049. 

It may be considered as corresponding with 

Kiitter’s formula :—# = 0*010 ; j* = o*ooi : when r=o* 4 foot 

# = 0*010 ; s = 0*0001 : when #=0*8 foot 

# = 0*012 ; s =anything : when r=2*8 feet. 

7 = 0*290, Class II, is founded on 261 observations, with r, varying from 
0*12 foot, to 3*6 feet; and s, from 0*0001 to 0*0084. 

It may be considered as corresponding with 

Kiitter’s formula :—# = 0*012 ; s = 0*001 : when #=0*5 foot 

#=0*012 ; .s* = o'ooo 1 : when #=1*30 feet 

7=0*833, Class III, is founded on 34 observations, with r, varying from 
0*3 foot, to 5*0 feet; and s, from 0*00007 to o'ioi. 

It practically coincides with 

Kiitter’s # = 0*017 ; for j=o*ooi ; for all values of r. 

I should point out that the mere description “ Brickwork,” or “ Rubble,” is 
insufficient to distinguish between this class and Class II. The plotted points 
representing the actual experiments indicate that two decidedly different classes 
exist, but the descriptions given by the original experimenters are not sufficient 
to enable the two classes to be separated before experiments are made. 

It would appear that carefully pointed rubble masonry may fall under 
Class II, but is usually placed in Class III. Similarly, brickwork is generally 
relegated to Class II ; but, if laid as in tunnel work, or if even small deposits 
of silt encumber the channel, it crosses over to Class III. 



475 


BAZIN'S NEW { 1897 ) FORMULA 

I usually adopt the following classification : 

First-class brickwork, or stone laid in the daylight, well inspected, and the 
whole work laid so as to secure smoothness, can be assumed to rank in Class 11 ; 
but may change to Class III, if it carries silted water, and the silt is allowed to 
deposit in the channel. 

Second-class work, laid carelessly ; or first-class work laid as in tunnel work, 
falls under Class III. 

I have found that good work laid by an ordinary builder, who is more 
accustomed to houses than hydraulic work, seemed to fall into a class 
approximately represented by 7 = 0*55. This value has been adopted in 
Germany for slime-covered sewers, whether made of bricks, masonry, cement, 
or iron. 

Y = i- 54 > Class IV, is founded on 42 observations; with r , varying from 
°'5 5 foot to 8 feet, and s, from o*oooi to 0*014. 

It practically coincides with Kiitter’s 22=0*021 ; .y = 0*0001 ; for all values of r. 

Now, up to this point, the classes may be said, so far as the experiments 
selected by Bazin show (and I believe that these include practically every 
recorded experiment that can be considered as of first-class accuracy), to have 
a real existence. No doubt points representing the experiments do not always 
fall (even approximately) on the lines representing these classes ; but there is a 
visible and marked concentration of the points about these lines, along the whole 
range of the values of r, included in the experiments. In the case of experiments 
included in the next two classes, which, as will appear, are mostly on natural 
river channels, the points fall in a very different manner. Concentrations exist 
near various values of r, and the lines representing these two classes are ad¬ 
justed so as to pass as close to as many of these concentrations as possible. 

A consideration of the graphic plots, or an arithmetical study of the actual 
results, shows very clearly that these are by no means the only lines that could 
be chosen ; and, as an illustration, the law: 

~ 180 


sj r 

seems to lead to a very fair agreement with many series of experiments on 
channels the descriptions of which are quite sufficiently close to be considered 
as a class in Bazin’s meaning of the word. 

It will therefore be apparent that the next two classes are really broad 
divisions, and that a natural channel may lie anywhere between say 7 = 2, and 

7 = 3 * 5 - 

Y = 2*35, Class V, as Bazin selects it, is founded on 221 experiments, of 
which only 68 are on artificial channels, r, varies from o*8 foot to 18*3 feet, and 
s, from 0*00003 to 0*0146. It may be considered as corresponding with 

Kiitter’s 72 = 0*030 ; s= o*ooi : when r=0*5 foot, 

72 = 0*025 5 o’ooi : when r= 6*4 feet, 

72 = 0*025 ; j = o'ooo 1: when r= 18 feet, 

V = 3*i7, Class VI, is founded on 74 experiments, of which only 24 are on 
artificial channels, r, varies from 0*25 foot to 7*4 feet, and from 0*00014 to 
0*17. It may be taken as corresponding with 

Kiitter’s-72 = 0*030 ; s- 0*001 : when 5 feet. 

22 = 0*030 ; j = o*ooooi : when r=6’2 feet. 




476 CONTROL OF WATER 


The original memoir deserves careful study, and may be found in A.P.C. 
4me. Trimestre, 1897. 

The impression left on my mind is that if a natural river channel permits 
such a surface slope to exist that it can be observed, it is probable that some 
formula of Bazin’s type will represent the facts fairly accurately. As it is, the 
s, which we should theoretically use, is the surface slope over a very short length, 
where the stream is gauged (theoretically speaking, infinitely short ; practically, 
perhaps 100 feet would suffice). 

Now, it can be briefly stated that such observations have never been made. 
What we actually observe is the surface slope over anything between 1000 and 
10,000 feet length of the river ; and evidently this may, or may not be the j, we 
assume to be used in the formula. Hence, quite apart from the difficulties of 
measuring large volumes of water, we really endeavour to compare the discharge 
with observations of a quantity that may bear little relation to the s, of theory. 

Summing up:—In channels of the first four classes, the formula is quite as 
accurate as the usual hydraulic formulas ; and, with care, it is possible to pre¬ 
dict, with a fair degree of exactitude, into what class any given channel falls. 
In Classes V and VI the formulas give average values, and all that can really 
be stated is that in ordinary work, if we observe v, s, and r, we may expect that 
C, lies between : ■ < : 1 

The limits Cx= -and, C 2 =— ^ 

I+ A. 1+31 

r V r 


The real value of Bazin’s formula is that for the same channel, and for 
alterations in r, and v, such as occur in a channel which does not visibly alter 
its regime, y is fairly constant. On the other hand, if Kiitter’s 11 is calculated 
under similar circumstances, it will usually be found to vary more than can be 
explained by possible errors in observation. 

The amount of permissible variation in r, and 2/, depends on circumstances. As 
general rules, however, v, should not decrease below about 1 foot per second ; and 
if r, increases so much as to alter -the general aspect of the channel {e.g.ii a river 
overflows its banks, and spreads over wide flats) y will probably increase materially. 

Inside these limits, we have: 


\l rs 1 


y 


-=■ = 0*0063 


5( I + J^) 


V C 157-6 1 57‘6 Vr 

Graphical Solution. 

Thus, we get a very neat graphical construction (see Sketch No. 135). 

Plot ——, as ordinates, and as a b sc i ss£ej f or each gauging of the 

v V r 

river. A large scale must usually be adopted, o"oi=2 inches being none too 
great in ordinary cases ; or, as in sketch the quantities, may be plotted to 
different scales. 

Find the mass centre of these points, either by calculation, or by estimation, 
according to the accuracy of the observations. Join this point to the point 
(o, 0-00635). 

The tangent of the angle between this line and Cbr, is y, and therefore y is 
easily measured. 

It will be found that the only practical method of calculating Kiitter’s n, is 
by trial and error. 








GRAPHIC SOLUTION 


477 


Limits of Application of KiittePs or Bazin's Formula .^Thrupp (. P.I.C.E ., 
vol. 171, p. 346) has collected the evidence on this matter, so far as it exists, 

Thrupp states that for slopes flatter than .? = 


100,000 


^0-7 9 1.25 


the mean velocity is given by ; v= 

0*000002819 

While I confess myself quite unable to place that confidence in the observa¬ 
tions which a formula containing three or four significant figures would indicate, 

I am at one with Mr. Thrupp in believing that for such slopes the v=C V rs, 
law is not even approxi¬ 
mately correct. 

Thrupp also states that 
between 




and s = 


1 


10,000 
there is a 
period, where : 


100,000 

transition 


v — 


7-0.61 j.0.25 


0'1442 

while for j, greater than, 


v— 


^o-oi 


cO-5 



10,000' 0^01256 

corresponding to 
C = 8or°* n 

in the usual formula. 

I agree that, logically 
speaking, there must be 
a transition period, but 
I do not consider that 
any great error will arise 
from applying Bazin’s for¬ 
mulas for slopes, as 

small as —-—, and that 
50,000 

is the flattest a practical 
engineer requires. 

There is also fairly 
good evidence to show 
that if r, is less than a 
certain value, the law also 

alters, very much as is the case in small pipes, due to capillarity. The matter 
is of small importance, as this critical value of r, is so insignificant that no 
practical applications are at all likely to occur with such small values of r. 

Silt-Bearing Waters. —The influence of silt on the values of Bazin’s y 
or Kiitter’s n, has been incidentally referred to in the preceding work. 

As a general rule, it may be stated that water which carries fine silt can be 
expected to show a somewhat higher value of C, (or lower values of ?i , and y) 
than clear water under similar circumstances. If the silt is allowed to deposit 















































CONTROL OF WATER 


478 

in the channel it may generally be concluded that all channels which, when 
unsilted, possess values of y exceeding 1*54, or values of n , exceeding o'020, 
will be improved in smoothness ; and these values may be considered as the 
maximum roughness which can occur in a regular channel of which the sides 
and bed are completely covered with a smooth lining of silt. Similarly, 
channels which are naturally smoother than the values given will become 
rougher, and may finally reach a condition specified by y=i*3o, or j7 = o’oi8. 

If, however, the silt deposits are so great that waves or ripples of silt form 
on the bed of the channel, y may rise to 2, and may rise to 0*027 (see 

p . 703). 

The circumstances which produce deposits of this nature generally occur 
when the flow is decidedly irregular; and since the area of the channel will 
rapidly become insufficient to pass the discharge for which it is designed, the 
calculations have but little practical importance. 

When metal, concrete, or brickwork channels are used to carry silted water, 
and the velocity is sufficiently high to prevent deposits, a relatively low value 
of y may be assumed, as the friction of the silt wears away small irregularities, 
and prevents incrustations and growths of weed or slime. Some very accurate 
gaugings of riveted steel tubes used to convey silted water on certain canals in‘ 
the Punjab show discharges which exceed those calculated by the ordinary 
rules for new cast-iron pipes by 5, and 6 per cent. The circumstances at 
entry and exit are peculiar, and some of the difference may thus be explained ; 
but there is no doubt that any allowance for incrustation and other effects of 
age was quite unnecessary. 

The simplified Tutton formula for pipes (see p. 427) and Manning’s formula 
for open channels (see p. 472) can both be expressed in the form: 

v=¥L%/r* V7=Kr°* 17 V^ 

Thus, if we put Kr°* 17 = C, we obtain the usual form v — C\lrs, which is 
convenient for calculation. The following table gives the values of C, for 
K= 100, for such values of r, as usually occur in practice: 


Diameter of 
Pipe in Inches. 

Hydraulic Mean 
Radius in Feet. 

C = IOOr 0 - 17 . 

1 

00208 

5 2 *4 

2 

0-0417 

5 8 '9 


005 

60-7 

'J 

0 

0-0625 

63-0 

4 

00833 

66-1 


o-10 

68-i 

5 

0-1042 

68-6 

6 

0-125 

707 

7 

oi 45 8 

72*5 


015 

72-9 

8 

o-1666 

74-2 

9 

01875 

75 - 6 


[ Table continued 
















MANNINGS FORMULA 


Table continued ] 


Diameter of 

Pipe in Inches. 

Hydraulic Mean 
Radius in Feet. 

C = ioo;- 0 - 17 . 


• 

0-2 0 

76-5 

IO 

0-2083 

77-0 

11 

0-229I 

78-2 

I 2 

0-25 

79-4 

14 

0-2917 

81-4 


0-30 

8i-8 


o- 3 i 2 5 

82-4 

16 

o -3333 

83-2 


°-35 

83-9 

18 

0-375 

84-9 


0-40 

85-8 

20 

0-4166 

86-4 

21 

o -4375 

87-1 

24 

0-50 

89-1 


o -55 

9°-5 

27 

0-5625 

90-9 


o-6o 

91-8 

30 

0-625 

92-5 


0-65 

93 ' 1 

33 

0-6875 

94 -o 


0-70 

94-2 

36 

o -75 

95-3 


o-8o 

96-4 

39 

0-8125 

96-6 


0-85 

97-3 

42 

0-875 

97-8 


0-90 

98-3 

45 

o -9375 

98-9 


o -95 

99-2 

48 

1-00 

100-0 


I-IO 

ioi*6 


1-20 

103-1 


1 - 3 ° 

104.5 


1-40 

105-8 


1-50 

107-0 


i-6 

108-2 


i -7 

109-3 


i-8 

no-3 


1-9 

m -3 


2-0 

I I 2-2 


2- T 

II 3 - 2 


2-2 

I I4-1 


2-3 

II 4-9 


479 


[ Table continued 




















480 


CONTROL OF WATER 


Table continued ] 


Diameter of 
i Pipe in Inches. 

Hydraulic Mean 
Radius in Feet. 

! _ 

C — ioor 0 - 17 . 


• 

2-4 

US -7 


2-5 

h 6*5 


2-6 

ii 7*3 


2*7 

1 i8-o' 


2-8 

118-7 


2-9 

119-4 


3 *° 

120-1 


3*2 

121-4 


3*4 

122-6 


3-6 

I23-8 


3-8 

124-9 


4-0 

126-0 


4-2 

I27-0 


4.4 

128-0 


4-6 

128-9 


4-8 

129-9 


S*° 

I3 0 -8 


Variable Flow in Open Channels. —The question of flow in a channel 
of non-uniform section is of extreme practical importance in cases where flood 
damages (caused by backing up of the water levels) need investigation. 

The following notation is unusual, but is that which is best adapted for use 
in practical applications. 

Let v=C^rs, be the friction equation for the stream under consideration. 
Let v, be the mean velocity, a, the area of the cross-section of the channel, and 
r, its hydraulic mean radius at any point distant /, feet downstream of a point 
designated by the suffix 2. 

Then, the ordinary Bernouilli equation, corrected for friction, and for the 
fact that the square of the mean velocity does not entirely represent the mean 
energy of the velocity of the water (see p. 15) gives: 



where z l2 , is the fall in the surface of the stream, measured from the point 2, 
to the point 1, and / 12 , is the distance between these points measured along the 
course of the stream. 

If we assume that a l — a 2 , and differentiate this equation, we get : 


dz— 


(1 + a) vdv v- 




C V 


dl 


where dz, represents a decrease in the reduced level of the water surface. 

The objections are obvious. We have no assurance that the fact that the 
motion is varied does not alter the value of C, from that obtained by experiments 














DISTRIBUTION OF VELOCITIES 481 


on steady motion. The value of a is uncertain, even in the case of steady 
motion, and is consequently still more so under varied motion. 

The question was experimentally investigated by Darcy and Bazin 
(Recherches Hydrauliques ), and less thoroughly by Ferriday (.Engineering 
News, July 11, 1895). The general result is that if a, and C, are assumed to 
possess the values found by experiments on similar channels in which uniform 
flow occurs, the observed values of z 12 , may differ as much as 22 per cent, from 
the calculated values. The mean error (no regard being paid to sign) is less 
than 8 per cent., and if the sign is taken into account is less than 3 per cent. 
Consequently, this last figure best represents the probable agreement of a 
calculated and an observed backwater curve, when C, and a, have been specially 
determined by experiments on uniform motion in the channel to which the 
calculations are applied. In practical applications, errors of 10 per cent, may 
be regarded as probable, since C, is not likely to be so accurately determined. 

The values of 1 +a, according to Darcy and Bazin (ut supra) are as follows : 


Channel of 

I “f* Ct* 


Rectangular shape ; in planed timber 

Do.; with battens, 4 inches apart . 

Do.; do., 2 inches apart. 

Wooden culvert .... 

Trapezoid; in planed timber . 
Masonry walls .... 

Semicircular channel in cement 

3 cement, 1 sand .... 
Semicircular; in timber . 

Do.; covered with gravel 

/ l ’° 5 2 
l 1-038 
1-078 

/ I-1 2 2 

t l ^S 2 

I>0 53 

1-048 

1-071 

1-025 

1-043 

i-° 3 8 

1-089 

In uniform motion. 

In varied motion. 

In uniform motion. 

In varied motion. 

In uniform motion, 
do. 
do. 
do. 
do. 
do. 
do. 
do. 


a evidently depends on the roughness of the channel, and also to some 
degree on its form. 

Darcy and Bazin suggest the following equation for uniform motion : 

. 

Now, let s , be the slope of the bed of the channel, which is assumed to be 
uniform, and/, be the depth of the water at any point. Then : 

z 12 = si 12 — Where f x , is downstream of f 2 . 

dz = sdl—df. Where df, is positive when the depth increases 

in the downstream direction. 

Now, if Qt be the quantity of water flowing in the channel, in cusecs, 

and in particular, v 1 = ~ ; and z/ 2 = ~ : 

U\ a 2 


we have in general: 

Q*. 


v= 


a 


and we can put : 



J12QI L 

C 2 a 12 2 r 12 


3 1 












482 CONTROL OF WATER 


where a 12 , and r 12 , are quantities which are, in a sense, the mean area and the 
mean hydraulic radius of the channel between the points i and 2, and can be 
calculated when the geometrical relation between a, r, and /, is known for each 
point of the channel. 

We thus obtain the equation : 


(/1-/2H 


Q 


A2 — 


'gf 1 


s — 


Qt 8 




I -f- a 2 ) 

a 2 J 


This form of the equation may be applied in cases where the cross-section 
of the channel alters but little in the length l 12 . Unless the relation between 
a and /, be such as to permit a 12 and r 12 to be accurately calculated, it is a 


mere approximation. 



Sketch No. 136.—Diagrams for Variable Flow, Jump, and Bore, in an 

Open Channel. 


In practice, the most accurate solution is obtained from the differential 
equation which gives : 


df_ (1 + °) Q 2 i d_ ( i\ . Ql 
dl g a dl \ a) a 2 C 2 r 


This equation can be integrated by assuming that: 

a — bf\ and r—f 

That is to say, the channel section is assumed to be approximately rectangular, 
and its breadth b , is assumed to be constant, and to be large in comparison 
with f 

We then get: 

f - Q * 2 

df = c 2 b 2 p 
dl T _I+« Q 2 t 
‘ b 2 / 3 


or 













































BACKWATER FUNCTION 


483 


or if F, be substituted for the value of f which occurs in uniform flow when the 
discharge is Q<, we have : 


and 


If we now put 

F 


Qt = <£FCV rs = 6F l ‘ 5 C gs 


dl 


—^( 7 ) 


/- 

x, the integration of this equation leads to : 


/ = F'- — F ^ 1 —0 +«)C 2 \ f 1 7 x 2 +x+i 

s Hj w 


— F'Z ■ 




g 

(l+a)C 2 

g 


1 ,7.x -f n 

~vrs + 

o J 


a constant. 


)<£(-*■) + 


a constant. 


Where 4 >( x ) is termed the backwater function. 

In the table on page 1006 (which is due to Bresse) it will be noticed that 

is tabulated in terms of an argument ~= (y)- This is liable to lead to 

confusion unless care is taken. With the help of this table we can plot the 
curve assumed by the water surface. The process is as follows: 

The value of is assumed as known from previous calculation. We 
assume a value of f 2 , and determine the distance / 12 , between the point where 
the depth is B, and that where it is/ 2 . 

It will be observed that the order now adopted is precisely the reverse of 
that used in the mathematical discussion. The change of order appears to be 
necessary, and while it may render the mathematical equations obscure, 
it greatly assists the practical calculations. Taking the integration from 
x — x 2 (i.e. f— f 2 ) to x = x 1} (i-e.y=/iX an d reckoning / 12 , as positive when 
measured upstream from 1 to 2, the equation becomes : 


7 _/i~ A 
T2-; 




The case most usually considered is where a dam, or other obstruction, 
exists in the stream. 

Thus,/x and f 2 are both greater than F, and consequently x 1 and x 2 , are 
greater than 1, although it must be remembered that the function 0 (x), is 

tabulated by arguments which are less than 1, being — and —, so that the 

equation might be better written as : 



(i + q)C 2 
g 



When a sudden fall occurs in the bed of the stream, f x and f 2 , are less than 
F, and consequently x , is less than 1. 

A similar investigation gives us : 




S 














484 


CONTROL OR WATER 


where x( x \ is another function, which is tabulated as the “drop down 
function.” This function is tabulated under the argument 

The above equations are subject to certain exceptions which produce 
phenomena termed “ standing waves,” and “ bores.” These occur when 
is infinite. 

The standing wave can be produced experimentally, and the following 
investigation is reliable. The short investigation given on the bore is due to 
Merriman, and, as he states, must not be regarded as in any way complete 
or reliable. 

(i) The standing wave, or jump, occurs when the value of ^ is infinite, and 
positive. Thus, if f 2 , represent the depth just before the jump occurs, we 

_ or 

have 7 / 2 ^'gf2, and s must be greater than ^ That is, if C = 100, the 

slope must be steeper than 0*00322. 

The water surface suddenly rises in a wave. The following formulas for j 
(the height of this wave) is given by Merriman, and agrees very well with the 
experiments of Bidone, Darcy and Bazin, and Ferriday. 

y 2 _ y 2 

The velocity head lost is represented by : —= l ——— and this is expended ; 

(j) In loss in impact, represented by : 


2.T 


(zz) In raising the whole of the water through a height^ 

2 

Thus, putting v 2 f 2 = vj x = v x (f a +j) we get: 


Since friction is neglected, the computed values are usually a little greater 
than the observed. 

(ii) The Bore.—Here also, ^ is infinite, but negative. That is to say, 

v 2 = V gf 2l and v 2 is greater than C V f 2 s, or s is less than 

For example, at Johnston, v 2 = 28 feet per second. Thus : 

28^ 1 

/2 = ^g7g = 24 feet ’ and the slo P e bein ^ about we find that C2 j is less than 

180x32*2, or that C, is less than 76. 

Practical Calculation of Backwater Curves. —This is most easily 
effected by dividing the flooded portion of the river into short lengths, over 
each of which the cross-section can be considered as approximately rectangular 
and of uniform breadth, so that the depth of the water alone varies. We then 
assume that 1 + a = 1, and use the following formula : 


A. ='^7 S + F (7-f 


S 








BACKWATER CURVES 485 


in order to calculate / 12 , for an assumed J' 2 , the depth at the point / = o, being 
assumed, or previously calculated as, equal to /j. 

A study of the cross-sections of the river bed will show whether the value of 
/12 thus obtained is sufficiently small, to permit us to consider the assumption re¬ 
garding the constancy of the breadth of the river over the length / 12 as correct. 
If this is not the case, we must assume a new value of f 2} which is somewhat 
largei than that first obtained, so as to secure a value of / ]2 , which will cause 
the assumption to be approximately correct. When a satisfactory value of / 12 
is obtained, we must consider the channel above the point 2 (i.e. the end of the 
reach of length / 12 ), and if necessary determine the new values of F, C, and s , 
sa Y F lf Cx, and which are appropriate to the reach above the point 2. We 
can then determine the length / 23 , in this reach, at which a depth f s , occurs, by 
the equation : 


f 23 


f2 ~fs 




The following calculation will render matters clear : 

Take a stream discharging 35*4 cusecs per foot of its width, and let s — o*ooi, 
and C = 100. 

In uniform flow we find that F = 5, and that v — 7-09 feet per second. Now, 
let a broad topped weir (i.e. weir co-efficient = 2*64 (see p. 128)), 5 feet high, be 
erected in the channel. The depth over the weir is 5'65 feet, so that the total 
depth of the stream just above the weir is f x = 10-65 feet. The flow above 
the weir will be variable, and we have : 

A2 = (/i-/ 2 )iooo+5(1000— 


= 1 °oo(/i —f 2 )+ 3447 {0(^2) ~ $(•*■ 1)} 
Assume that f 2 = 9'65 feet. We consequently get: 


= 0-469. —=—7-= 0-518 

*i fi 10 65 ^ v x 2 9-65 3 

<t>( X 2) — <t>(-Xl) = O’1 423 — O’I I 49 = 0’0274. 

Therefore, / 12 = 1000 + 3447 x 0-0274 = 1000 + 94-5 = 1094-5 

So that the effect of the back water is to put the depth 9-65 feet, 94-5 feet 
higher up the stream than would be the case if the water surface was parallel 
to the bed of the stream. 

Proceeding in this manner, we get : 


Depth 
in Feet. 

I 

X 

< p(x ). 

< p ( x 2) - (p{x 1). 

1000 + 3447{0(* 2 )- 0(^)!- 

Distance 
above the 
Weir in Feet. 

10-65 

0-469 

O'l 149 


• • • 

0 

9'65 

0318 

°’ I 4 2 3 

0*0274 

1094-5 

1094*5 

8-6 5 

0378 

0-1818 

o -°395 

1136*1 

2230-6 

7 ' 6 s 

0-654 

1 

0-2431 

0-0613 

1211 ‘ 1 

344 i *7 


This table permits the backwater curve to be set out, and, if necessary, the 
calculations can now be repeated with shorter intervals between the successive 


























CONTROL OF WATER 


486 

depths, and more correct values for C, and s , if a study of the cross-sections 
indicates that this is desirable. 

Let us, however, suppose that at a distance of 3500 feet above the weir, the 
channel alters its shape, slope, and roughness, so that it is better represented 
by s = 0*0005, and C = 80, and that the breadth is now double what it was 
before. We easily find the new value of F, say F x = 4*6 feet, and the initial 
depth f 4 , can be taken with all necessary accuracy as equal to 7'6 feet. 

We now get, i { x 4 ='~ y x 5 = ; 

* 1 * 1 

l 4 s = 2ooo(/ 4 -/*) + 4*6 (2000-^°-) {<£(*5)- < t >( x 4 )} 

= 2000(/ 4 - f 5 ) + 8295 {( p ( x 5 ) - ( p ( x 4 )}. 


The tabulation is : 


Depth 
in Feet. 

1 

X 

( p ( x ) 

;• j, , 

-r 

H 

■©- 

1 

-e- 

H 

*©• 

1 

5 

ON 

M 

00 

/. 

Distance above the 

Change in Section 

in Feet. 

7'6 

0*605 

0*2019 




0 

6*6 

0*697 

0*2852 

0*0833 

691 

2691 

2691 

5-6 

0*822 

o* 45 Sl 

o*i 729 

1434 

3434 

6125 

5 ' 1 

0*903 

0*6590 

0*2009 

1866 

2866 

899 1 


d he curve can thus be set out, and can be corrected as already suggested, if 
requisite. The fact that a has been made equal to o, might also be allowed 
for, but it is only very rarely that our knowledge of C, is sufficiently accurate 
to permit this. For instance, were it known that i+« was 1*06, the formulae 
m erely require us to use 6400(1*06) = 6784 for C 2 , or the effective C, would be 
V6784 = 82*4 say, and accuracy of this character in observations which deal 
with floods is not likely to be easily attained. Of course, in the case of 
laboratory experiments, such precision may be arrived at, and may prove a 
useful exercise. 

When s, is equal to, or greater than ~ 2 (which will be obvious when the 

calculation is first attempted), a standing wave occurs. Its position can be fixed 
by calculating the depth just upstream of the wave, and its height by the 
formulae already given. We thus obtain the depth just downstream of the 
wave, and this can be put for / 2 , in the general equation, and /, the distance 
from the weir to the wave can then be calculated. Standing waves occur in 
certain cases in irrigation canals. I have applied the formulae in order to 
calculate several actual observations. The results are not as satisfactory as 
might be expected. On the other hand, the drop-down curve before the wave, 































TRANSPORT OF MATERIAL 


487 

agrees fairly well with calculation. A change in the value of a may be sus¬ 
pected, or, in such large scale examples shock may play a greater part than in 
small experimental channels. 

The case of a drop-down curve can be similarly treated. Such cases are 
very infrequent in practice, so that a detailed example is not necessary. As a 
general principle, the occurrence of drop-down curves should be prevented by 
a correct design of the channel. Backwater conditions only produce trouble 
(other than flooding) in water which contains silt. Drop-down curve conditions 
tend to produce erosion, and if this occurs the water becomes charged with silt, 
and all the attendant silt troubles may have later to be faced. 


Symbols connected with Transport of Material 


a, is a coefficient employed by Lechalas in the equation, P — a (z> 2 -o'67). 

b, is the bed width of the river in feet. 
d , is the depth of the stream in feet. 

k, is a coefficient in the equation q = kv n (see p. 491). 


M, is a coefficient in the equation 


v - 1 '33 


v 


M = 


o '0002 


p 


^s a rule, d =^——, so that M=^, M-- L13’ ( se e p. 491). 

p p v r ^ 

. , . Quantity of silt carried for ward __ q 

P’ 1S e ra 10 • Q uan tity of water carried forward Q 

P, is the total force transporting the silt. 

q, is the number of cubic feet of silt carried forward per foot width of the bed. 
the discharge of silt = bq cusecs. 

Q, is the number of cubic feet of water carried forward per foot width of the bed. 

the discharge of water = bQ cusecs. 

v 0} is the velocity of the water at the bottom of the stream, in feet per second. 

v s , is the surface velocity. 

v, is the mean velocity of the stream. 

Vj and V 2 (see p. 490). 


Thus, 

Thus, 


Summary of Formula 
Lechalas’ investigation of Phases I and II : 


q=“( V< ?- 0 ' 6 1 ) 
b 

Deacon’s investigation of Phase III: 

y = o'ooooo28^ 5 


d= M 


■V* 


* '33 


v 


, O'0000028 4 

d = - v*. 


General Rules. 

I. Fine Silt — _ 

Clear water scour when v, is greater than—040 d. _ 

Silted water does not deposit when v , is greater than i'05 s Id. 
Silted water scours when v , is greater than 1 ’37 ^d. 

II. Coarse Sand — 

Clear water scour when v, is greater than i'6<f 0 * 33 

Silted water does not deposit when v, is greater than 2'2 d°- sz 

III. Coarse Gravel — 

Clear water scours when v, is greater than 2*0 d °'“ 5 

Silted water does not deposit when v, is greater than 2'5^ °' 2 '’ 

IV. Boulders are moved when v, exceeds 0,25 









CONTROL OF WATER 


488 


Transporting Power of Currents of Water. —This is one of the 
least understood subjects in hydraulics. 

Deacon ( P.I.C.E ., vol. 118, p. 93) gives a very detailed description of the 
motion of sand in a trough with glass sides. 

The first movement began with a surface velocity of 1*3 foot per second, 
and was confined to the smaller isolated grains. If this velocity was main¬ 
tained, the grains arranged themselves in beds perpendicular to the current, 
in the form of the well-known sand ripples of the seashore. The profile of 
each ripple had a very slow motion of translation, caused by particles running 
up the flatter slope, and toppling over the crest. At a surface velocity of 1*5 
foot per second the sand ripples were very perfect, and travelled with the 
stream at a speed of about °f ^ ie surface velocity. At a surface velocity 
of 175 feet per second the ratio was reduced to 1)5 Vq, and at 2 feet per second 



Surface Velocity % of - 5 Water 4 in 5 ft 6 per 7 sec. 

Sketch No. 137.—Deacon’s Experiments on the Transportation of Sand by Water. 


was reduced to 4 |^. A critical velocity was reached£atjVi2 5vfeet per second, 
the sand ripples becoming very irregular ; the particles rolled up the flat slope, 
and in place of toppling over the steep incline were occasionally carried by the 
water direct to the crest of the next ripple. 

At about 27 feet per second another critical velocity was reached, and 
many of the little projectiles cleared the top of the first, or even of the second 
crest. At surface velocities of 2*6 to 2*8 feet per second, the sand ripples 
became more and more ghost like, until at 2*9 feet per second they were 
wholly merged in particles of sand rushing along in suspension in the water. 

The above description clearly shows three phases of sand motion. 

Firstly, a discontinuous rolling motion, with surface velocities between 1*3 
and 2'i feet per second. 

Secondly, a discontinuous suspension in the lower layers of the current 
between 2 - i and 2‘9 feet per second. 

Thirdly, a continuous suspension at surface velocities above 2*9 feet per 
second. 

































PHASES OF TRANSPORT 


489 

It will also be plain that the above velocities only apply to the smaller 
grains of sand. The bottom velocities are not given, nor is the size of the 
sand grains, so that the observations are qualitative only. 

We are thus faced with the following difficulties:— 

I. Any substance occurring in Nature is a mixture of grains of different 
sizes, and visual observations are liable to give figures relating to the smaller 
grains alone, as their motion renders the movement of the larger grains 
invisible. 

II. The phenomena appear to depend on the magnitude of the velocity at 
points close to the bottom, possibly (as Flamant suggests) also on the rate of 
variation of these velocities with the distance from the bottom. All that can 
be readily measured is the surface, or the mean velocity ; and the mere fact 
that transport of material is taking place will plainly alter the relation which 
the velocities near the bottom bear to the surface, or mean velocities. 

Thus, any general theory of the transport of materials by water is likely 
to prove very complicated. 

The present treatment follows the method of Lechalas’ investigation of 
Sainjon’s observations on the motion of sand in the Loire ( A.P.C ., 1871, 
vol. 1). The difficulties above referred to are very forcibly brought out, and it 
can be stated that 

If v 0 , represent the velocity in feet per second, at or near the bottom of 
the river 

Vs, the surface velocity of the river 

v, the mean velocity of the river, or probably, more accurately, the 
mean velocity over the vertical (see p. 52). 

Then, for sand with grains of a mean diameter of 0*04 inch we have as 
follows : 

Until v 0 , exceeds o'82 foot per second (or v, exceeds ri8 foot per second, 
or v s , exceeds 1*27 foot per second), there is no motion (corresponding to 
Deacon’s v s — 1*3 foot per second). Once motion begins, v 0 , cannot be 
directly observed, but the state corresponding to Deacon’s v s — 2*9 feet per 
second, is reached with ■z's = 3’33 to 3*38 feet per second. 

Lechalas assumes that the force available to move the sand, when v 0 , 
exceeds 0*82 feet per second, is : 

P = a (v 0 2 — cr82 2 ) = a (v 0 2 — o'6y) 

and this he puts equal to bq, where q, is the amount of sand transpoited pei 
foot width of the river, which is assumed to have a bed width of b feet. 

We thus have q = ^-{v 0 2 -o‘6 7) so long as v s , does not exceed 3*33 feet 

per second, and Lechalas finds that-^ - = '0004, where q, is expiessed in cubic 

feet per second per foot width of the bed. This equation refers to a case wheie 
the sand “ripples” were some 2*7 feet high ; but the scouring action is stated 
to be normal, the height of the ripples being caused by irregular flow. 

Since the quantities thus calculated agree very accurately with the observed 
velocities of the profiles of the sand ripples, we may infer that the motion of 
sand or gravel under the influence of a current of water may be very fairly 
represented as follows : 


490 


CONTROL OF WATER 


So long as the velocity measured close to the bottom of the current does 
not exceed a certain value, which I propose to call that of first scouring, equal 
to V 1} the particles remain undisturbed. 

If this velocity of first scour is exceeded, motion begins according to Phase I, 
and gradually passes over to Phase II, but there is no abrupt change in char¬ 
acter, until Phase III is reached, with a bottom velocity which I propose to 
call that of the second scouring, equal to V 2 . When the bottom velocity 
exceeds this value, the whole of the bottom layers of water are charged and 
clouded with sand, and this cloud rises higher and higher as the velocity is 
increased. 

Our knowledge is best for coarse sand, the particles of which have a mean 
diameter of 0*04 inch approximately. 

Here V x = 0*82 foot per second, and V 2 is about r8o foot per second. 
The values corresponding to V L , for other substances are fairly well established, 
and are tabulated in the second column of the annexed table. 

Now, in the case of clear water flowing in an earth channel, it is plain that 
once the bottom velocity exceeds V 1? the channel will be scoured, and scour 
will continue until by the increase in size of the channel the bottom velocity is 
reduced to the value of V l5 corresponding to the material of which the channel 
bed and sides are formed. This action must be provided for in designing the 
cross-section of the channel. 

It is only very rarely that clear water flows in natural, unlined channels. 
Usually the water carries some silt before it enters the channels ; and it is 
plain that if we design the channel so that the quantity of silt carried forward, 
is equal to that already in the water we obtain a channel which neither 
silts nor scours, and which carries both sand and water. The bottom velocity 
which prevails in this channel may obviously have any value which is greater 
than V x , and will depend solely upon the value of g. 

Thus, assuming Lechalas’ law, we have as follows : 


q in Cubic Feet 
per Second. 

Bottom Velocity in Feet 
per Second. 

Remarks. 

| 

• • • 

0-82 

Clear water, commencement 
of first phase of transport. 

0-00013 

1-00 


0-00031 

1-20 


0-00052 

1-40 


0-00076 

I* 60 


0-00103 

i-8o 

Probable beginning of third 

• • • 

... 

phase of transport. 

0*00132 

2*00 

_ I 


Lechalas investigated the laws of transport at velocities which exceeded 
‘Z/ 0 =r8o foot per second, but* his results are not confirmed by Deacon’s 
experiments, and he does not appear to have had personal experience of the 
case. 

The above table requires careful consideration. It must be remembered 














RATIO OF SILT TO WATER 


491 


that q , is an absolute quantity, and is not a ratio. Thus, let us con¬ 
sider that ^ = o , ooo3i. We find that a channel which carries o'ooo3i cubic 
feet of sand per second per foot width of its bed must have a bottom 
velocity of i‘2o foot per second, whatever its depth may be. Let us assume 
a depth of 1 foot. The mean velocity is about 17 foot per second, and 

the ratio ——-— is approximately equal to o‘ooo2. But if the channel is 10 feet 

deep, the mean velocity which occurs when the bottom velocity is 1*20 foot 
per second will, if anything, be slightly greater than 17, and the ratio of the 
silt to the water will be 0^00002, or only one-tenth of that existing in the 

shallower channel. Now, in water as it exists in Nature, the ratio -- 

water 

is usually fairly constant along the whole course of the river, or artificial 
channel. Hence we arrive at the general principle that water which carries 
a fixed quantity of sand per unit volume of water must increase its rapidity 
of flow when the bed width of the channel decreases. Therefore, if the volume 
of water and silt carried down the channel is constant, the deeper the channel, 
the greater is the mean velocity required to prevent the deposition of silt. 
If we assume Lechalas’ figures are correct, we have as follows : 

Putting Q = the number of cubic feet of water flowing per foot width of 
the stream bed per second, and d=the depth of the stream in feet: 


then, Q = vd—' v ^ say, and q=PQ, where /, is the ratio - S1 — 

07 water 

/ f) r u d 

Thus, o’ooo4 (tv 2 — o’67) = —— or substituting in terms of v, we get : 

0.7 ’ 


d 


_v z — 1*33 
vp 


X 0'0002 = M 


V J 


i*33 


V 


say, 


as the relation between v, and d, when/, is given. This relation may be taken 
as typical of the conditions during the first and second phases of motion. 
During the third phase, it is believed that, q = fcv n . 


Thus we get, d = — 

P 

Through the courtesy of Mr. Martin Deacon I have been enabled to 
consult the experiments already referred to. In these the water was 8 inches 
deep, and during the third phase of motion the relation q = 078 v s 5 , was found 
to hold where <7, is expressed in pounds per hour. 

Assuming that v s = 1*05 v, which is probably approximately true for a trough 
with glass sides, and that 1 cube foot of sand weighs 100 lbs., we have : 
q = o'ooooo 28 v 6 , or o - ooooi66 v 0 5 , in cube feet per second. 

The rule bears no resemblance to Lechalas’, but this is hardly surprising, 
as the observations were nearly all made during the third phase of the 
transport of the sand. 

Thus, in the case of the Mersey sand used by Deacon, we find that: 


d= 0 ' 000002 & 





is the relation between the velocity and the depth in a channel which neither 
scours nor silts. 







CONTROL OF WATER 


49 2 

Similar rules could be deduced for any other substance provided that 
proper experiments were available. At present it is impossible to give rules 
which will permit the effect of the size of the individual grains and the ratio 

» — S1 ^ - - to be accurately allowed for. I have, however, for many years noted 
water 

and plotted the velocities and dimensions of all the silt-carrying channels 
which I have been able to observe. Taking the term clear water to mean 
water which is clear to the eye in bulk, as seen in the river, but which probably 
rolls some silt along the bed of the river, I find that the following rules hold 
good : 

I. For fine silt, with a mean diameter of about o’oi inch, using feet and 
feet per second as units, it would appear that : 

(i) Clear water scour is of importance if v , exceeds 0'40 V d. 

(ii) Heavily silted water gives no deposit if v, exceeds ro5 \f d. 

(iii) Heavily silted water begins to scour noticeably if tz, exceeds 

i*37 d'd 

II. For coarse sand, say with a mean diameter of 0*04 inch, we have : 

(i) Noticeable scour in clear water if v, exceeds i*6 d°' ss . 

(ii) Heavily charged water does not deposit if v , exceeds 2’2d 0 ’ 33 . 

III. For coarse gravel, say pea-size : 

(i) Scour begins if v, exceeds 2'od 0,25 . 

(ii) Heavily charged water does not deposit if v, exceeds 2*5 d 0 ’ 25 . 

IV. Boulders are moved along if v, exceeds 5 d 0 ' 25 . 

The whole of these results are only approximate, and, except for the first 
two cases, rest on very slender experimental evidence. 

If we may assume that the experiments conducted by Lechalas and Deacon 
give the general laws of silt transport correctly for the motion during the three 
phases previously defined, it is fairly plain that the observations on fine silt and 
coarse sand (Classes I and II) refer to rivers where the ripple method of 
transport occurs, and that the coarser materials of Classes III and IV ( i.e . 
coarse gravel and boulders) were only moved when sand was being shifted 
continuously as in Phase III (see p. 491). I do not, however, consider 
that the experimental data are yet sufficiently extensive to permit so definite 
a statement to be made. The particular case of Punjab silt has been very 
carefully investigated by Kennedy, and his laws are considered on page 755. 

I consider the general rules that the deeper the channel the less likely it 
is to scour, and that the coarser the material, the less marked the effect of the 
depth, are quite reliable. In this connection I would refer to a paper by Thrupp 
(P./.C.E., vol. 171, p. 346), which is well worth reading : 

Thrupp’s curves for depths over d— o'4 foot, agree very well with : 


Mud and silt not moved 

i 7/, is less than 

o*4oz/ 0 ' 5 

Fine silt moved 

if v, exceeds 

0*40 d 0 ' 5 

Fine sand moved 

if 7 \ exceeds 

i*5 d 0 ' 35 

Coarse sand moved 

if v, exceeds 

i*5 d 0 ’ 30 

Pea-sized pebbles moved 

if v, exceeds 

2’2 d 0 ' 3 

Large pebbles (egg-sized) moved 

if exceeds 

5*o d °‘ 25 

Large stones moved 

if v , exceeds 

1yd 0 ’ 15 




THRUPP'S OBSERVATIONS 


493 


Thrupp’s curves show a well marked change in the laws of scouring, and 
silting, when the hydraulic radius passes through a value approximately equal 
to o # 4o feet. 

This may be regarded as most doubtful, since Deacon’s experiments agree 
very well with the laws deduced from large natural channels. In actual experi¬ 
mental work, however, it would appear advisable to use a fairly big channel, 
where say r=o* 5 o foot at least. My own experience with small channels leads 
me to consider that the transport of sand is considerably affected by accidental 
disturbances such as shaking, or waves in the water. 

The general agreement of my rules with those of Thrupp is encouraging, 
but cannot be taken as indicating extreme accuracy. The terms “pebbles,” 
“ large boulders,” etc., are mere figures of speech in such cases. Samples of 
the river bottom can be secured, but it is not fair to infer that these accurately 
represent what is moved. As an example, I mention that boulders are moved if 
v, exceeds 5 *o^ 0 - 25 , and Thrupp states that this is the velocity at which egg-sized 
pebbles are moved. As a matter of fact, I am aware that trouble from the point 
of view of maintenance begins at this velocity in rivers which contain boulders, 
while Thrupp has evidently investigated what produced the trouble. Thrupp’s 
values are therefore the more scientific, while mine are probably the more 
useful in practical design. As a matter of experience, an engineer may always 
suspect that any larger stones which are markedly rounder than the smaller- 
sized material, are not moved. The more angular the material, the more likely 
it is to be moved. 

The physical meaning of these equations deserves some slight consideration. 
We have the usual “ Chezy ” equation, as follows : 

w=C 'I ds, and v = ad n , where a, and n , depend on the amount of silt carried, 
and its mean size. 


— 1 * t 
Thus, we get, s~ —^—5 which may be regarded as fixing the slope at which 

a channel of given depth and roughness will remain in quasi equilibrium. 


As an example, take the case, 
Bazin’s y=i’54 class, 

v= 1*05 ^ d. 

We have, determining C, as for 

When d=i’o 

C = 61*9 

or 

>* = Won approx. 

When d= 4 'o 

C — 89*0 

or 

70W approx. 

When d=9‘o 

C = io 3 ‘o 

0 

>-« 

< 

II 

Ml 

©|M 

Ol 

s =ii 5 T>o 6 approx. 


and if the slopes exceed these values in any given case, it is a matter of common 
knowledge that the channel takes up more silt by scouring, and thus, where 
possible, adjusts itself to the increased slope, and also if able to “meander,” 
increases in length, and so diminishes the slope. 

A very wide-spread idea exists among engineers that a canal will be found 
to be free from troubles arising from silt or scour provided that it is so pro¬ 


portioned that the ratio is the same in the canal as in the river from 

which it takes out. The above investigations may be regarded as an indication 

silt 

that this rule has a certain foundation. The ratio is probably some¬ 

what less in the case of the canal than in the river, and will be considerably smaller 
if the headworks are properly designed and are intelligently handled. On the 





494 


CONTROL OF WATER 


other hand, the velocity will probably be somewhat decreased, as the bed slope 
of : the canal will be less than that of the river, and it is plain that if we can 

silt 

arrange to decrease A (the ratio -) to the same extent as the depth is 

water 

decreased, we may succeed in so adjusting the canal that it will carry its own 
proportion of silt. We may, however, overdo the matter, and (as has actually 
occurred in some canals) arrive at a canal which will scour its banks owing to 
the fact that it has not drawn the proportion of silt from the river correspondin > 
to its depth and velocity. 

The logical method is to estimate the average silt in the river, and to see 
what fraction is likely to be drawn into the canal, and then experiment on the 
transport of the silt in a manner similar to that employed by Deacon or 
Lechalas, and calculate the required velocity in the canal. 

The estimation of the percentage of silt which is carried by the river is best 
effected by observing its mean velocity, and noting the quantity which is carried 
in the experimental trough at this velocity, and allowing for the difference in 
the depth of the trough and the river by the methods which have already been 
indicated. 

The one fact which stands out among all the uncertainties is that if v, is 
kept constant, d must increase or decrease in the same ratio as i, increases or 

P 

decreases. 

The preliminary method of dealing with such a question is best illustrated 
by an actual example. M. Mougnie (“Etudes des variations du lit de l’lsere 
a Montrigon,” published in vol. iii. of the Reports of the French Service des 
Etudes des Grandes Forces Hydrauliques ) gives 22 detailed gaugings for the 
Is£re, for the low-water seasons of 1905-6, 1906-7, and 1907-8, with the cross- 
sections of the river for each low-water season. Eighteen of these are low- 
water gaugings of the seasons 1906-7, and 1907-8. From the cross-sections 
we find by logarithmic plotting (see Sketch No. 22, p. 94) that if H, represents 
the gauge reading in metres, g, the hydraulic mean radius, or the mean depth 
in metres (the two quantities only differ by about o*8 per cent.), and 2/, the mean 
velocity in metres per second : 

During the low-water seasons of 1907-8 : 

g— H -t-0'34 and v= r 102 t £‘ 1,69 

During the low-water seasons of 1905-6 : 

^•=H-f-o , 35 and 2/= 1*213 Jp' 5T 

Thus, taking the mean value for the Is£re at this station during low water, 
we find that the equation of silt transport is given by : 

q = kv 1+ i t 63 = kv'* X 


During the low water of 1905-6, the river probably carried about ro6 times 
as much silt per unit volume of water as in 1907-8. This is confirmed by the 
fact that the mean surface slope was 0*0008 in 1905-6, and 0*0006 in 1907-8. 

The high-water gaugings are not sufficiently numerous to permit a study to 
be made, but the logarithmic plotting shows with a fair degree of accuracy that 
approximately 50 per cent, more silt was carried than in 1905-6. 

The method is liable to certain difficulties. 



SCOURING VELOCITIES 


495 


Thus, if the silt transport equation is : 

q — kv z 

we find that v — Qld. 

This is the usual equation for the motion of water which does not carry silt. 
In practice, however, I believe that this will rarely cause difficulty, since in 
the 28 cases of silt-bearing rivers which I have studied, in which the relation 
v = CLd, held good, the fact that scour occurred was always quite obvious. 

As the method illustrated here is original, it seems advisable to state that I 
have but rarely found that it leads to results which conflict with actual observa¬ 
tions of the quantity of silt carried. The statement is of course a relative one, 
as it is impossible to measure the absolute quantity of silt carried by a stream 
with any degree of accuracy. I am of the opinion that the value of n, in the 
relation q — kv n , largely depends upon the phase of the transporting motion. 
Where, as in the low-water stages of the Is£re, the river carries but little 
suspended coarse silt, we may expect to find that n= 1*5 to 2*5, and the transport 
is of the character termed Phase I (see p. 488). Values of n , ranging from 
2*5 upwards, indicate Phase II. In Phase III, values of /z, as great as 6 have 
been found to occur. The physical meaning is obscure, and I am inclined to 
suspect that the necessary inaccuracies of flood gaugings affect the results. 
The practical applications of the method are generally confined to rivers 
carrying silt in the modes termed Phases I and II, and in these cases a very 
useful insight into the laws of silt transport in a river or canal can be obtained. 

The following table gives the values of V l5 which is the bottom velocity that 
just produces motion in the substances under consideration. The values are 
approximate, but, so far as the information goes, they may be considered as 
minima values for clear water : 


Material. 

Velocity. 

Remarks. 

Soft earth . 

Ft. per Second. 
0-25 


Fine clay . 

0*25 


Soft clay . 

°*5 

Very variable, and depends 

Finest sand 

°' 5 ° 

upon the adhesion of the 
clay particles. 

Such sand as is left when clay 

Fine sand . 

070 

is eroded. 

The usual fine sand of rivers. 

Coarser sand 

o*8o 


Gravel, or Coarse sand 

1 ’o 

Largely depends upon the 

Pebbles, 1 inch in 


shape of the grains. Round 
gravel of say 0*05 inch size 
is rolled along a smooth 
surface at 0*30 foot per 
second. Pea size at o*6o 
foot per second, and bean 
size at 1’i foot per second. 

diameter 

2 'O 



[ liable continued. 


















496 


CONTROL OF WATER 


Table continued. ] 


Material. 

Velocity. 

Remarks. 


Ft. per Second. 


Pebbles, egg size 

Stones, 3 inches in 

3 to 3*3 

At this velocity the shape of 
the individual masses ceases 
to have a very marked effect. 

diameter 

5 *° 

These values are probably 
not very accurate, and it is 
extremely doubtful whether 
the velocities given ac¬ 
curately represent the bottom 

Boulders, 6 inches to 

8 inches in diameter 

6-6 

velocities. 

Boulders, 1 foot to 18 
inches in diameter 

IO'O 

• 1 


The following values of V 1} were obtained by current meter measurements in 
the Rhine (Deutsche Bauzeitung , 1883). Being obtained in a deep river, they 
are probably more reliable under such circumstances than the former values, 
which were mostly obtained from small scale experiments. 


Material. 

1 

Velocity in P'eet per Second. 

' 1 

If Disturbed. 

If Undisturbed. 

Gravel— 

Pea size ..... 

2*46 

3'87 

Bean size .... 

2*95 

4 * 3 ° 

Hazel to walnut size 

3'48 

4‘9 2 

Pigeon egg ... 

3' 6 7 


Weight, £ lb. 

4-92 


Weight, 5 lbs. ■ 

5'9o 


o*6 foot diameter . 

6*56 

• • • 

f " ■ : 


The above figures must be considered merely as representing ideal cases. 
If the water carries silt, scour of the finer materials will not occur until the 
tabulated velocities have been exceeded in a ratio which depends upon the 
quantity of silt which is already present in the water. A river which carries a 
large quantity of sandy silt is able to roll along gravel and boulders at smaller 
velocities than those indicated in the table. The action appears to be due to 
the fact that the lower layers of the river being heavily charged with silt, in 
reality form a fluid which has a density greater than that of pure water. The 
extra flotation thus obtained renders the stones more easily moved. Exact 
figures cannot be given. 












































FILTRATION AND PURIFICATION OF WATER 


SUMMARY OF PRESSURES REQUIRED IN FILTRATION 

Bacterial Investigation of Water.— Water-borne diseases—Normal death-rate 
from water-borne diseases—Bacteriological tests—Koch’s test—Specification— 
Criticism—Collection of samples—Importance of after-pollution—Special risks 
attending concentrated pollution. 

Apparent Failures of Filtration Systems .— Washington filters — Statistics- 
Criticism—Possible explanations—Unsewered cities. 

Bacteriological Reports. —Percentage of removal of bacteria—Maximum number of 
bacteria. 

Special Bacterial Investigations .— B. coli—Observations at Lawrence — Other 
bacterial indicators—Thresh’s investigations. 

Chemical Analysis of Water.— Hygenic qualities — Mineral qualities — Interpreta¬ 
tion of a chemical analysis—Free ammonia—Albuminoid ammonia—Chlorine— 
Nitrates and nitrites—Oxygen absorbed—Hardness, temporary and permanent— 
Organic carbon and nitrogen—Metallic impurities. 

Site of PAltration Plant. —After pollution—Deposits in pipes—Straining through 
gauze screens—Treatment of zinc and lead-solvent waters, and acid waters, by 
neutralisation with chalk or lime. 

Methods of Water Improvement.—Must be judged by bacterial tests—Popular 
standards—German preference for ground water—Not shared by vegetarian races— 
American standards of bacterial purity—British preference for slow sand filters— 
Sedimentation—Filtration—Chemical methods—Colloids—Coagulation. 

Slow Sand Filters.— Schmutzdecke — Zooglea — Relative value in bacterial removal — 
Probable role of Zooglea—“ Raw ” and “ ripe” sand—Practical conclusions concern¬ 
ing the thickness of the sand layers—Ruptures of the Schmutzdecke. 

Constructional Details. —Velocity of filtration—German rules—British practice— 
Removal of population from catchment areas—Area of filters—Design of filters— 
Depth of water—Covering of filters—Thickness of sand layers—“ Dalles filtrantes ” 
.—Thickness of gravel layers—Specification for a filter—Specification for sand—Head 
consumed in gravel layers—Spacing and sizes of drain pipes—“ Friction discs” or 
equalisers—Precautions for securing a uniform rate of filtration over the whole area 
of a filter—Brick and tile floors—Checks in side walls—Precautions round the columns 
of covered filters. 

Working of Filters.—Formation of the Schmutzdecke—Filtration—Cleaning by 
scraping. 

Abstract of Particulars of British Filters.—Depth of water-—Sand—Gravel—- 
Cleaning—Description of Derwent filters—Influence of character of water on the 
rate and interval between cleanings of filters—P'uertes’ formula for filter area— 
Quantity filtered between two cleanings as a function of size of sand—Effect of 
climate—Depth of sand scraped off—Replacement of sand—Standard of pollution— 
Effect of turbidity on sand filters—Colours, tastes and odours—Necessity for 
sedimentation—Rate of deposition of particles—Mechanical entanglement of 
bacteria—Difference between European and American waters—Houston’s views on 

storage_Criticism—Slow sand filters best adapted for stored, or sedimented 

water. 


CONTROL OF WATER 


498 


Practical Details. 

Sand Washing Apparatus.— Ripe sand—Washing by hosing—Trough, or conveyor 
washers. 

Ejector Washers. —Hoppers—Mixing sand with water—Design of ejectors—“Effi¬ 


ciency ” of an ejector—Ratio 


Total discharg e —y/[ 0 q 0n 0 f a mixture of sand and 
Discharge of jet 


water in a pipe—Frictional resistance—Minimum velocity. 

Washing of the Sand. —Quantity of water used—Weight of the mixture—Washing 
of raw sand. 

Washing OF Filters.—R aking under running water—Scraping by suction pumps— 
Agitation by compressed air and water under pressure—Cleaning in frosty weather— 
Grab scraper—Sand layers with a waved surface. 

Preliminary Filtration Processes. 

Degroisseurs or Roughing Filters. —Suresnes—Bamford—Shanghai single coarse 
filters—Double filtration—Bremen—Conditions—Criticism. 

Flood-Waters.—Turbidity—Pollution—Results obtained in London. 

Processes Supplementary to Slow Sand Filtration.— Preliminary Chemical 
Treatments. —Treatment with metallic iron—Anderson process—Burnt sulphur 
process, Polarite, Oxidium, and other processes—Ozone—Sterilisation by heat— 
Chemical sterilisation—Neutralisation—Straining. 

Removal of Visible Impurities from Water. 

Sedimentation. —Reduction of bacteria—Reduction of turbidity—Assisted sedimenta¬ 
tion—Coagulation—Sedimentation of Thames water—Sedimentation, or Storage- 
General British practice—American practice—Storage basins for tiding over periods 
of bad water—Nile water—General rules—Sedimentation and sand filtration—Con¬ 
struction of sedimentation basins—General design—Albany basin—Cleaning of 
basins—Velocity of Water through the basin—Inlets and outlets —Summer and 
winter conditions—Velocity of fall of particles—Hazen’s investigation. 

Coagulation.— Definitions—Alkalinity—Calculations—Lime and magnesia alkalinity 
—Practical determinations—Coagulation and slow sand filters. 

Sulphate of Alumina Process.—Effect of clay particles—Table of quantities of 
coagulant required—Pre-sedimentation—Chemical details—Deficiency in alkalinity—■ 
Quality of the coagulated water—Period of coagulation—Method of adding the 
coagulant—Motion in the coagulating basins—Addition of lime—“ Basic alum. 15 

Practical Details. —Solution of the “alum”—Mixture with the raw water—Period of 
coagulation and sedimentation. 

Ferrous Sulphate Process. —Two chemicals are used—Consequent difficulties— 
Advantage over alumina sulphate—Chemical reactions—Case where ferrous 
sulphate is first added—Case where lime is first added—Ferrous sulphate process 
without filtration—Ferrous sulphate and live steam process—Contrast between the 
waters produced by the ferrous and alumina sulphate processes—Weight of 
chemicals required—Results obtained at Cincinnati—Ferrous sulphate as applied to 
coloured waters—Burnt sulphur process— Practical Details —Mixing of milk of 
lime—Incrustations in the pipes. 

Mechanical Filtration. —General—Turbidity and pathogenic bacteria—Circumstances 
favouring the adoption of mechanical filters—Rate of filtration—Grading of sand- 
irregularities in bacterial results—Formation of the artificial Schmutzdecke—- 
Method of working after washing—Difference between filtrates which are perfectly 
clear and those which are bacterially safe—Practical methods of working filters. 

Bacterial Tests of Coagulation as Applied to Mechanical Filters.—Schreiber’s 
results—Frequency of cleaning as affected by the dose of coagulant—Criticism. 

Practical Details. —Loss of head—Area of filter units—Design of strainers—Dead 
water spaces—Sizing of gravel—Sizing of sand—Screen between sand and gravel— 
Working head'—Rate of filtration—Effect of size of sand—Usual sand. 

Washing of Sand in Mechanical Filters. —Raking—Washing by lifting the sand 
bodily, either by water or air and water—Effect of design of strainers—Level of 
escape channel—Washing of Cincinnati filters by water—Washing by raking—Loss 
of head in strainers—Russell’s formula—Washing by compressed air—Volume of 
wash water—Volume of effluent rejected after washing—Disinfection of filters. 

Deferrisation, or Enteisenung.—Troubles produced by iron and manganese salts— 
Conditions under which these salts occur—Proportion of iron causing trouble— 
Precipitation by oxidisation—Removal by coarse filters—Size of aerators and filters 




499 


PRESSURES REQUIRED FOR FILTERS 

—Removal of colloidal iron by forming a precipitate in the water—Calcium car¬ 
bonate—Anderson process—Sulphate of alumina and clay—Aeration probably 
unnecessary—Mixture of waters at Posen. 

Coloured Waters. —Colour and iron salts—Peat coloration—Tropical Waters— 
Removal of vegetation—Stripping reservoir sites in New England—Methods of 
purification—Example—Anderson process—-Tray aerators—“Critical head ”— 
.filtration, or coagulation after aeration—Slow filtration through aerated filters— 
Charcoal, or carbon filters— Colloidal Colour —Coagulation after addition of clay 
—Formation of the coagulating precipitate previous to addition to the water. 

Odours a.yd Tastes in Waters. —Causes—Copper sulphate process—Aeration- 
Coagulation—List of possible processes-—Frogs and fish—Dissolved gases—Ground 
waters. 

Softening Processes. —Clark’s process—Reactions with lime and magnesia—Other 
water softening processes—Effect on bacteria—Practical details—Size of precipitar 
tion basin mainly depends on the magnesia content—Incrustation—Re-carbonation 
processes—Atkins’ cloth filters—Archbutt process. 

Regulating Apparatus Employed in Filtration. —Valve on outlet pipe—Weir 
for measurement—Telescopic tube—Floating tube—Burton’s balanced valve 
regulator—Theory—Details—Weston’s diaphragm—Sliding weir—Effect of leakage 
—Numerical example. 

Influence of Climate on Processes for Water Purification. —Coagulation 
—Biological processes—Sand filters— Degroisseurs—Chemical processes. 


SUMMARY OF PRESSURES REQUIRED IN FILTRATION 

Any summary of formulas connected with filtration is impossible. The 
figures relating to the head or difference of pressure required are the least vari¬ 
able, and since they are important in preliminary investigations concerning the 
site of the filters or the horse power of the pumps, they are very roughly tabu¬ 
lated below. 

Excluding the resistances of the connecting pipes and channels : 

(i) A sedimentation basin and its valves consume about 6 inches head. 

(ii) Each gravel filter, such as Peuch’s degroisseur (p. 544), requires 6 to 9 
inches head. Each fall for aeration between the filters also consumes about 6 
inches. A prefilter, such as that used at Steelton (p. 570), or Philadelphia, 
requires about 2*5 feet when clogged. 

(iii) Thorough aeration in most waters can be secured by four falls of 6 inches 
each. Tray aerators consume about 6 feet. No definite figures can be given 
for aeration by fountains, but it will usually be found that the larger the indi¬ 
vidual jets the greater is the head required. The figures in all cases depend 
considerably on the quality of the water. 

(iv) Slow sand filters when clogged consume from 2‘5 to 4 feet head. The 
smaller the available head, the more frequently cleaning is required. 

(v) An efficient coagulation basin requires a head of 6 inches to 1 foot, 
although 3 inches often suffices. 

(vi) Mechanical filters when clogged require from 12 to 25 feet head, the 
usual limits being 15 to 20 feet. 

Bacterial Investigation of Water. —The main facts as to the bacterial 
origin of most diseases are generally known. For a waterworks manager, the 
practical result is that certain diseases are now held to arise from minute organ¬ 
isms conveyed to the human body by means of water. Such diseases are 
generally termed “water-borne,”—and typhoid, or cholera, may be taken as 
typical examples. If in any town the death-rate from such diseases rises above 
the normal, the water supply should be regarded with suspicion. A numerical 



5 °° 


CONTROL OF WATER 


statement of the normal death-rate is quite impossible. Large groups of 
American cities are satisfied with a typhoid death-rate which, in Germany, or 
Great Britain, would probably lead to legal proceedings being taken against the 
waterworks’ authority. My personal experience both of typhoid and cholera, 
leads me to consider that the water is sometimes unreasonably condemned. 
But such isolated cases form no ground for the assumption that unfiltered, or 
badly filtered water, is healthy ; and a waterworks’ manager must be content to 
do his best. He is only justified in asking for investigations on other lines 
when he has proved that the water supply is above suspicion. I may, however, 
state that there is sufficient evidence, ( e.g . at Melbourne and Buenos Aires) to 
show that a perfectly satisfactory water supply may be accompanied by a high 
death-rate from typhoid, if the drainage is bad. The probable explanation is to 
be found in the sequence ;—open closets, flies, and food. 

The present methods of proving that a water supply is satisfactory (other 
than the large scale proof of a death-rate from water-borne diseases well below 
the normal) are bacteriological. 

In principle all bacteriological tests consist in placing the bacteria contained 
in a given volume of water in a situation which is favourable to the development 
of seme or all of the various species. Consequently, each individual of these 
species generates a group of bacteria, and after an appropriate interval of time 
has elapsed these groups or “ colonies ” can be counted, and the various species 
identified. The details of such bacteriological methods do not concern 
engineers ; but it should be realised that the methods of favouring the growth 
of the bacteria can be indefinitely varied, and in this way a single species, or a 
restricted class, of bacteria can be separated out from the others. 

Thus, the reports may state the number of bacteria which are found by 
Koch’s method, or by other more specialised tests. Koch’s method favours 
the growth of bacteria which produce the typical water-borne diseases, but 
some of the resulting colonies are also derived from other allied species which 
are probably harmless. The special methods can, however, be so adjusted as 
to select definite species of bacteria for counting purposes. For example, 
B. coli and other sewage bacteria, or special disease-producing bacteria (such as 
B. typhosus ), may be separated from other species. 

Some European waterworks are managed by skilled bacteriologists, but the 
usual practice (as also in Great Britain and America) is for a bacteriologist to 
be retained to examine the water, and report to the responsible engineer or 
superintendent. 

Many filtration works are still managed with success by rule of thumb, and 
without any bacterial investigations whatsoever, but there is little doubt 
that daily examinations of the effluent from each individual filter should be 
carried out wherever the raw water is badly polluted. This is an ideal con¬ 
dition, and a daily examination of the mixed effluent, supplemented by special 
investigations whenever any irregularity in the working of the filters occurs is 
usually considered sufficient. 

My own experience leads me to believe that money could be saved by more 
systematic examinations. 

The standard at present generally adopted is that laid down by Koch, who 
stated that filtered water should not contain more than ioo bacteria per cubic 
centimetre, as ascertained by counting the colonies after four days incubation on 
nutrient jelly, at 20 degrees C. Thus, the test really proves that one cubic 


KOCH'S TEST 


5°* 

centimetre of filtered water contains less than ioo individuals capable of propa¬ 
gating themselves under the special conditions laid down by Koch. It may 
therefore be inferred, and has actually been proved, that many other bacteria 
which are incapable of reproducing themselves under the above conditions may, 
in reality, exist in the sampled water. The conditions to which the sample is 
subjected in Koch’s test are those which, in his opinion, are best suited to the 
propagation of the species of bacteria producing typhoid and cholera, and, as a 
matter of fact, many other closely related and probably harmless species also 
flourish under these circumstances. 

ihe standard being a local one (i.e. suitable for German conditions), is ob¬ 
viously open to objection, and might be considered as illogical as a description 
of venomous snakes referring to European species only. As a matter of fact, 
however, the standard always secures a water which is satisfactory when judged 
by the death-rate test. Under certain conditions (principally American) it may 
possibly be too stringent. Likewise, it may eventually be discovered that for 
waters drawn from rivers flowing through thickly populated Asiatic countries, it 
is not sufficiently severe. These statements are, however, founded on very 
scanty and unreliable information, and it will probably be many years before 
the standard is superseded. The information required for this purpose is 
neither bacterial, nor engineering, but rather statistics of the public health of 
well sanitated tropical cities, with a w'ater supply passing Koch’s tests. 

Certain differences in detail exist in the application of the test. For 
example, in France a period of 7 to 15 days’ incubation is usual. This is 
apparently a higher standard of purity, but comparative figures cannot be 
given, although in one case it appeared that a water which produced 120 
bacteria per c.c. under the French test, yielded only 55 bacteria per c.c. 
under the test as carried out in strict accordance with Koch’s methods. 

The usual way of specifying the test is as follows : 

“ The number of bacteria per c.c. in the filtered water shall not exceed 
100 under Koch’s test, the sample being kept in an artificially cooled receptacle 
(i.e. packed in ice) during transit. If the bacteria in the raw water exceed 3300, 
as tested by Koch’s method, the filtered water count may exceed 100, (but the 
percentage of reduction must not then be less than 97).” 

This last clause is illogical, since the fact that the raw water is highly 
polluted, is, per se, an indication that the 3 per cent, of the bacteria that do 
escape are rather more likely to be pathogenic than if the raw water were less 
polluted. It has the practical justification that slow sand filters alone (how¬ 
ever carefully worked) are unlikely to produce better results unless the 
supervisor is unusually capable. Nevertheless, I consider that the clause 
should be omitted, even if in practice it turns out that the latitude must be 
allowed, since the supervisor should not be encouraged to remit his efforts to 
obtain a satisfactory filtrate on the very occasion when danger is most prob¬ 
able, and treatment supplementing sand filtration is most required. 

The bacteriologist should, of course, give his own instructions lor the 
collection of water for test, or, better still, take his own samples. Where no 
instructions are given, the glass bottles and stoppers should first be cleaned 
with strong sulphuric acid, then in freshly boiled distilled water, and should 
afterwards be steamed for 15 minutes, cooled in a steriliser, and finally 
stoppered, and wrapped in cotton wool, the water being poured into them 
without being touched, from a similarly treated tap or vessel. 


5 o2 CONTROL OF WATER 

The bottles should then be packed in ice, which should be renewed until 
they reach the laboratory. 

The chemical methods of testing water are discussed later. At present it is 
sufficient to state that they can only be regarded as preliminary to bacterial 
tests. It is occasionally (e.g. in isolated localities) necessary to rely on their 
indications alone. Nevertheless, it cannot be too strongly stated that if the 
chemical indications are at all doubtful, bacterial tests must be applied. 

As already indicated, many species of bacteria exist in water (even the 
purest natural waters contain some bacteria), and so far as our present know¬ 
ledge goes, the majority of these species are harmless when consumed by 
human beings, some indeed actually being beneficial. Even if the above 
remarks are restricted to those species of bacteria which flourish under Koch’s 
test, it is probable that the majority are quite harmless. Thus, logically speak¬ 
ing, no numerical standard of bacterial purity can be applied to all localities. 
A proper specification would take into account the probable proportion of 
disease-producing and harmless bacteria which exist in the raw water. Con¬ 
sidering the subject from this point of view, it is evident that a numerical 
standard which secures safety when applied after filtration to a water drawn 
from a river which is known to be heavily polluted by sewage, may be far too 
stringent when applied to a case where the raw water is drawn from a source 
not exposed to sewage pollution. 

Also, the possibilities of an increase of the harmful bacteria after filtration 
should be considered, since an increase may occur on a large scale in the filtered 
water, if the conditions in the mains and reservoirs favour the propagation of 
these bacteria. 

Thus, not only should the water be tested immediately after filtration, but 
tests should also be made of samples drawn from the supply mains, so as to 
ascertain the bacterial condition of the water at the moment when it is actually 
used by the consumers. 

The results of many tests (which are apparently confirmed by the circum¬ 
stances attending several epidemics of water-borne disease) indicate that the 
disease-producing species have afar greater chance of increasing in water to 
which they gain access, if but a small number of bacteria are originally found in 
this water. The reason seems fairly obvious : Disease-producing bacteria are 
not, apparently, those which are best suited to exist in water (their most 
favourable environment being the human body). When, therefore, they find 
themselves exposed to the competition of a large number of other species of 
which the normal home is water, the disease producers are unable to survive the 
competition of the better adapted species. 

This competition is less severe in comparatively pure water, and disease pro¬ 
ducing species are able to multiply. It is evident, therefore, that an engineer 
must carefully consider the possibilities of pollution after purification, and 
should consider after-pollution as a very serious matter, for bacteria are then 
not only provided with a clear path of access to the human body, but the 
purified water affords them a favourable incubating ground. 

The special risks attending concentrated pollution must be pointed out. 
The matter is somewhat difficult to define, as the precise conditions are 
unknown ; but it can be best illustrated by the statement that if a “ pound ” of 
pollution must enter the water either before or after filtration, it is better, from 
the point of view of health, to receive the “pound” in 7000 separate “grains” 


FAILURE OF FILTRATION PROCESSES 503 

lather than in one mass, even though the water received from the individual 
souices is afterwards thoroughly mixed, and the “grains” finally reach the 
consumers simultaneously. 

If this principle is once grasped the extreme danger of concentrated pollution, 
which is also local, needs no discussion. One typhoid patient whose dejecta go 
straight to the intake of a water supply system is more dangerous than 100 
cases whose dejecta reach the river from which the intake derives the water 
at various isolated points. If a waterworks’ manager knowingly permits a 
peison suffering from “summer diarrhoea ” to remain on or about the works, 
even although in the neighbourhood of the raw water channels only, he should 
not be allowed to retain his position as manager. 

Apparent Failures of Filtration Processes — In certain cities, 
cases have occurred where the introduction of a purified water supply has 
not been followed by a decrease in the number of cases of, or deaths from, 
those diseases which are classed as water-borne. The example which has 
received most investigation is at Washington, where the circumstances were 
as follows. 

From 1883 to 1903 the typhoid death-rate ranged from 40 to 104, and was 
usually between 65 and 80 per 100,000. 

In October 1905 slow sand filters of a very excellent type were introduced, 
but the death-rate from typhoid month by month during 1906 was approximately 
the same as in 1905, and the total number of cases (fatal and non-fatal) was 
greater. 

The public at once inferred that the slow sand filters were useless, and there 
is no doubt that the figures are extremely disheartening to those who are con¬ 
vinced that a polluted water supply is always a public misfortune. 

The exact figures are as follows : The deaths from typhoid for 1906 were 
44 per 100,000, and this was the average of the years 1903 to 1905. A figure of 
20 to 25 .deaths per 100,000 from typhoid in towns situated under circumstances 
like those found at Washington may be considered to indicate a satisfactory 
water supply. 

Thus, a rate of 19 to 20 deaths per 100,000 needs explanation. A study of 
the yearly death-rates of the period 1883 to 1906 given in Trans. Am. Soc. of 
Civil Eng., vol. 57, p. 430, provides a partial explanation. 

In the first place, the typhoid death-rate oscillates up and down in very 
much the same manner as the annual rain-fall of any locality does (it must not 
be inferred that any connection is intended, the oscillating character of both 
figures is alone referred to). Judging by the run of the curves, the typhoid 
death-rate was low from 1903 to 1905, and therefore a rise might have been 
expected about 1906. Thus, it is possible that the filters did actually produce a 
real, although not an apparent, decrease 'in the death-rate. This argument is 
somewhat flimsy when relied upon to justify an expenditure of many millions 
of dollars. It is therefore fortunate that the curves show very clearly that 
after 1895 the sedimentation in the Dalecarlia reservoir produced a marked 
decrease in typhoid, and that a second, although a less pronounced, decrease is 
indicated after 1902 or 1903, when another sedimentation basin (the Washington 
reservoir) was brought into use. It may consequently be inferred that the 
Washington figures, as they stand, show fairly clearly that an amelioration of 
the water supply does produce a decrease in the typhoid rates, even although 
the effect of slow sand filters is not evident. If, however, slow sand filters 


CONTROL OF WATER 


5°4 

alone are considered, the results must be regarded as justifying adverse 
criticism, and it is highly regrettable that such hostile testimony should arise 
from the results of filtration.when introduced into so important a city. It 
is the more lamentable in that, at the present date, filtration (as compared with 
European practice) is just being adopted in American cities. I do not, however, 
believe that the many skilful American experts in filtration will allow this case 
to remain either unexplained, or without remedy. The circumstances are some¬ 
what obscure, and pollution of the milk or fruit supplies has been suggested 
as being the true source of the disease. 

I suggest three possibilities : 

{a) As already explained, the character of the raw water may be such as to 
require a more stringent standard of bacterial purity in this particular case 
than has been found necessary elsewhere. 

(i b ) The daily consumption of water per head in Washington is 200 U.S. 
gallons, a figure which (for a residential city with comparatively few factories) 
suggests a large amount of waste, and the possibility of leaky mains, so that 
after-pollution cannot be considered as impossible. 

( c ) The raw water at Washington is drawn from a river which at certain 
periods of the year carries large quantities of extremely fine clay. Waters of 
this type are known to be less easily purified by sand filters than the clearer 
waters which are found in Europe. As a general rule, such waters have been 
treated by coagulation processes, or have been passed through degroisseurs 
previous to slow sand filtration. The typical method of purification is coagu¬ 
lation followed by mechanical filtration. Now, there is no evidence which 
permits us to state that the European method of slow sand filtration alone, as 
practised at Washington, is necessarily effective in removing pathogenic 
bacteria from waters of this type. Although the Washington methods were in 
accordance with the very best practice, it is quite possible that the official order 
prohibiting any addition of coagulant was an error of judgment. This sug¬ 
gestion deserves careful consideration, especially by British engineers, who* are 
notoriously too prone to rely on slow sand filters exclusively. 

I put the suggestions forward with some diffidence, but would remark that 
although they may be conclusively proved to be inapplicable to the case of 
Washington, they are certainly factors that no investigator could afford to 
overlook. 

It must be remembered that while every case of apparent failure is reported 
and discussed, the usual result of the introduction of a purified water supply 
is a marked decrease in water-borne disease, and such successes being normal, 
they are rarely, if ever, matters of more than local interest. 

In this connection it is as well to state that the introduction of a copious 
supply of water into a city in exchange for a scanty one may be expected to 
produce an unfavourable effect on public health, unless a sewerage system is 
simultaneously (or has been previously) introduced. The reason is fairly 
obvious :—Such cases generally occur in dry climates, and so long r as water is 
economically used, the subsoil is not water-logged, and garbage and refuse are 
dried up by the air before they become markedly decomposed. On the intro¬ 
duction of a copious water supply, however, the waste liquid saturates the subsoil, 
and garbage is less rapidly dried up. 

The real lesson is therefore to introduce a sewerage system and a water supply 
simultaneously, and never to consider waste of water as unimportant. Typical 


BACTERIOLOGICAL REPORTS 


5°5 


examples illustrating the above are Buenos Aires, and Melbourne, and in the 
latter case proper sewers have produced a satisfactory state of affairs. 

To sum up :—The methods of bacteriological testing at present practically 
employed are (as a rule) excellent guides, but they are by no means infallible. 
Thus, if the real tests of a process of purification (i.e. the health statistics of the 
community) give an adverse result, an engineer is justified in requiring the 
bacteriological experts to adopt more searching tests than the routine “bacterial 
counts ” ; and until these have been systematically applied in many cases, our 
present knowledge does not permit us to condemn either the routine methods of 
filtration, or the customary “ bacterial counts,” as useless. 

I need hardly say that in cases where success is not attained, the filtration 
process must be carefully overhauled, but under the social conditions usually 
obtaining, engineers are somewhat too prone to accept routine bacteriological 
work as sufficient in all cases. 

Bacteriological Reports.—T he, engineer should insist on the actual 
counts being reported in every case. I have noticed that, especially when re¬ 
porting the results of tests on proprietary systems of purification, there is a 
custom (happily a decreasing one) of recording figures other than the actual 
number of bacteria per cubic centimetre. 

A figure commonly reported is the “ percentage of removal of bacteria,” i.e. 


f t _ Number of bacteria per c.c. of purified watery 
V Number of bacteria per c.c. of the raw water/ 


This is quite useless as an index of the safety of the water, since the figure 
is almost independent of the number of bacteria in the raw water, because 
any well-arranged system will usually effect a reduction of 99 per cent., and it 
is very rarely that the figure falls below 95 per cent. 

This method may be useful in comparing the relative efficiencies of two 
different systems of purification, but the fairest way of holding such com¬ 
parative tests is to supply the same raw water to each system. Consequently, 
all that can be said is that the figure is not necessarily misleading. 

The custom of reporting not the results of each test, but the average result 
of all the tests during a month, falls under quite a different head. In my own 
practice I look upon such reports as valuable only as an index of the variability 
of the process, and believe that in most cases the detailed figures are intention¬ 
ally concealed. There is very little doubt that an individual who constantly 
consumes polluted water (should he survive) acquires a certain immunity, and 
finally can drink water that would in many cases cause a serious illness in any 
one less accustomed to pollution of this character. 

It is therefore evident that a supply which, for say 30 days in the month, 
attains the requisite standard of purity, but, on the 31st day (owing to careless¬ 
ness or irregularity in the process of purification), delivers a badly polluted 
water, is in some respects more dangerous to health than a system of supply 
that always delivers a slightly polluted water. 

Consequently, it is only fair to assume that where the results of bacterial 
tests are uniformly satisfactory, they are published in detail, and when the 
literature states average results only, the process is in reality markedly irregular 
in its working, and is therefore unsuitable for adoption. These remarks cannot 
of course be applied to reports in which averages are stated, and likewise the 
maxima counts obtained in each period over which the averages are taken. 




506 CONTROL .OF WATER 

Special Bacterial Investigations . —Routine “Standard Bacterial 
Counts,” such as the Koch test, should not be considered as indicating the 
total number of bacteria present in the water under examination. The method 
is avowedly such as to favour the propagation of the bacterial species which 
exist in sewage. If special processes are employed, it is possible to obtain 
counts of bacteria far exceeding those yielded by the usual methods, but the 
extra number thus secured consists of species that do not in any way indicate 
pollution. The results of such counts therefore possess no interest for the 
waterworks’ engineer. 

On the other hand, it is also possible to arrange a count of the individuals 
of a single species, and such investigations are worth consideration. In our 
present state of knowledge, the most important of these special species counts 
is the one referring to the Bacillus coli. B. coli occurs in human intestines and 
fecae, and also, it is believed, in similar situations in several animals. Whilst, 
therefore, its presence does not necessarily indicate pollution by human beings, 
its habits and occurrences are such that we may assume that a process of 
purification which removes B. coli will also eliminate the bacilli producing 
typhoid, and probably those giving rise to other water-borne diseases as well. 

The occurrence of B. coli is therefore a very valuable index of the efficacy of 
a process of purification, and of the safety of the filtrate. 

An excellent illustration of its efficiency as an indicator is found in a case 
occurring at Lawrence, Mass. (Clark and Gage, Significance of Appearance of 
B. coli communis in Filtei'cd Water). Here, owing to repairs to the under¬ 
drains of a filter, a leak or a weak spot in the sand was produced, in 
November 1898. 

In December 1898 B. coli was found in 72 per cent, of the samples 
examined and 12 cases of typhoid occurred. 

In January 1899 the figures were 54 per cent, and 59 cases. 

In February „ the figures were 62 per cent, and 12 cases. 

In March „ the figures were 8 per cent, and 9 cases, all in the early 
part of the month. 

The example is very instructive, and the figures make the following con¬ 
clusions fairly clear : 

(a) That the disease lags behind the appearance of B. coli. 

( b) That B. coli is not in itself a disease producer, but some accompany¬ 

ing factor which is only roughly proportionate to the abundance of 

B. coli. 

and this is exactly what bacterial investigators would have us believe. 

B. coli is an easily recognised indicator of the possible presence of disease- 
producing organisms which are far less readily discovered, and it is from this 
point of view that counts of B. coli are valuable. Taking 1 c.c. of water for 
investigation, it would appear that where B. coli are found in more than the 
normal numerical proportion of these counts, danger exists. The danger line, 
however, cannot be rigidly fixed, since it depends on the results found during 
the normal working of the filter, and varies with each town. At Lawrence, 
Mass., 8 per cent, was normal, and was considered satisfactory. In a town 
supplied with very pure water, a far smaller percentage might indicate a 
dangerous state of affairs. 


BACILLUS COLL 


507 


It has been proposed to consider such organisms as Klein’s B. enteriditis, 
or certain streptococci, as indicators of danger. These, unlike B. coli , have 
never been discovered except in sewage, or sewage-polluted water. The 
proposal is at present of more or less doubtful utility, except for British waters. 
So far as can be inferred the difficulty lies in the fact that these organisms are 
not present in all sewages, although they appear to be characteristic of British 
sewages. It is plain that a standard which is so local in its application, 
requires further investigation. It must also be remembered that indicators 
which only apply locally are likely to prove more useful for those particular 
localities, than any general indicator such as B. coli. 

The British semi-official standards are : 

For deep wells. —No B. coli should be found in 10 c.c. of water. 

For moorland and upland waters. —No B. coli should be found in 1 c.c. of 
water. 

For shallow wells. —No reliable indication can be drawn from the presence 
of B. coli. 

It will consequently be evident that the standard is not an absolutely 
numerical one, but rather one of variations from the normal number. 

The nett result of the discussion is summed up by Thresh (7 'he Exami- 
nation of Waters and Water Supplies ), and in explanation it must be stated 
that he worked with sewage obtained from a town possessing a small supply of 
water (I believe 15 gallons per head per day), and but little trade waste. His 
sewage, therefore, is comparatively concentrated, and free from other than faecal 
matter. 

I. In a water recently polluted by sewage, in a proportion of more than one 
part per million, both typical B. coli and Klein’s B. etiteriditis can be detected. 

II. In a water not recently polluted by sewage, or manurial matter, the above 
bacilli may be absent, but intestinal bacteria occur, i.e. other forms, some of 
which are very closely allied to the typical B. coli , and only distinguishable by 
special tests. 

III. Unless some of those forms closely resembling B. coli occur, the 
presence of other “intestinal bacteria” has no significance. 

Now, in ordinary tests for B. coli , I and II would be classed together; 
but I is certainly dangerous, while II is possibly safe. 

It may therefore be inferred that towns with a satisfactory death-rate (as 
regards water-borne diseases), wffiere B. coli is found in a fairly large percentage 
of the samples of filtered water, are really supplied with safe waters, resembling 
Class II, or are possibly less polluted with sewage than one part in a million. 
But it will be clear that a sudden increase in the number of B. coli contained 
in samples may indicate a change to the dangerous portion of Class II, or even 
to Class I, owing to the pollution becoming more intense, or being more 
rapidly transmitted to the town, e.g. by floods, or a breach in some stratum 
which had previously delayed the progress of the polluted water. 

Chemical Examination of Water. —In all calculations connected with 
the chemical reactions of water it is convenient to note that : 

1 part per 100,000 = 4-375 = 4”- grains weight per cubic foot. 

= 07 grain per Imperial gallon. 

= 0*58 grain per U.S. gallon. 

Also, 1 pound = 7000 grs. 


CONTROL OF WATER 


508 


A chemical analysis of water is undertaken with two objects. The more 
important is to ascertain its suitability for human consumption from the point 
of view of health. Such an investigation is really only a substitute for a 
bacteriological test, and can hardly be regarded as sufficient if the results are 
at all doubtful. Secondly, as a rule, it is also desired to ascertain whether the 
water, besides being free from organic pollution, is otherwise satisfactory. In 
these latter cases it is necessary to determine the content of mineral substances, 
not only such as arsenic, lead, or zinc, which are obviously undesirable, but 
also of such salts as calcium and magnesium or iron carbonates, which may 
cause the water to be unsatisfactory (as being too hard, or likely to produce 
deposits in the pipes, etc.). The methods of removing, or ameliorating these 
conditions, where necessary, are dealt with under Softening and Deferrisation. 

It is not proposed to describe the methods employed in the chemical 
analysis of water. An engineer should be able to interpret a chemical 
analysis, and to draw inferences from the data it affords ; and the following 
notes are directed to that end alone, and are principally concerned with the 
hygienic qualities of the water. 

If a study be made of all the available evidence relating to the connection 
between the contents of a water as disclosed by chemical analysis, and its 
fitness for human consumption, it will at first sight appear that no close 
relationship exists. This, in reality, is merely an instance of the tendency of 
human nature to give undue weight to exceptional instances. 

Deductions drawn from the quantity of any single substance present in a 
water are liable to prove quite erroneous. In practice, however, the indications 
are not usually isolated facts, and the inference drawn from, say, the presence 
of chlorides in a water is usually confirmed either by other chemical indications, 
or by the results of an examination of the origin of the water and its exposure 
to possible sources of contamination. Thus, the chemical analysis of a water, 
combined with information obtained from an examination of its source, almost 
invariably enables a definite statement to be made as to the fitness of the water 
for human consumption. 

The processes generally employed by chemists when preparing a report on 
water which is intended for human consumption are as follows : 


(i) 

(ii) 

(iii) 

(iv) 

(v) 


(vi) 

(vii) 
(viii) 


)> 


55 


55 


55 

Nitrites 


55 


55 


55 


Determination of the free ammonia. 

albuminoid ammonia, 
chlorine, 
total solids, 
nitrates. 

tested for qualitatively, and if present 
is very rarely the case) are estimated 
quantitatively. 

Determination of the oxygen absorbed. 

temporary hardness, 
permanent hardness. 


are 
(which 


55 


55 


55 


55 


Occasionally (ii) and (vi) are not reported, but the quantities of organic 
nitrogen and organic carbon are given instead (see p. 512). This is the 
information usually provided, and if more is required the engineer should ask 
for it. The additional information needed when coagulation processes are 
contemplated is considered on pp. 556 and 565. The questions concerning the 


AMMONIA CONTENT 


5°9 

zinc- and lead-solvent properties of the water are discussed on page 514. In all 
these cases the engineer should be prepared to afford full information to the 
chemist, and should state his requirements in a definite form. 

Taking the eight quantities detailed above in order : 

(i) and (ii) Free Ammonia and Albuminoid Ammonia.—These are occasionally 
reported as ammoniacal nitrogen, and albuminoid nitrogen. The conversion 
factor is given by : 

Nitrogen x 1*214 = Ammonia. 

The albuminoid ammonia content is by far the most important factor in 
determining the fitness of a water for human consumption. If less than 0*002 
parts per 100,000, the water can be passed as pure, even if large quantities of 
free ammonia and chlorine are present. If the content of albuminoid ammonia 
exceeds 0*005 parts per 100,000, the quantities of free ammonia and chlorine 
should be considered, and if these are high a bacteriological examination is 
necessary. Anything exceeding 0*008 parts per 100,000 is suspicious, and if 
the albuminoid ammonia exceeds 0*01 part per 100,000, a bacterial examination 
is. required however favourable the other indications may be. 

A proportion of albuminoid ammonia in excess of 0*015 parts per 100,000 
requires very strong bacterial evidence before the water can be considered as 
fit for human consumption. In these cases if the chlorine content is low (say 
less than 1 part per 100,000) the pollution is probably of vegetable rather than 
animal origin. While a water so heavily charged with organic matter cannot 
be considered as first class it may possibly prove bacterially satisfactory, and is 
certainly a better raw material for filtration processes than a water of equal 
albuminoid ammonia content, containing chlorine in quantities (say over 3 per 
100,000) which indicate pollution of animal origin. 

In waters derived from deep wells, free ammonia has no definite significance. 
The average value is o*oi per 100,000, but 0*03 is not uncommon, and 0*1 is not 
unknown in bacterially pure deep well waters. The free ammonia in these 
cases results from the reduction of nitrates, and therefore indicates a pollution 
of even more remote date. 

In safe spring waters, 0*001 is the average, and 0*01 is rarely exceeded. 

In upland surface water the average content is 0*002, and 0*008 per 100,000 
is rarely exceeded if the water is safe. 

In water derived from cultivated land, the average is say 0*005, and 0*025 is 
rarely exceeded if the water is safe. 

In shallow wells, nil to 2 per 100,000 is found. 

The figures must be read in conjunction with the albuminoid ammonia 
content, and the local normal content of free ammonia, as discussed under 
Chlorides, must be ascertained. 

(iii) Chlorides.—These usually indicate the presence of common salt, which 
in itself is unobjectionable. Seventy parts per 100,000 are distinctly perceptible, 
and anything exceeding this indicates a brackish water, although some people 
find even 20 parts distasteful. If, as is usually the case, all the chlorine is 
present as common salt, the weight of the latter is 1*65 times that of the 
chlorine (if the results are thus reported). 

The real importance of chlorides is as an indicator of sewage pollution. 
Human urine contains about 1 per cent, of salt, and consequently sewage 
derived from a town supplied with say 30 gallons (36 U.S. gallons) per head 


5i° 


CONTROL OF WATER 


per day, will contain about 5 parts per 100,000 more chlorine than the original 
water. Hence, before we can lay down any standard for a suspicious water, we 
must know the normal content of unpolluted water in the district under 
consideration. In England, 4 parts of chlorine per 100,000 may be taken as 
the probable value for normal ground waters. Therefore, if in a district where 
well water usually yields 4 parts, we find wells near the centre of population 
yielding 30 parts (as sometimes occurs), it is hard to avoid the inference that 
the water (although possibly quite fit for human consumption) is sewage, which 
has been used over and over again ; and bacteriological examination is obviously 
necessary in order to make certain that the natural filtration through the ground 
has destroyed all sewage bacteria. 

In the United States it would appear that away (i.e. 150 miles or more) 
from the sea, chlorine contents equal to o'8 per 100,000 are normal ; so that in 
such localities a content of even 3 parts (allowing for the fact that the average 
water supply of an American city greatly exceeds 30 gallons per head, per day) 
may be regarded as suspicious. 

As a contrast to these figures, cases exist of waters of undoubted bacterial 
purity, containing 50 to 70 parts per 100,000. 

It must also be remembered that salt is a very common mineral, and may 
be present in appreciable quantities in bricks, mortar, or wood (due to soaking 
in sea water) so that in a new well, the materials composing the lining may 
affect the analysis. 

(iv) Residue left on Evaporation.—This may vary from 5 to 6 parts per 
100,000 in upland surface waters, to 150, in the case of waters drawn from 
sandstone strata. Unless the water contains more than 50, or even 60 parts of 
solids per 100,000, no exception need be taken to the solids as such. The in¬ 
formation is mainly useful as indicating the necessity for a complete analysis 
where the weight of chlorides, nitrates, and hardness found, does not account 
for all, or nearly all of the weight of the residue. 

Charring may be considered as indicating the presence of organic 
matter. If accompanied by an offensive odour, this is probably of animal 
origin. 


(v) Nitrates.—These should be reported as parts of nitric nitrogen per 
100,000, not as nitric acid (HN 0 3 , conversion factor, - 1 - tri ^ aci( ^ = nitrogen), or 

nitric anhydride (N 2 O s , conversion factor, — nitrogen). 

0 . 00 


Nitrates are derived from the oxidation of nitrogenous matter of animal origin, 
and may therefore indicate animal pollution at some past period, which, in 
certain cases at least, has been traced back to as remote a date as 1640. 

Owing probably to the fact that nitrates are the final product of the 
decomposition of organic matter, no definite standard of purity can be 
given. 

A well water containing more than 7 parts per 100,000 of nitric nitrogen must 
certainly receive a searching bacterial investigation, but many waters con¬ 
taining less than 7 parts per 100,000 are also unsafe. Generally speaking, up to 
1*5 parts per 100,000 is considered to be innocuous, but the amount of manuring 
which the surrounding soil receives must be taken into account ; and, if this 
does not explain the content of nitrates, bacteriological examination is indicated. 
In the case of a well, the most favourable time for the recognition of the 




HARDNESS 


5 1 * 

bacteria, that the presence of nitrates indicates are likely to be found, is soon 
after heavy rain. 

A water is unsafe in which both chlorides and nitrates occur in more than 
the normal quantity ; as also is a well water which becomes opalescent, or 
turbid, after rain, and in which an excess of nitrates can be traced. 

It must also be noted that rain water invariably contains about o'o3 parts 
per 100,000 of nitric nitrogen. 

Nitrites if occurring in deep well waters, have no definite significance ; since 
they are probably produced by the reduction of nitrates, the total content of 
nitrogen in the nitrates and nitrites should be considered when drawing 
deductions as to the quality of the water. In a river, however, the presence of 
nitrites is extremely significant, since it almost invariably indicates so recent a 
pollution by sewage that the river has not had time to begin to purify itself. 
Unless the presence of nitrites can be otherwise accounted for, such water is 
hardly fit for human consumption even after filtration, unless it is also 
sterilised. 

(vi) Oxygen Absorbed.— This is usually determined by Forcheimer’s test 
for “Three hours at 80 degrees Fahr.” Some chemists make two determina¬ 
tions, at “15 minutes,” and at “4 hours.” A marked difference between the 
two results indicates vegetable rather than animal pollution. 

Frankland gives the following standards for oxygen absorbed : 



Parts per 100,000 

In Upland Surface 
Waters. 

Other Waters. 

Water of great purity 

„ medium purity . 

„ doubtful purity . 

Impure water . 

Under o'io 

» °’ 3 ° 

„ 0-40 

Over 0*40 

Under o’o5 
» 0*15 

,, 0*20 

Over o*2o 


Ceteris paribus , the greater the proportion the oxygen absorbed bears to the 
organic nitrogen or albuminoid ammonia, the better the water is. 

The mere fact that two standards are given is sufficient to show that 
in considering this quantity we must take into account (even more than 
is necessary with other chemical data) the nature of the .water, and its 
source. 

(vii) and (viii) Hardness, Temporary and Permanent.— These are important 
quantities in coagulation processes. They are usually reported in parts per 
100,000 of calcium carbonate, although German chemists report in parts per 
100,000 of calcium oxide, and some English chemists in grains per imperial 
gallon, of calcium carbonate. 

1 grain per gallon of calcium carbonate = i’428 parts per 100,000 of 
. calcium carbonate. 

I part per 100,000 of calcium oxide =1786 parts per 100,000 of calcium 
carbonate. 
















512 


CONTROL OF WATER 


What chemists really measure is the number of molecules of calcium, or 
magnesium, present in the water. Consequently, the fact that say io parts per 
100,000 of calcium carbonate are reported, merely indicates that 2'8 grains per 
imperial gallon of metallic calcium, or its molecular equivalent in magnesium, 
exist in the water, combined with one or more of the “acids” enumerated 
below. 

If these metals are combined as carbonates (CaC 0 3 , and MgCO s ), or rather, 
as double carbonates [Ca(HC 0 3 ) 2 , and Mg(HC 0 3 ) 2 ], the hardness is temporary, 
and if the metals exist as sulphates (CaS 0 4 , or MgS 0 4 ), chlorides (CaCl 2 , or 
MgCl 2 ) or other salts, the hardness is said to be permanent. 

Using the term degree for i part of CaC 0 3 , per 100,000 we find as follows : 

Any water under 5 degrees is classed as very soft. 

Any water between 5 and 10 degrees, as fairly soft. 


55 

10 „ 15 

55 

neither soft nor hard. 

55 

15 „ 20 

55 

moderately hard. 

55 

20 „ 30 

55 

hard. 


Over 30 degrees the water may be considered as objectionably hard, 
especially for washing purposes, although several large towns use waters which 
are harder than this. 

Moderately hard waters are usually held to be best for public health. 
Waters with less than 4 degrees of temporary hardness generally act on lead, 
zinc, and iron, and should consequently be tested for this property. 

In those cases where the Organic Carbon and Nitrogen are deter¬ 
mined in place of oxygen absorbed and albuminoid ammonia, the following 
standard may be used : 


TOTAL ORGANIC CARBON AND NITROGEN IN PARTS PER 100,000 



In Upland Surface 
Waters. 

Other Waters. 

Water of great purity 

„ medium purity . 

„ doubtful purity . 

Impure water . 

• 

Under o’2 

,, 0’2 to 0-4 

„ 0-4 to o - 6 

Over o’6 

Under o‘i 

„ o*i to 0*2 

,, 02 to 0 4 

Over o f 4 


» 


Metallic Impurities. —The facts in regard to iron are given on page 584. 

Zinc and Lead are both dissolved by certain waters, and, in view of their 
poisonous properties, and use in construction of water pipes, the action of the 
water on these metals is quite as important as the amount that may already be 
in solution. 

Waters which dissolve zinc are generally very soft (i.e. 1 to 4 degrees of 
temporary hardness), as also are some of the lead solvent waters. In such 
cases, passing through chalk (see p. 549) is an effective remedy. 

The modern bacteriologists’ view of chemical analyses is best illustrated by 
Houston’s reports to the London Water Examiner (years 1907-1910). The 


















SITE OF FILTERS 


5 ! 3 


“ chemical ” analyses report the following quantities in parts per ioo,ooo, unless 
otherwise stated : 


Ammoniacal nitrogen 
Albuminoid nitrogen — 


free ammonia 

_ • _ • 

1*214 

albuminoid ammonia 


1*214 


Oxidised nitrogen, i.e. in nitrates and nitrites, if these latter occur. 
Chlorine. 

Oxygen absorbed from permanganate, 3 hours at 80 degrees Fahr. 
Turbidity in terms of saccharated carbonate of iron. 

Colour (by tintometer), Burgess’ method, mm. brown, 2 feet tubes. 
Total hardness. 

Permanent hardness. 


Houston states as follows : 

“The albuminoid nitrogen, and oxygen absorbed from permanganate, tests 
are relative measures of the nitrogenous and carbonaceous organic matter in 
the water.” 

“ The turbidity test measures approximately the suspended matter in the 
water, and the colour test the degree of brown colouration.” 


The chemical tests for organic matter must therefore be considered merely 
as suggestive. The value of such indications is greatest when they are cor¬ 
roborated either by the presence of minerals, such as chlorides, or by the results 
of an examination of the local conditions affecting the source from which the 
water is drawn. If the organic chemical tests are isolated facts only, a water 
which, when thus regarded, is “ very pure ” may disseminate typhoid, or other 
diseases, and an “impure water” may be quite harmless. 

Site of Filtration Plant. —The best location for Purification Works is 
plainly that which gives least opportunity for after-pollution. Hence, in most 
cases, the site selected is as close to the town as possible. On the other hand, 
unpurified water is liable to incrust and foul the supply channels ; and where 
the water is drawn from sources far distant from the town supplied, it is occasion¬ 
ally advisable to submit it to some preliminary process of purification before 
entering the supply works. Such cases are most frequent in storage reservoirs, and 
the methods employed are generally designed to prevent action on, or deposits 
in, the pipes, or conveying channels ; and the bacterial purification which may 
occur is of secondary importance. 

The three most usual troubles to be dealt with are (see p. 437) : 


(i) Slime deposits. 

(ii) Deposits of iron or manganese. 

(iii) Erosive action, whether on metals or cement. 

The first two are somewhat intimately connected. The best method of 
dealing with either appears to be aeration, followed by a rough filtration, or the 
installation of Peuch-Chabal or other degroisseurs. 

The Derwent reservoir plant may be considered as typical (see p. 530). It is 
probably more elaborate than is usually advisable, since it is frequently difficult 
to find a favourable site for any large installation close to a storage reservoir ; 
and the saving in money expended on pipes, due to the suppression of slime 
alone, is not very considerable, except in cases where large volumes of water 

33 





CONTROL OF WATER 


5 x 4 

(from the point of view of a town supply) are carried. It must be remembered 
that slime deposits usually occur only in the first five or ten miles of the 
channel. 

Thus, as a rule, engineers are content with straining the water through fine 
mesh copper screens. The utility of the process is doubtful (see pp. 438 and 549 )* 

The circumstances which generally prevail close to a storage reservoir 
(water available at a fairly high pressure and small space for filter) are admirably 
fitted for rapid or mechanical filtration ; and if this filtration is combined with a 
properly selected chemical treatment, all types of incrustation and deposits in 
the supply main can be regarded as impossible. The saving in money thus 
effected is by no means small, and may (especially in long mains) fully justify 
an elaborate preliminary treatment, even in cases when the possibilities of after¬ 
pollution are such as to render a second filtration nearer to the town absolutely 
necessary. 

Certain waters act on lead, zinc, or other metals. In view of the fact that 
lead is an accumulative poison, and is not eliminated from the human body, no 
water that continuously attacks lead can be regarded as safe for human con¬ 
sumption. The tests must, however, be conducted with a view to ascertaining 
whether the water acts on lead continually, or not ; since many waters are 
found to attack lead at first contact, but very rapidly cover the metal with a 
protective coating which prevents any further action. Such waters may be 
considered as safe, and require no further treatment. 

Many waters, principally those drawn from moorlands containing peat bogs, 
dissolve lead and deposit no protective coating. Such waters, as likewise those 
which act in a similar manner on zinc or copper, must be treated before they 
are passed through metal pipes. 

The method at present adopted (apparently with universal success) is to 
neutralise the water. This is generally effected by passing the water through 
a filter bed containing limestone, or chalk, finely powdered. This process is 
usually combined with sand filtration, the powdered limestone being mixed with 
the sand bed. 

A similar process has been found useful in the case of waters which attack 
lime, or cement. These are usually peaty moorland waters of acid reaction, 
and cases have occurred where their corrosive action has been so intense as to 
seriously damage the cement linings of the water channels. The danger is 
especially acute when the concrete aggregate is composed of limestone. (See 
F.LC.E., vol. 167, p. 153.) 

Methods of Water Improvement.—Any method for the improvement of 
water intended for human consumption must be judged almost exclusively by 
the degree in which bacteria are diminished, although popular prejudice as to 
the suitability of the water is greatly influenced by other, and in reality adventi¬ 
tious qualities, such as clearness, softness, and absence of taste, odour, or colour. 

Consequently, it is fortunate that a process which proves successful from a 
bacterial point of view, generally produces a water gratifying to popular taste. 
In certain cases, however, special processes have been introduced with a view 
to softening water, or removing taste, colour, or odour, and these will be 
described later on. 

The conditions usually giving most trouble to officials responsible for public 
health, are those where the existing water supply is clear, sparkling, and in 
every way in conformity with popular ideas, but impure from a bacteriological 


LOCAL STANDARDS FOR WATER 515 

point of view. Such conditions are very frequent, especially in the ground 
waters of thickly populated countries, and it is often difficult to persuade 
the community that such a supply is dangerous to health. Popular ideas of a 
good water vary somewhat in different countries, and this variation has not 
been without effect on scientific standards. In view of the fact that outside 
Western Europe and the United States, the official analyst and bacteriologist 
is frequently a German, either by nationality, or by scientific training, it should 
be borne in mind that (principally, I believe, due to military considerations) the 
German standard of good water is a typical, good, ground water. Such experts 
therefore frequently recommend, in all good faith, a ground water supply, even 
when better water (from an English or American point of view) is available. 
While their choice may be assumed to be unexceptionable, from a scientific point 
of view, it is always well to remember that this preference for a ground water is 
not shared by other European nationalities, and that (especially among races 
largely vegetarian in diet), a hard water, even though pure, is liable to be 
unpopular when introduced to replace a soft one, even though the latter is 
polluted. Two such cases have come under my personal observation ; in one of 
them, the introduction of the hard water supply was followed by stomach 
troubles, to such an extent that the revenue of the Water Supply Company was 
materially diminished. The inconveniences were rendered more acute because 
the native population, being accustomed to boil all drinking water, had been but 
little affected by the pollution existing in the original supply. 

Similarly, it must be remembered that American experts are accustomed to 
deal with waters drawn from sparsely populated (from a European, or Asiatic 
standard) catchment areas, which contain a large number of bacteria, but 
apparently not so great a proportion of disease-producing species as is usual in 
England or Germany. Hence, it sometimes follows that they are prepared 
(where economy is the ruling factor) to remain satisfied with a purified water 
containing a number of bacteria far in excess of any usual European standard. 
Such opinions, when put forward concerning waters drawn from sources exposed 
to pollution from a dense population, should be received with suspicion. The 
danger, however, is not so acute as in the case of Germans and ground water, 
since the best American practice is as stringent as the best European. 

It is somewhat difficult for an English engineer to criticise the methods in 
which he was trained, but I consider that the English practice is rather too 
prone to rely exclusively on slow sand filtration, and to regard a moorland 
water stained with peat somewhat too leniently. From practical experience, I 
am well aware that peat-stained waters are often quite as objectionable to a 
population thoroughly unaccustomed to them, as a good German ground water 
is to a non-German population. I am also inclined to believe that these 
objections have a very fair foundation in the shape of a somewhat higher death- 
rate from diseases such as infantile diarrhoea, and other minor stomach 
ailments. It is therefore always advisable to consider carefully whether the 
nationality and experience of the bacteriologist recommending the source of 
supply are such as to enable him to gauge local prejudice accurately. 

The methods employed for water purification may be divided into three 
classes : 

(i) Sedimentation. 

(ii) Straining, or filtration. 

(iii) Chemical methods. 


I 


516 CONTROL OF WATER 

This classification can only be regarded as a practical one ; for, when care¬ 
fully investigated, even the slow sand filter is found to produce chemical 
changes, and its working is largely conditioned by the amount of sedimentation 
that takes place before filtration. 

Consequently, it appears more logical to describe and investigate the slow sand 
filter, and to consider the other methods mainly as supplementary, or alternative. 

It should be understood that I do not wish to advocate slow sand filtration 
in every case. It is a very excellent treatment for most waters, but is not 
applicable to all. Probably the error most frequently made in hydraulics by 
English engineers is its application to waters better dealt with by other pro¬ 
cesses. The idea that a good process of purification necessarily entails the 
use of a slow sand filter is responsible for much unjustifiable expenditure of 
money. 

The actual facts are that slow sand filters, when properly worked, are 
capable of satisfactorily removing bacteria. They are, however, readily 
clogged, and rendered temporarily useless by substances existing in a colloidal 
state (i.e. in a state resembling very diluted glue or jelly). Where the water 
is turbid (much over 50 parts per million), and the particles producing the 
turbidity are of, or close to, bacterial size, the sand-becomes dirty to such 
an extent that cleaning is difficult, and a portion of the turbidity is not 
removed by the filters. In such cases, preliminary treatment is necessary, 
e.g. the colloids are precipitated by aeration, or by treatment with iron ; or 
the turbidity is rendered filtrable by coagulation with aluminium sulphate or 
lime, with or without iron sulphate. 

Thus, all waters can be rendered fit for purification by the process of slow 
sand filtration. But it must not be assumed that this method of treatment is 
necessarily either the most effective, or the cheapest. 

Slow Sand Filters. —Practical details of the working of slow sand filters 
are principally due to English engineers. Our scientific knowledge of the 
system, and its rationale, is mostly of German origin. 

Postponing constructional details for the moment, it may be stated that the 
effective portion of the filter is not the sand, but the Schmutzdecke, and the 
Zooglea. These may be defined as follows : 

Schmutzdecke, is the layer of fine sediment containing bacteria and other 
organised matter (algm, etc.) that forms on the surface of the sand layer. 

Zooglea, is a glutinous coating, also containing bacteria, and probably 
entirely of bacterial origin, which forms on the individual grains of sand. 

Sand, in itself, can hardly be supposed to exercise any straining action on 
bacteria, for it forms far too coarse a filter. The relative size of a bacterium 
and the passages between the grains of sand are such, that we might just as 
well expect a sieve with holes one inch square to retain grains of fine sand. 

If a filter which has been at work for some period is examined, a thin crust 
of “ dirt” will be found on the top of the sand. This forms the Schmutzdecke, 
or rather, the Schmutzdecke is contained in this crust. Also, the individual 
grains of sand will be found to be no longer sharp and gritty to the touch, but 
coated with a gelatinous, transparent substance, resembling a whitish coloured 
glue when viewed under a lens. This is the Zooglea. 

The action on bacteria is believed to be somewhat as follows: The 
passages through the Schmutzdecke are so small that the bacteria are retained 
in it, and are consumed there by the living organisms composing a portion of 


SLOW SAND FILTERS 


5 T 7 

the Schmutzdecke. Until lately, this was generally considered to be the only 
effective portion of the filter. More recent investigations make it probable that 
a certain fraction of the bacteria pass through the Schmutzdecke, and are 
arrested by the Zooglea (probably by some action more resembling that of a 
layer of stones covered with bird-lime, than a sieve), and are there consumed, 
ffhe relative value of the Schmutzdecke and Zooglea in removing bacteria is 
somewhat uncertain, and careful investigations are desirable. It is plain that 
if the Schmutzdecke alone were the active agent, the layer of sand could be 
made considerably thinner than is usual in good practice ; and there is no 
doubt that of later years there has been a decided tendency to decrease the 
thickness of the sand layer. On the other hand, should the Zooglea prove to 
be more important than is at present believed, it is probable that some 
advantage might be gained by thickening the sand layer. 

So far as our present evidence goes, it appears that the Schmutzdecke 
performs most of the work. I would, however, point out that the evidence is 
by no means conclusive. The fact that comparatively few living bacteria are 
found below the Schmutzdecke may only mean that the destructive action of 
the Zooglea is very rapid. The practical results of filtration through thin 
layers of sand are not always sufficiently satisfactory to enable us definitely to 
say that : “The thickness of the sand layer need only be adequate to support 
the Schmutzdecke, and to prevent accidental Assuring.” 

The practice which the London Water Companies had arrived at before 
modern bacteriological investigations had been made, is probably not very far 
from the truth. If this practice is accepted as correct, we may deduce the 
following principles. 

When the filter is working normally the Schmutzdecke is probably quite 
capable of destroying all the bacteria existing in the raw water, unless this is 
abnormally polluted. Every filter, however, is cleaned at fairly frequent 
intervals, and the efficiency of the filtration system as a whole greatly depends 
on the rapidity with which a filter attains its normal power of destroying 
bacteria after cleaning. 

Now, cleaning is essentially the removal of the Schmutzdecke, and normal 
working only commences after the formation of a new Schmutzdecke. The 
almost universal practice of waterworks’ engineers is to replace the sand 
scraped off in cleaning by old filter sand that has been washed (“ripe sand”), 
and which is still coated with Zooglea. Since, in many cases, this washed ripe 
sand is more costly than the freshly dug article, it appears that practical 
experience favours the idea that some extra expenditure in order to obtain a 
certain thickness of sand coated with Zooglea is advantageous. 

Thus, British engineers had come to the conclusion that while equally good 
results could be obtained with filters containing only 18 inches or 2 feet of sand 
as with those containing 3 or 4 feet of sand, yet the results obtained with the 
thinner layers of sand were less consistent, and were more easily detrimentally 
affected by carelessness in working, or by sudden changes in the condition ol 
the water, or of the weather. 

This practice is still standard, and although a skilled bacteriologist is now 
able to ascertain the exact causes producing these detrimental effects, the 
average supervisor of filters is not a skilled bacteriologist, and is therefore likely 
to be easily led into error by wrongly applying his experience. Thus, the 
practical view of the matter appears to be that a choice must be made between 


CONTROL OF WATER 


5i8 

thick layers of sand and (relatively speaking) a low grade of supervision, or 
thin layers of sand, and skilled, scientific supervision. 

In connection with this question it is also as well to point out that rupture of 
the Schmutzdecke must occasionally occur, especially in the summer months, 
and that after such Assuring a satisfactory filtrate can be obtained, provided 
only that the break is not so marked as to cause the formation of definite 
channels through the sand. In some instances indeed, it has been found 
advantageous to purposely rupture the Schmutzdecke, and resume working- 
after say, six or seven hours’ rest (see Rutter, P.I.C.E ., vol. 146, p. 258). 

In both cases it seems hard to avoid the deduction that a fair thickness of 
sand coated with Zooglea is in itself a very efficient filter. 

The question is also of importance in connection with degroisseurs, and 
mechanical filters, and will be referred to later on. 

Constructional Details. —The area of filters required to purify a given 
volume of water daily depends entirely upon the quality of the raw water. 
Systematic preliminary tests should be made, as the necessary expenditure may 
easily be recouped several times over. 

The German Government has definitely laid down that the maximum 
permissible velocity of filtration must not exceed 4 inches per hour. This 
means a yield in filtered water of 8 cubic feet, say 50 gallons (60 U.S. gallons) 
per square foot of filtered area per day ; or, taking the usual, but illogical units, 
2 ’i 8 million gallons (2*61 million U.S. gallons) per acre per day. 

It is to be hoped that no such cast-iron rule will be introduced into other 
countries. Such enactments may be considered as a bureaucratic extension of 
the principle,—“a ton of bricks we understand, an ounce of brains is beyond 
our intellect.” 

Baldwin Wiseman (P.I.C.E., vol. 165, p. 352) has collected the filtration 
velocities used in forty-one British waterworks. 

The mean value is 9’17 feet daily, or say 2'5 million gallons (3 million U.S. 
gallons) per acre per day. 

The maximum value is 20’4 feet per day, at Falkirk. At Ripon, where the 
water receives some preliminary treatment, it is 17*8 feet. All cases where the 
velocity is over 12 feet a day occur in small country towns. 

The minimum value is rq foot per day, but this, it is believed, is due to the 
filter being too large for the present supply ; and 2 to 2*4 feet daily is probably 
the true minimum. 

I have been unable to trace any connection between these figures, and such 
of the death-rates from typhoid in the above towns as are accessible to me. 
I therefore consider that such variations are permissible in good practice, and 
are entirely caused by variations in the quality of the raw water. 

It is, however, possible to classify the figures given by Wiseman according 
to the source from which the raw water is drawn, as follows : 

Waters from storage reservoirs (27 cases). 

Mean value .... 8*93 feet per day. 

Maximum value.... 20 - 4o „ „ 

Minimum value. . . . 2'5 ,, 5J 

and in this last instance the gathering-ground is 
thickly populated, and the water is therefore 
unusually exposed to pollution. 


RATE OF FILTRATION 


5 X 9 


Waters from rivers (7 cases). 

Mean value.5-60 feet per clay. 

Maximum value .... 9*30 „ „ 

Minimum value .... 4^60 „ „ 

Waters from wells , or springs, i.e. ground waters (7 cases). 

Mean value .... 9^60 feet per day. 

Maximum value. . . . 14T0 „ „ 

Minimum value . . . • 3‘5 „ 

The number of cases is hardly sufficient to allow of any very reliable 
deductions being drawn, more especially in view of the fact that many of the 
filter beds are known not to be as severely worked as they will be when the 
population increases. 

There is, however, a very clear connection between the density of the 
population inhabiting the drainage areas, together with the amount of control 
the Waterworks’ Authority possesses, and the velocity of filtration. It appears 
that it is cheaper to expropriate any small existing population, rather than to 
build the extra area of filters necessitated by habitation of the catchment area, 
owing to the reduction in filtration velocity. There is also an apparent con¬ 
nection between a large annual rain-fall on the catchment areas, and high 
velocities of filtration. Whether this is a real connection, or only indicates that 
wet catchment areas are thinly populated, is uncertain. 

The filtration velocities employed in America vary to a far greater extent, 
and in most cases these variations are justified when the qualities of the raw 
waters are considered. American practice, as opposed to English, is not so 
exclusively founded on experience of slow sand filters alone, and I consequently 
consider the American figures more applicable to methods which include not 
only sand filters, but also auxiliary processes. 

Having, either by special experiments, or from experience in neighbouring 
cities using similar waters, selected the appropriate velocity of filtration, we can 
determine the nett necessary area of filters by the equation : 

. . . Maximum daily consumption in cubic feet 

Area m square feet=- yield of filters per square foot / 

To this nett figure must be added an allowance for the filter area which is out 
of use during cleaning. As a matter of experience, filters require cleaning most 
frequently during the season when the consumption is at a maximum ( i.e . the 
hot weather season). Burton ( Water Supply of Towjts) suggests the following 
rule : 

For a population of 2000 : 

Allow 2 filter beds, 1 of which can deal with the maximum con¬ 
sumption. 

For a population of 10,000 : 

Allow 3 filter beds, 2 of which can deal with the maximum con¬ 
sumption. 


For 

60,000 population, 

4 beds 

55 

200,000 

55 

6 „ 

55 

400,000 

55 

8 „ 

55 

600,000 

55 

12 „ 

55 

1,000,000 

55 

16 „ 


55 




520 


CONTROL OF WATER 


When the number of filter beds exceeds 8, the possibility of 2 of them having 
to be cleaned simultaneously should be allowed for (see p. 531). 

Design of Filters. — It is first necessary to fix the total depth of the whole 
filter, including the drains, the gravel and sand layers, and the depth of water 
above the sand, as this generally determines the design and cost of the whole 
filter. 

The depth of water is usually about 3 feet, to 3 feet 6 inches. If a smaller 
depth than 3 feet is adopted, it will be found that the water tends to become 
unduly warm in summer, even in so temperate a climate as that of the British 
Isles. Such a depth, with a freeboard of 6 inches to 1 foot will cause the upper 
surface of the sand layer to be about 3 feet 6 inches, to 4 feet 6 inches below 
the top of the filter. 

It is probable that a greater depth of water might be advantageous in warmer 
climates, not so much with the object of keeping the water cool, as to minimise 
the activity of vegetable and animal life in the Schmutzdecke. This practice 
has not as yet] been largely adopted, and the extra cost entailed is obvious. 
Nevertheless, tropical installations of slow sand filters are far too frequently 
designed on lines found suitable in temperate climates, and it is possible that 
many of the troubles then met with are due to an insufficient depth of water 
over the sand. Whether the correct solution lies in a greater depth of water, 
or in the installation of mechanical filters, or in some previous chemical treat¬ 
ment, is a question which the local peculiarities of the water must decide. 

In any case, the adoption of portable ejectors for lifting the sand removed 
in cleaning, minimises the difficulty previously met with in working filters 
where the sand layer was much over 5 feet below the top of the filter, this 
being nearly the maximum height that a wheelbarrow can be rolled up a plank 
of ordinary size, laid from the sand to the top of the filter. The depths of 
water in typical British filters are tabulated on page 529. 

Covermg of Filters .—In cold climates, it is usual to cover the filters with a 
vaulting of concrete, or brick arches, in order to prevent the water from freezing. 
Covered filters are more costly, and are bacterially less efficient than the open 
type (see p. 531). Hazen states that while open filters are worked in climates 
where the mean temperature of the coldest month is as low as 27 degrees Fahr., 
yet, where this temperature is less than 31 degrees Fahr., newly constructed 
filters are almost invariably covered. 

It is becoming usual in tropical climates to shade filters by a light roof of 
galvanised iron, or slate, supported on columns. In many cases, where dust 
storms are of frequent occurrence, some such shelter is almost indispensable, 
and there is no doubt that working is rendered more easy in hot weather. 
Many tropical installations, however, succeed without any shelter being 
provided. I am not aware that any difference in bacterial efficiency has 
yet been observed between filters thus protected, and the ordinary unshaded 
filter. 

Thickjiess of Sand Layers .—The evidence in favour of the belief that ripe 
sand in itself exercises a destructive action on bacteria, has already been 
given. A certain minimum thickness of sand is desirable in practical working, 
if only to prevent the formation of definite channels in the sand, which 
would permit the passage of unfiltered water if the Schmutzdecke were 
ruptured. 

We have also to consider the working of the filter after it has been cleaned, 


:THICKNESS OF SAND 521 

and while it is well known that a filter does not yield properly purified water 
foi some period (say 24 hours) after each cleaning, yet a satisfactory filtrate is 
delivered after a far shorter interval than is required to form a good Schmutz- 
decke. It is therefore considered that the Zooglea is important since it 
permits earlier delivery of properly purified water. Thus, until more detailed 
evidence is forthcoming, it is inadvisable to lay too much stress on the theory 
of the Schmutzdecke alone, and a smaller thickness of sand than say 1 foot 
10 inches does not appear to be desirable even in favourable cases. The 




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!t>art F?Cement,to5ofGrdvd 


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- 

- - 1 - 3 / -1 

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Detail of Slabs 


Sketch No. 139.—Filters at Ivry. 


matter concerns not only the design of filters, but their working, since it 
appears advisable to provide a large thickness of sand when the preliminary 
studies indicate that the filters will have to be cleaned frequently, so as to be 
able to start the hot weather of each year (or that period during which the 
filters require most cleaning) with a good depth of sand. This depth may then 
be diminished to the minimum thickness either by special removal, or by the 
accumulated effect of scraping, as the season approaches when cleaning is less 
frequently necessary (see p. 532). 

The principles are plain In polluted water of a character such that the 
filters must be cleaned at short intervals, a large thickness of sdnd is indicated, 




















































5 22 


CONTROL OF WATER 


and this should not be too much diminished by scraping unaccompanied by 
any replacement of sand. In less polluted water, and where the filters do not 
need frequent cleansing, the Schmutzdecke may be considered as capable of 
effecting the whole work of purification without any assistance. Thus, a thin 
layer of sand, the thickness of which may be largely diminished by scraping, 
is indicated, and the consequent reduction in the total depth of the filters permits 
a material saving to be made in first cost. 

The Ivrybeds (Sketch No. 139) are extremely thin, gravel and drains being 
replaced by “ dalles filtrantes.” The water is subjected to a careful preliminary 
treatment (p. 547 ). The sand layer at Albany (Sketch No. 140) performs the 
whole work of filtration, and is as thick as is ever found in a scientifically 
designed filter. Sketch No. 142 shows London practice before the Schmutz¬ 
decke theory was fully grasped, and would now be considered defective, the 
later designs having 2 feet 9 inches of sand. The drainage arrangements are 
not recommended, but the whole “ machine ” produced admirable results with 
very little scientific assistance. 

The 1-foot thickness of sand which is used in the Bamford filters (see 
p. 530) is about as small as is likely to be adopted in good practice. Cases 
where filtration through 9, or even 6, inches of sand is considered sufficient 
can be found, but either, as in Holland, the sand is extremely fine or (as at 
Bamford) the water is known to be but slightly subject to pollution, or 
receives additional treatment. Some four or five cases occur which cannot 
be explained by such circumstances, but I have been unable to ascertain 
whether the local death-rates from typhoid are normal. 

Hazen (.Filtration of Public Water Supplies ) has indicated rules for 
determining the head consumed in forcing water through sand layers of varying 
thickness, and effective size. The matter is treated at page 25. The subject is 
not important in filters, since the rules would only give the minimum head 
required before the Schmutzdecke was formed, and under such circumstances 
the filtrate would be unsatisfactory. 

The thickness of sand adopted in typical British installations is tabulated 
on page 529. 

Thickness of Gravel Layers .—Modern investigations on the subject of filtra¬ 
tion. have shown very clearly that the gravel layers exercise no purifying action 
on the water. The gravel layers merely form a sieve to retain the sand. Thus, 
theoretically speaking, since the diameter of the void spaces between grains 
of sand, or gravel of fairly uniform size, is about one-third that of the individual 
grains, all that is required is a layer of gravel underneath the sand, the effective 
size (see p. 25) of which is a little less than three times that of the sand. This, 
in its turn, might rest on a layer of still larger gravel, the effective size of which 
is just under three times that of the first layer. This succession of layers might 
be continued until a size has been reached which cannot enter the open joints 
of the tile, or brickwork drains. 

The annexed specification is a very fair model for a filter suitable for 
British conditions. 

Depth of water over the sand, 2*5 feet. Thickness of sand layer, 2 feet 
6 inches as a maximum, reduced to 1 foot 8 inches by scraping. 

The sand should have an effective size of o'36 to CV42 mm., and a uniformity 
coefficient between 2 - o and 2*5 (see p. 25), and, except in acid waters, should 
not contain more than o’5 per cent, of carbonates of lime, or magnesium, and 


DRAINAGE SYSTEMS 523 

should also be carefully washed, so that the content of clay is less than 0*4 per 
cent, by weight. 

A layer of 6 inches of gravel should be laid below the sand, approximately 
|th ol an inch in size (i.e. the effective size should be about 0’04 inch), 
and below this should be a layer 6 inches thick of §th-inch gravel resting on a 
continuous layer of brick drains (Sketch No. 141), or a 4-inch layer of §th-inch 





Sketch No. 140.—Covered Filters at Albany. 


gravel resting on a 5-inch layer of i-inch gravel, in which 4-inch agricultural 
drain-pipes are buried, these being spaced not more than 15 feet apart (Sketch 
No. 140). 

The specification of the uniformity coefficient is probably unnecessary. A 
high value of the uniformity coefficient indicates that the grains of sand vary 
considerably in size. Thus, when the uniformity coefficient is large, the void 
spaces are likely to be smaller than is usually the case, and therefore the water 










































































524 CONTROL OF WATER 

will pass through the sand less readily than is indicated by the effective size of 
the sand. 

Reference is made to this matter on page 530. What is required in filter sand 
is that the sand shall permit water to pass as easily as is usual in a sand of 
similar effective size, and this could be secured just as well by specifying the 
percentage of voids, as the uniformity coefficient, were it not for the questions 
regarding the wetness of the sand and the amount of shaking previous to the 
measurement of the voids which a litigious contractor might raise. 

The following specification appears to secure all that is really required : 

“ The sand shall contain no clay, dust, or organic impurities, and shall 
not disintegrate when exposed to air or water. 

“ The quantity of the sand in which the grains are less than 0*13 mm. 
(o’oo5 inch) in diameter shall not exceed 1 per cent, by weight, and 
not more than 10 per cent, by weight shall be less than o'2j mm. 
(o'oii inch) in diameter. At least 10 per cent, by weight shall be 
less than o - 36 mm. (say o'oi4 inch) in diameter, and at least 70 per 
cent, shall be less than 1 mm. (0^04 inch) in diameter, “and no grains 
shall exceed 5 mm. (o’eo inch) in diameter.” 

In practice this specification produces the following results : 

The effective size of the sand is from o'29 mm. to o - 32 mm., with an average 
of 0*31 mm. (o’oi 2 inch). The uniformity coefficient is 2’2 to 2'5* average 2*3, 
and the void spaces are about 40 per cent, of the total bulk. The specification 
may possibly be considered likely to produce a sand of somewhat smaller 
effective size than is generally desirable. The water was known to be more 
than usually turbid. In specifying for sand to be used to filter a clearer 
water, it might be advisable to increase the o'27 mm. to 0*30 mm., and the 0*36 
mm. to o‘4o mm. ; but the properties of the available raw material must be 
ascertained before drawing up the specification. 

A satisfactory sand can probably contain a percentage of carbonates greatly 
in excess of that specified. Many good filter sands contain 2, or even 2} per 
cent, of lime and magnesia carbonate ; and (see p. 549) in some filters which 
treat acid waters, carbonates in the form of chalk or limestone powder are 
purposely mixed with the sand. 

The variations necessary to suit local conditions are obvious. In hotter 
climates, a greater depth of water, and (in view of the liability to rupture of the 
Schmutzdecke) a larger thickness of sand are required. 

The thickness of sand specified is probably sufficient for all except highly 
polluted waters, provided that the Schmutzdecke is not ruptured, and may be 
reduced under more favourable conditions than those usually existing in Great 
Britain. On the other hand, if the water is occasionally very turbid, a minimum 
thickness of 3 feet, or even 3 feet 6 inches, of sand may be required to permit 
of the water being satisfactorily filtered. In the United States 3 feet usually 
suffices during periods when the turbidity is as high as 125 parts per million, 
provided that the turbidity does not prevail for longer than two or three days. 

It must be pointed out that each layer of gravel means a certain extra depth, 
and the real object merely being to retain the sand, the thinner the whole series 
of layers, the better. Looking at the question from this point of view, it will 
be evident that Sketches No. 139 and No. 140 show somewhat more economical 
methods of retaining the sand layer than the specification. 


HEAD LOST IN DRAINS 


5 2 5 


Sketch No. 139 indicates the dalles filtrantes (filtering paving) adopted at 
Ivry for the water supply of Paris, and it will be seen that a depth of about 
8 inches is economised. Gravel can also be saved by laying the lateral 
drains in inverts formed in the bottom of the filter. In some cases the laterals 
are laid in small trenches formed in the concrete lining. So far as is known 
the system is satisfactory, although it obviously may give rise to difficulties if 
the rate of filtration is high. The drainage system specified is generally suffi¬ 
cient for velocities of filtration up to 4 million gallons per acre, or 15 feet vertical 
per twenty-four hours. If higher rates are proposed, the design of the drain 
system, and the thickness of the lowest layer of gravel, require consideration, 
and the gravel beds must be made deeper and the drain pipes larger. 

According to Hazen (Filtration of Public Water Supplies') the head consumed 
in forcing water through the gravel to the drains may be calculated from the 
formula (see p. 26) : 


Head lost — distance between drains) 2 x rate of filtration 
2 X average depth of gravel in feetXe 


feet. 


The values of c, are as follows : 

VALUES OF c. 


Effective size of Gravel 
in Millimetres. 

The Rate of Filtration being 

expressed in— 

Millions of Gallons 
per Acre per Day. 

Millions of U.S. 
Gallons per Acre 
per Day. 

Vertical Depth in 
Feet per Day. 

5 = o’2 inches 

19,000 

23,000 

70,000 

10 = 0*4 „ 

54,000 

65,000 

199,000 

15 = 0*6 „ 

92,000 

110,000 

337,ooo 

20 = 0*8 ,, 

I 33 )°°° 

160,000 

490,000 

25 = 1*0 

192,000 

230,000 

704,000 

3 °= 1 * 2 

250,000 

300,000 

918,000 

35 = 1 '4 

325,ooo 

390,000 

1,193,ooo 

40=1*6 „ 

400,000 

480,000 

1,469,000 


The lateral drain pipes are usually spaced about 16 feet apart, and are rarely 
more than 20 feet distant. Hazen gives the following table of maximum per¬ 
missible velocities of water in filter drain pipes : 


Diameter of Pipes. 

Maximum Velocity. 

4 

inches 

0*30 

feet per second. 

6 


o-35 

>5 55 

8 

>> 

0*40 

5 ? 

10 


0*46 

>> 

12 

5 ) 

0-51 

j ? >> 

Over 12 


°'55 

it 


- .. --—.• -—---1 ■ • — —1- 











































CONTROL OF WATER 


526 

These formulas may seem somewhat unnecessary, but a little consideration 
will show that the low velocities are adopted in order to equalise the total 
frictional resistance at all points of the filter bed. It will be plain that close to 
the main drain outlet the resistance to the passage of water is merely that 
arising from percolation through the vertical thickness of sand and gravel ; 
while at a point midway between the ends of the farthest removed laterals the 
resistance is that caused by the vertical thickness of sand, about 9 feet of gravel 
(assuming a 16-feet spacing of laterals) and pipe friction in the full length of a 
lateral and the main drain. Even with such low velocities as are above specified, 
this inequality of resistance (especially when the Schmutzdecke is thin) may 
give rise to great differences in filtration velocity. In normal working the 
resistance of the Schmutzdecke is usually sufficient to produce practical equality 
in filtration rates, but the apparently unnecessary size specified for the lateral 
and main pipes is now known to ensure a rapid attainment of the normal state 
of affairs. 

In large filter beds each lateral is sometimes fitted with a brass “friction 
disc,” in order to equalise frictional resistances. This, however, merely cuts 
out the disturbing influence of friction in the main drain, and introduces certain 
constructional complications. Except in very large installations, the expense of a 
series of discs of various sizes is hardly justified by the economy effected in pipes. 

As an example, when a certain filter is working at its maximum rate, the 
head lost in the main drain is about 1 inch, and the frictional resistance in the 
sand, before the Schmutzdecke forms, is also about 1 inch. Thus, the rate of 
flow through the portion of the filter drained by laterals entering the main 
drain near its exit will be about double that through the area drained by the 
laterals entering near the far end of the main drain. 

A brass disc containing an orifice of a size such that it will pass the quantity 
of water which the first lateral 'carries under 1 inch head, is inserted at the 
junction between the first lateral and the main drain. Similarly, in a lateral half¬ 
way along the main drain, the orifice is calculated so as to pass the water under 
half an inch head, etc. 

In the above example, the mean velocity in the main drain is 1*2 foot per 
second. It is plain that if we had designed the main drain for a velocity o'6 
foot per second, the 1 inch difference would have been reduced to \ inch, and 
might have been neglected, but the main drain would have been doubled in area. 
For formulae for the loss of head in lateral and main drains, see p. 613. 

It will also be plain that when the filter has been working for some weeks, . 
and the head lost in the Schmutzdecke and sand has (owing to the increased 
thickness of the Schmutzdecke) become say, 1 foot, the friction discs have no 
appreciable influence on the working. . For this reason, both friction discs and 
the application of Hazen’s rules are frequently regarded as unnecessary. There 
is a good deal to be said for this view, but the period which elapses between 
scraping a filter and delivery of a bacterially satisfactory filtrate is a critical one. 

It is then, and then only, that there is any considerable danger of impure water 
entering the mains. Any small expenditure of money that assists the supervisor 
to reduce this period is well spent, and devices for equalising the rate of flow 
through the various portions of the filter area are the one obvious assistance 
that the designer can give. It must always be remembered that bacterial 
investigations take time, and, although Flouston in London has successfully 
solved the problem of indicating dangerous (or rather potentially dangerous) 


INEQ UALITY OF RESISTANCE 5 2 7 

filtrates on the same day that the samples are received, it is but rarely that the 
supervisor receives any bacterial evidence until the third day after filtration. 
Ihus, in practice, filtrates are really classed as safe or unsafe by turbidity tests 
alone. I he method works exceedingly well in practice, but that does not justify 
a total neglect of the possible danger by the designer. 

A study of the proportions of modern filters indicates that a sufficiently 
uniform rate of filtration over the whole area of the filter bed is secured if the head 
lost by friction in the longest path through the under-drains (i.e. in the full 
length of a lateral and the full length of the main drain) does not exceed one- 
quarter, or, at the most, one-third of the head required to force the water from 
the surface of the sand, through the sand and the gravel, to a lateral drain 
before the sand has become clogged by the formation of the Schmutzdecke. 



Sketch No. 141.—Brick Filter Drains. 

Hazen’s figures (see pp. 25 and 269) maybe employed to estimate this head. 

The rule is merely empirical, and in actual practice the time that elapses, 
and the thickness of the Schmutzdecke which forms, before any water is drawn 
off for use in the town mains should be considered. The rule is valuable, as 
unequal rates of filtration will probably not cause trouble in a filter thus pro¬ 
portioned unless it is very carelessly handled. Typical actual figures are : 

The head required to force water through sand at the commencement of 
working is about 1^ inch to 2 inches. 

The head lost in the under-drain is fths of an inch to \ inch. 

It will be evident that frictional inequalities are greatly minimised by such 
drainage systems as the flooring of brick or tile drains generally adopted in 
England (Sketch No. 141) or the dalles filtrantes used at Ivry. In brick or tile 
floors, however, this simplicity is gained at a cost of an extra depth of 3 to 7 






























CONTROL OF WATER 


528 

inches (according as the pipe drains which form the alternative method are, or 
are not, sunk below the general floor level). 

Among other details, it is as well to draw attention to the possibility of un- 
filtered water creeping down the vertical faces of the side walls. This, I consider, 
is best prevented by making these faces rough, i.e. of rubble masonry, or 
unrendered concrete. 

At Ivry, a circumferential drain (Sketch No. 139) is constructed, but this 
appears likely to provide a trap for stagnant water, and possibly reduces the 



r.n.L. 



Fine Sand 

3" Stone Ftaa 





'S'*#Pigeon Holes 
~V'brick on End I I A 


<ri 


Ffne Gravel 
MediumGravd 
^ Coarse Grave/ 


V y ‘ i ^ Hsihatte/ :/ 

Section through Main Drain 



effective area of the filter bed. The step in the face shown in Sketch No. 142, 
is usual in English designs, and seems to be equally effective. 

The danger is most acute in covered filters, where each pier provides a 
possible passage. Consequently, in such cases it is usual to stop the gravel 
layers at some distance from the piers and walls, as shown in Sketch No. 140. 
This appears safe, and quite unobjectionable, except that sand is employed to 
replace the less costly gravel. 

Working of Filters.—The constitution of the Schmutzdecke and Zooglea 
has already been discussed. The formation of the Schmutzdecke (as judged 
by the production of a satisfactory filtrate) occupies from 12 hours to 2 days. 

























































































BRITISH FILTERS 


529 


The period of formation depends upon the quality of the raw water, and it may 
usually be stated that a slightly turbid, and somewhat polluted water, favours 
the rapid growth of a good coating. As, however, the process is essentially 
biological in character, the temperature of the water and the weather generally 
markedly affect the process. There is also a certain amount of evidence to 
show that ripe sand (i.e. well coated with Zooglea) has a favourable influence. 
Once the coating is formed, filtration (accidents apart) proceeds normally, and 
regularly. 

It will be found that the head necessary to force water through a filter at 
the required rate, increases daily, but irregularly. Finally, the necessary head 
becomes too great for economy, and the filter has to be cleaned. This is 
accomplished by removing the top layer of sand. Usually a depth of three- 
quarters of an inch is found sufficient, but the practical condition is that all 
sand which is visibly dirty is scraped off with flat spades (see also p. 542). 

British Filters.—The details of filters, as constructed in England, are 
mainly useful in determining the depth of water over the sand, the thickness of 
sand, and the size and thickness of the upper layer of gravel. The facts are not 
of great importance in the case of the lower layers. The designs are by rule of 
thumb, and take no account of the modern investigations into the rationale of 
the process, which show that the sizing and spacing of the lower layers may be 
very badly designed, without much detriment to the results. 

An abstract of the particulars as given by Baldwin Wiseman is as 
follows : 


Depth of Water .— - 


f 31 cases varying between 11*5 and 075 feet. 
121 „ „ 3*o „ 1*42 „ 


The details are as follows : 

3-0 feet ; 1 case 2*5 feet ; 5 cases 2*o feet ; 7 cases 

175 feet ; 3 cases 1*5 feet ; 4 cases 1*42 feet ; 1 case. 

All except three cases lie between 3*5 and ro feet. 

Sand— Fine sand is used in 26 cases. The maximum thickness is 4 feet 
2 inches, and the minimum 6 inches, but this is underlain by 9 inches of ^th-inch 
gravel. 1 foot 6 inches is the minimum where th-inch gravel is not also used. 
Between 3 feet 6 inches, and 1 foot 6 inches, we have 21 cases as follows : 


3 feet 6 inches ; 4 cases 3 feet 1 inch ; 1 case 3 feet o inches ; 5 cases 
2 feet 6 inches ; 2 cases 2 feet o inches ; 6 cases 1 foot 8 inches ; 1 case 

1 foot 6 inches ; 2 cases. 

Gravel. —In 5 cases the sand is succeeded by : 

1 foot 9 inches ; in 3 cases 6 inches ; in 2 cases 

of igth-inch gravel. 

In 14 cases sand is succeeded by Jth-inch gravel of the following 

thickness: * 

6 inches j in 6 cases 5 inches 5 in 1 case 4 inches , in 1 case 
3 inches ; in 1 case. 

In 1 case by 3 inches of ^th-inch gravel; 

In 2 cases by 1 foot and inches of §th-inch gravel ; 

In 2 cases, 6 inches of ^ _ inch gravel; 

and in 2 cases the sand rests direct on brick drains. 


34 


CONTROL OF WATER 


53° 

Neglecting abnormal cases, the usual layer below y the sand is consequently 
6 inches of ^th-inch gravel. This is generally followed by 6 inches of fth-inch 
gravel, or in some cases by 1 foot of §th-inch gravel, containing drains. 

Cleaning .—The average interval between cleanings is 24 days, the actual 
figures given being: 

7 to 21 days in 1 case 10 to 12 days in 1 case 14 days in 5 cases 

18 days in 1 case 21 days in 2 cases 21 to 42 days in 1 case 

24 days in 1 case 28 days in 4 cases 30 days in 1 case 

31 days in 1 case 42 days in 4 cases 190 days in 1 case 

365 days in 1 case : 

where the 190 and 365 can hardly be considered as good practice. 

The following description of the sand filters used by Sandemann at the 
Derwent Valley reservoirs represents the most advanced British practice, except 
in the thickness of sand, which is less than usual, owing probably to the 
character of the water and to the installation of degroisseurs (see p. 544). Each 
filter is 125 feet x 200 feet in area, and is worked at the rate of 12 feet 
per day. 

The sand layer is 2 feet thick, and is reduced by scraping to 1 foot before 
replacement of sand occurs. The sizes of the grains of sand are specified as 
follows : 

All the sand passes a x \th inch circular hole. 

70 per cent, passes a ^th inch square hole. 

10 per cent, passes a y\jth inch square hole. 

This is stated to procure a sand of approximately the same percolating 
properties as that used in the London filter beds. The effective size is 
o'35 mm. = o‘oi4 inch, and the uniformity coefficient about 2*5 or less. 

Proceeding downwards, the gravel layers are as follows : 

3 inches of fine gravel, passing a y^th-inch sieve, and retained on a 
T 3 gth-inch sieve. 

3 inches of medium gravel, passing a i-inch sieve, and retained on a 
T 5 B th-inch sieve. 

9 inches of coarse gravel, passing a 2-inch sieve, and retained on a 
i-inch sieve. 

The whole of the area of the filter is floored with bricks, forming 4^-inch by 
3-inch drains, 9 inches apart. 

The central drain is 2 feet square, and sunk below the level of the filter 
bottom. 

Thus, the total depth of the filter is 6 feet 6 inches. The velocity of the 
water in the central drain is about 0-9 feet per second. This is somewhat less 
than the 2 to 3 feet per second which is usually adopted in British practice, 
when the filter is floored with brick drains ; but it appears advisable in view 
of the thin layer of sand and the somewhat high rate of filtration. 

In older British filters, the velocity of the water in the tile drains was often 
as high as 2 feet per second, when the coarse gravel extended to 6 inches over 
the top of the drains. Phis is probably somewhat high, unless the water passes 
through the gravel as well as through the tile drains. 

The following figures show the influence which the character of the water 
has upon the rate of filtration, and upon the frequency of cleaning. The figures 


SIZE 01 FILTERS 


53 * 

are selected from filtration plants which are known to be very scientifically 
managed. 

At Hamburg, the water is highly polluted, black, and muddy. The sedi¬ 
mentation basins have a capacity equal to four days’ supply, and the water 
after three, or occasionally only two days’ sedimentation is filtered at the rate 
of 4*9 feet vertical (1*33 million gallons=r6 million U.S. gallons per acre) per 
24 hours. The average interval between scrapings of the filters is about 18 
days, the maximum being 50, and the minimum 10. 

At Berlin, ordinary clear lake water is passed direct on to filters, and is 
filtered at a rate of 7*9 feet (2*13 million gallons = 2’56 million U.S. gallons 
per acre) per 24 hours. The filters are scraped, on the average, every 30 days ; 
the maximum period being 80 days, and the minimum 10 days. 

At Zurich, a perfectly clear water drawn from a large lake, and entirely free 
from sediment, was filtered at a rate of 23 feet (6*25 million gallons = 7'5 million 
U.S. gallons per acre) per 24 hours. The average period between scraping 
was 21 days, the maximum being 47 days, and the minimum 9 days. Contrary to 
usual experience, the covered filters are here found to be more efficient than the 
open filters. At present the Zurich water is treated by a double filtration process. 

Fuertes (Water Filtration Works) gives for the gross filter area : 


Area = - 1 + 



1 + 


cn 

p + c 


n— 1 


cn 


square feet 


P+c) 


Where «, is the number of beds, 

/, the ordinary number of days between cleaning, 
c , the number of days taken to clean and get the filter into a fit 
condition to deliver satisfactory filtrate, 

and represents the area which would be required if the filters worked 

continuously. 


The standard size of individual filter beds where not fixed by such rules as 
Burton’s, may be taken as about 200 feet square to 200 feet X 250 feet, i.e. 
approximately 0-9 to ri acres ; ij acres being about the maximum. 

According to Hazen, the total quantity that can be satisfactorily passed 
through a filter between two cleanings, is unaffected by the rate of filtration, 
i.e. the greater the rate, the sooner the filter has to be cleaned. In this respect, 
the working of the filter is influenced by the effective size of the sand, and 
Hazen’s figures may be taken for comparative purposes : 


Effective size of Sand in Millimetres. 

Total Quantity of Water Filtered between 
successive Cleanings in Million U.S. 
Gallons per Acre. 

°’39 

0^29 

0‘26 

0*20 

0*14 

CXO9 

_ _ — - —— - - - 

79 

70 

57 

54 

49 

14 



















532 


CONTROL OF WATER 


The absolute interval between cleanings is entirely dependent upon the 
weather and the quality of raw water. Speaking generally, in moderately 
cold weather (English winter) a filter will run between cleanings about three 
times as long as in moderately warm weather (English summer). In climates 
where the seasonal difference is more marked, as in India and China, a ratio 
of 6 : i is not uncommon. 

The depth removed by scraping is affected by the weather, but is more 
influenced by the amount of turbidity existing in the raw water, and even 
more so by the effective size of the sand. It has been found that if the effective 
size greatly exceeds 0-40 mm., the sand becomes dirty to such a depth that 
cleaning is troublesome. 

Modern filters are constructed with a view to limiting the head that can 
possibly be utilised in forcing water through the filter. I consider that this 
is a mistake, as all available evidence indicates that the rate of filtration alone 
affects the working of the filter, and any head that can be applied has no 
appreciable result in consolidating the filter sand. Any constructional limitation 
of head is therefore only justified when extremely careless management is to 
be apprehended, and it would appear better to procure a good manager and 
give him every facility for tiding over seasons of intense demand. 

If fresh sand be placed on a filter bed, the effluent is unsatisfactory for a 
certain period. The duration of this period is increased if the depth of fresh-sand 
placed on the filter increases ; and, as a rule, the period is longer when the sand 
is raw {i.e. has never been previously used in a filter) than when the sand is old 
and ripe {i.e. sand which has been removed from a filter and has been washed). 

In practice, as already stated, engineers are accustomed to replace sand 
only at long intervals (say one replacement per 15 to 30 scrapings). This 
entails replacing approximately 18 inches depth of sand, and some 10 to 15 
days may then elapse before the effluent is satisfactory. 

Certain experiments at Albany, N.Y., seem to indicate that this period is 
shortest in the spring months. As a matter of practice, it has long been the 
custom in England to replace sand as far as possible only in the spring, or in 
the autumn. 

Applicability of Slow-Sand Filters.—The above description cannot be 
considered as a complete account of the process of water purification by slow- 
sand filters. 

When properly worked, a slow-sand filter will remove a large proportion 
of the bacteria, and the filtrate will pass Koch’s test, and will be satisfactory 
as regards such matters as freedom from turbidity, tastes, colours, and odours, 
provided that : 

The water which enters the filters : 

{a) Does not contain much above 2000 bacteria per c.c. (counted by Koch’s 
method); 

ip) Is fairly free from turbidity, especially from that produced by very 
minute particles, i.e. diameters less than say 0-0005 inches. Definite figures 
applicable to all cases cannot be given, since the larger particles, although 
effective in producing turbidity, have but little effect on the working of the 
filter ; but, as a rule, the limits may be stated as follows : 

A water containing 125 parts per million of turbidity causes trouble at once, 
and the filters require to be cleaned if the turbidity exceeds 50 parts per 
million for more than 36 hours. 


FILTERS AND SEDIMENTATION 533 

( c ) neither very deeply coloured, nor markedly affected by tastes and 

odours. 

It will therefore be plain that very few natural sources exist, other than 
springs or wells, which, during the whole year, yield a water which can be at 
once passed on to a slow-sand filter with the assurance that a satisfactory 
filtrate will be obtained by slow-sand filtration alone. Therefore, in practice, it 
will be found that a process of sedimentation, or some other form of preliminary 
treatment, invariably precedes slow-sand filtration. Sedimentation is effected 
either in special sedimentation basins, or, in cases where the water supply is 
drawn from a reservoir, storage in the reservoir itself forms a very efficient 
sedimentation. 

The result of sedimentation is twofold :— 

(i) The suspended matter sinks to the bottom of the basin, or reservoir, and 
the turbidity is consequently reduced. The rate at which this action goes on 
can be calculated when the sizes of the particles producing turbidity are known. 
The results are not of great importance, as that portion of turbid matter which 
is prejudicial to filtration is composed of such extremely small particles that 
their deposition would only be effected in periods of time measured by months 
or years, and the benefits of sedimentation are really due to the fall of the 
larger particles which carry with them (mechanically caught) a portion of the 
extremely fine particles. Roughly speaking, particles exceeding 0*0005 inches 
in diameter will settle to the bottom of a still water basin 10 feet deep in less 
than three hours, and would therefore be deposited in any sedimentation basin 
with the least pretensions to efficiency. Particles of one-tenth this size (i.e. 
under 0*00005 inches in diameter) will remain suspended for at least 300 hours, 
and will not therefore be deposited in any sedimentation basin of practical size 
unless they are entangled and carried down by larger particles. Regarded 
from this point of view, it will be obvious that in many cases the more turbid 
the water originally, the better the relative improvement that may be expected 
from a short period of sedimentation. The reasons for the addition of artificial 
turbidity, as sometimes practised, consequently become obvious. 

(ii) The heavier sediment also carries down bacteria, and therefore sedi¬ 
mentation reduces the number of bacteria which remain to be removed by the 
filters. 

(iii) Storage and sedimentation have also certain beneficial effects on the 
coloration, taste, and odour of water, but cannot be considered as effective 
remedies when these are marked. 

It will consequently be evident that slow-sand filters, combined with more or 
less efficient sedimentation, produce a satisfactory filtrate in such cases as are 
usual in England, France, or Germany. The factor mainly determining the 
quality of the water in the above countries is its bacterial content. The 
geological structure of these countries is such that their waters very rarely 
contain an excessive amount of extremely fine turbidity, and the climate being 
temperate, coloration (excluding that produced by peat), and tastes, or odours, 
are rarely so marked that anything worse than temporary inconvenience arises. 

In countries such as the southern United States, which have not recently 
(geologically speaking) been exposed to glacial action, the waters are frequently 
laden with extremely fine particles, which remain undeposited after any reason¬ 
able period of natural sedimentation, and therefore processes of coagulation 
become necessary. 


CONTROL OF WATER 


534 

In climates hotter than those of Northern Europe, tastes, odours, and 
colours often manifest themselves to a marked degree, and special methods 
are required for their removal. 

The various processes can therefore best be illustrated by first considering 
natural sedimentation (p. 550). It should be remembered that the usual 
British reservoir with a valve tower, enabling water to be drawn off from 
various levels at will, forms a very efficient sedimentation basin. Such cases 
require no further discussion. 

The above statements explain the principles usually accepted concerning 
sedimentation or storage basins. According to Houston (a very excellent 
precis is found in the Report of the London Water Exaininer for 191°)) 
systematic storage is the only absolutely certain method of securing a water 
which is bacterially safe, if the raw water contains large numbers of excre- 
mental bacilli. Since sand filters do not apparently exercise a selective action 
on pathogenic bacteria, but merely reduce the number of all the species of 
bacteria present in the water, in about equal proportions, it is plain that if one 
individual pathogenic bacillus can cause infection, drinking the effluent from a 
filter which secures a reduction of 99 per cent, in bacteria is the same thing as 
drinking a mixture of one part of the raw water with 100 parts of sterilised 
water. According to this line of reasoning, therefore, the only way to insure 
safety is to destroy the pathogenic bacteria before filtration. Houston’s tests 
prove that storage for about 30 days does effect this in the case of Thames 
water (see p. 552). Houston therefore considers storage as a necessary pre¬ 
liminary to the slow-sand filtration of polluted waters. 

The following deductions may be made : ' 

(a) The reduction in the number of bacteria previous to filtration secured 
by storage can generally be attained more cheaply by other treatments. 

(b) Houston’s own experiments prove that it is extremely improbable that 
the typhoid bacillus exists in the polluted raw water in such quantities that 
infection (even if producible by one bacillus) would result from consuming the 
raw water in dilutions of 1 : 100, provided that substances capable of supporting 
the life of the pathogenic bacilli were removed from the mixture. 

(e) Slow-sand filtration apparently does remove these substances. 

The report deserves careful study, and is encouraging, as showing that 
storage and sedimentation are more effective than was generally believed to be 
the case. 

On the other hand, the report has greatly strengthened my personal views 
concerning the inadequacy of slow-sand filters, when unassisted by any other 
process, in producing an absolutely safe filtrate from water originally highly 
polluted, except when the water has been drawn from a storage reservoir. The 
general excellence of the water-borne disease death-rates in British towns has 
always, in my opinion, been an indication not so much of the efficiency of slow- 
sand filters per se , as of their fitness for treating stored or sedimented water 
(see also pp. 519 and 552). 

Practical Details .— The practical details of filter design are mostly 
concerned with questions affecting the water-tightness of the walls and bottom 
of the filter. This is usually secured by a puddle wall and base surrounding 
the whole filter, as shown in Sketch No. 145 (which is a sedimentation basin). 
It is extremely doubtful whether such filters are ever entirely water-tight, 
except for a few years after construction, although the puddle and sand that 


CONSTRUCTION OR FILTERS 


535 

fill any cracks which may form in the puddle layers probably form a filter and 
provide a very effective shield against the entrance of any polluting matter. 
The construction is, however, radically bad, if the subsoil water level is above 
the bottom of the filter, as the puddle is exposed to variable loads (owing to the 
alteration in weight produced when water is let into or drawn out of the filter), 
and the concrete or masonry work will certainly, and the puddle work 
probably, crack. 

Sketch No. 142 shows a design with asphalte or bitumen as a water-proofing 
material, which produces less noticeable cracking, and which probably remains 
water-tight, but which does not afford such an effective protection against 
pollution should cracks occur. The lowest level of the filter should therefore 
be well above the subsoil water level. It will be noticed that the asphalte layer 
lies on 6 inches of concrete, and is covered by 12 inches of the same material. 
This affords greater security against leakage into the filter than the alternative 
designs where the top layer is thinner than the under layer. Each layer of 
concrete should be laid in squares, approximately 10 feet by 10 feet, or 12 feet by 
12 feet, and the interstices between these squares should be filled in with 
say jfths of an inch of asphalte. The squares in the two layers should break 
joint, so that the angle of each square in the upper layer lies vertically above 
the centre of a square in the lower layer. The side walls should have expansion 
joints at intervals of 20 feet, and the joints nearest the corners of the filters 
should be provided with steel plates. It is believed that these precautions 
will secure a water-tight filter. In London filters are usually surrounded by 
a puddle wall carried down to unite with an underlying clay stratism, and 
the included area is pumped dry during construction. When local circum¬ 
stances permit, this forms an ideal solution of the problem. In some cases 
the filters are built on the top of clear water reservoirs. Space is thus 
economised, and, if clear water reservoirs of such a size are really required, 
the combination is economical. The danger of pollution, however, is not 
appreciably minimised, since, although the filters to a certain extent shield 
the bottom of the clear water reservoirs from changes in temperature, cracking 
is knov/n to occur unless the precautions already indicated are taken. The 
practice of supporting the filters on sedimentation basins is a very excellent 
solution as regards any danger of pollution, but it obviously entails an additional 
complication in the pumping machinery. Further, the power employed in lifting 
water through so small a height as 12 or 16 feet, is uneconomically expended. 

Sand Washing Apparatus. —As already stated, after a filter has been at 
work for some time, the sand grains become coated with Zooglea, and such 
sand produces better filtration results. When the sand removed from a filter is 
washed to cleanse it from dirt, a certain amount of this coating is removed, and 
this removal is the more marked the longer the sand remains absent from the 
filter. Nevertheless, the general experience of water works’ engineers is that 
the use of old, washed sand (ripe sand) is advantageous, and it is only in very 
special circumstances, where fresh sand is cheaply obtainable, that the washing 
of dirty filter sand can be dispensed with, although (as will later be seen) the 
cleansing of freshly dug natural sand from dirt is a far easier process. 

The simplest method of washing filter sand consists in hosing it while lying 
on a concrete or brick platform. The lighter dirt is carried away by the 
escaping water, and with care and a sufficiency of water, good results are 
obtainable. The method is costly in labour, and entails a large expenditure of 


CONTROL OF WATER 


536 

water, and is therefore only advisible in very small installations where the total 
quantity of sand to be washed is so small as to preclude the economical use of 
machinery. 

Machines for washing sand are generally divided into two classes, which 
may be called the “ Trough,” and “ Ejector” types. 

In the first class, the sand is passed along a trough by means of a system of 
paddles or screw conveyers, and is washed by a current of water passing in the 
opposite direction. Machines of this type consume but little water compared 
with the ejector types ; and further, the water is not delivered at a high pressure. 
On the other hand, the rotary paddles or conveyers consume a certain amount 
of power, and although the actual nett power may be less than that expended 
in pumping the water under pressure that is used in ejector washers, it is 
generated by small and inefficient machines, intermittently worked, and the 
gross power expended (in the form of coal burnt, etc.) may easily exceed that 
necessary to pump the quantity of water consumed by the ejectors. The use of 
trough washers is therefore only advisable when economy in filtered water is 
desired, and especially in cases in which filtered water under pressure is not 
required for other purposes {e.g. in a gravity distribution, where no pumping is 
done at the filtration works). 

In ejector washers, the sand is lifted (usually six to seven times) by water 
under pressure. The washing is effected by the water carrying the dirt forward 
faster than the sand, which is caught in troughs or boxes. These are usually 
provided with internal irregularities to break up and disperse the dirt while 
collecting the heavier sand. It will be noticed that in these machines 
relatively clean water acts on comparatively dirty sand, whereas in trough 
machines the cleaner water acts on the cleaner sand. It is therefore not 
surprising that all ejector washers consume more water per cube yard of sand 
than the trough type. On the other hand, ejector washers can easily be 
combined with a pipe system for conveying the mixture of sand and water to 
any required point, and especially where portable ejectors are used for lifting 
the sand out of the filter beds, the large amount of wheel-barrow work entailed 
in conveying the dirty sand to the washers is dispensed with. Also in cases 
where the water is distributed by pumping, the power consumed is very cheaply 
obtained, and in view of the large excess over the normal pump horse-power 
that must in any case be provided in order to supply the demands caused by 
hot weather or fires, it is unnecessary to debit the sand washing with any charge 
for an extra investment in pumping machinery. It is therefore probable that, 
except in purely gravity distributions, the ejector process always proves the 
cheaper. 

The design of the ejectors and communicating pipes was very carefully 
considered in the case of the Washington, D.C., filters, and the problem of 
using clean water to act on clean sand seems to have been partially solved, 
while the minutiae of the process have been so carefully considered that an 
abstract will prove useful. 

Ejector Sand Washers. —The problem involved includes three 
processes : 

(i) The sand has to be mixed with water in order to form a quasi¬ 

fluid mass. 

(ii) This fluid mixture has to be lifted up and driven along pipes by the 

energy of the water issuing from the ejectors. 


SAND EJECTORS 


537 


(iii) Simultaneously with, and after the above process, the sand must be 
washed, and later when the washing is complete, the sand must 
be separated from the dirty water. 

The Washington experiments of Hazen and Hardy {Trans. Am. Soc. of 
C.E ., vol. 57, p. 307) seem to completely answer all questions. 

It is found that process (i) is best effected by shovelling the sand into a 
hopper the sides of which slope at 1*8 : 1, with the ejector chamber bolted on 
to the bottom, as shown in Sketch No. 143. At the bottom of the ejector 
chamber an auxiliary water supply is introduced, which produces a slow, 
upward current of water through the sand in the hopper, and thus transforms it 
into a quicksand. In this way it is found that the sand is more readily moved 
by the ejectors than if (as is usually the case) it is sprayed with water under 
pressure from above 

(ii) The proportions of the ejector are of great importance. 



Sketch No. 143.—Washington Ejectors, and Raw Sand Washer. 


As is indicated in the theoretical treatment of the question (see p. 819), the 
ratio— 


Area of jet orifice _ a _ 

Area of throat of ejector cone ~ a 2 ’ Sa ^’ 
is of cardinal importance. 

The best value of J, increases as the total lift (including friction) increases. 
Calculating the ratio for new, unworn cones, we have as follows : 

For merely shifting sand along a short length of pipe, 

with a static lift of 3 to 4 feet . . . . J = 0*34 

For the lifting ejector, static lift about 26 feet . . J = 0*48 

For the movable ejector, the static lift being about 

10 feet but with lengths of pipe up to 100 feet . J = 0*59 
The larger the throat {i.e. the smaller J) the more sand that can be shifted, 
but the pressure at D, the entrance to the pipe (see p. 820) measured in lbs. per 

square inch, decreases steadily, and is approximately proportional to —. 

a % 
































































CONTROL OF WATER 


538 


Since the above ratios are found best for practical work, the ratios which 
would be obtained by theoretical treatment of the question correspond to a 
somewhat worn throat, and are probably some 5, to 10 per cent. less. 

The batter of the diverging discharge cone DE, is found to have a large 
influence on the working, and the best results are obtained with a batter of 
1 : 22, although in the lifting ejector (Case II above) 1 : 14 is used in order to 
save space, and in earlier designs (such as at Albany, and Philadelphia) fair 
results were secured with a batter of 1: 6. 

Hazen and Hardy define as follows : 

The efficiency of an ejector is the ratio between the pressure of the jet and 
the pressure at the discharge of the ejector. That is to say : 


The efficiency = 


Ho hb 
H 3 — hb 


= V, say, 


where H 3 , is the absolute pressure at the base of the discharge cone of the 
ejector, or the cross section a 3 , in the theoretical investigation (see p. 822). 
Hazen and Hardy also put: 




Total discharge through ejector pipe _ av-\~cu 
Discharge of jet av 


The relation between q, and q, for a given value of J, is very approximately 
linear, and hence the value of 77 can be calculated from the figures tabulated 
below, which are obtained by scaling from the original diagrams. 


J- 

q for q = r. 

d 

II 

Sm 

Jh 

ss- 

q, for best 
working. 

Remarks. 

o *54 

0-48 

o'i6 

1 ‘8 (?) 

Cone is of the Venturi 
form, batter 1:22. 

o'6o 

0*41 

• 

O'OO 

1 '45 

Philadelphia form of 
cone, i.e. discharge 
batter 1 :6. 

°’ 5 I 

°- 3 6 

C07 

170 

Batter 1:22. 

°'49 

0-30 

0*06 

p 

Rough cone, batter 

1 :22. 

0-38 

O '20 

°'°85 

• • • 

Batter 1:22. 

°- 3 6 

0*2 I 

0^090 

• • • 

j j >> 

0*27 

O ’ I 2 

o'o6 

2 '00 

55 55 

0-25 

O'lO 

°‘°55 

• • • 

55 55 

0*16 

o'o6 

C04 

• • • 

• 

- 

5) 55 


The best point for practical working is obtained when the product qq, is a 
maximum, and is given in Column 4. 

The percentage of sand is not specified, but seems to have but little 
influence on the values of q. 

The figures are not well adapted to test the theory of the apparatus, but 
are obviously very well fitted for practical purposes. H 0 , is not accurately 
stated, but H 0 — h b) the pressure of the ejector water, was approximately 90 lb. 
per square inch, or 210 feet head of water. 























MOTION OF SAND IN PIPES 


539 


In driving the mixed sand and water through pipes, certain conditions must 
be fulfilled. The experimental results are as follows : 

Taking V, as the average velocity of the mixture of sand and water in the 
pipe, i.e. : 


V 


av-\-cu 


area of pipe section 


If V is less than 2 feet per second : the sand drops, and the pipe “ silts solid.” 


V = 2*5 feet per second : the flow proceeds irregularly, and is sometimes 

maintained, and is sometimes stopped by “silting.” 

V = 3 feet per second : stoppages by “ silting ” almost cease. 

V = 4 feet per second, and over : the flow is nearly as steady as for pure 

water, but the frictional resistance is far greater. 


Since these results were obtained on pipes which were 3 inches and 4 inches 
in diameter, our present knowledge of hydraulics justifies the statement that 
they will not be found to hold without correction, in pipes which are, let us say, 
9 or 12 inches in diameter. 

In practical operation, the sand and water taken up by the jet increase the 
volume by one-third (i.e. q — 1*33), so that V, may be considered as four-thirds 
of the velocity given by considering the volume of water discharged by the jet, 
and the mixture in the pipe is about 75 per cent, water, and 25 per cent. sand. 
The percentages of sand are calculated without reference to the fact that the 
sand has about 40 per cent, of void spaces, so that theoretically the ratio : 


Water : Sand grains, 

is about 85 : 15, assuming that the sand contains 40 per cent, voids. 

Such excellent results are only attained by carefully following the Washington 
rules. At Philadelphia, the best results appear to have been about 82 per cent, 
of water to 18 per cent, of sand, and this was attained with J = 0*30, and the 
jet orifice if inch away from the throat. To judge by the Philadelphia 
results, this distance has but little effect upon the efficiency. The Washington 
experimenters seem to have kept it constant at about 2| inches, when J = 0*59, 
and at about 3 inches when J = o’33. 

The frictional resistance of the pipes appears to vary very nearly as V, when 
the percentage of sand is constant. The table at top of p. 540 is scaled from 
Hazen’s diagrams, and it is known that the effective size of the sand influences 
the results. 

Comparison with the Philadelphia results given in the discussion of Hazen’s 
paper seems to indicate that the form of the injectors has some influence on 
the velocity at which the sand packs ; but the friction is much the same in 
both cases. 

The effective size of the sand used was about 0^40 mm. 

Some very accurate experiments were made by Miss Blatch (tit supra, 
p. 406) on the motion of sand in i-inch pipes, and are compared by her with 
less accurate figures for 32-inch pipes. 

It would appear that while Hazen’s table is sufficiently accurate for 
practical necessities, the correct law of friction is more complicated. Apparently, 
for velocities which are less than those given in the column headed “Velocity at 
which Flow becomes steady,” the resistance for a given percentage of sand is 
independent of the velocity, and is approximately constant, and equal to that 




540 CONTROL OF WATER 



s for V = 4 Feet 
per Second. 

r 

s for V = 6 Feet 
per Second. 

s for V = 8 Feet 
per Second. 

Diameter of 
Pipes 

3 Inch. 

4 Inch. 

3 Inch. 

4 Inch. 

3 Inch. 

4 Inch. 

Percentage of 
Sand. 

35 • 

0*144 

0-137 

0-173 

0-157 


• • * 

30 . 

0*130 

0-123 

0-158 

0*141 

... 

• * • 

25 . 

0-113 

0-107 

0-141 

0*127 

0-177 

o'i 54 

20 

0*098 

0-093 

o*i 26 

0*11 2 

0-163 

0-138 

15 • 

0*084 

0-078 

O'l 12 

0*097 

0*146 

0-123 

10 

0-070 

0*063 

0*097 

O-082 

0*133 

0*108 

5 • 

0-054 

0-047 

0-082 

0*067 

0*117 

0-093 


TTTt Friction head in feet of water 

Where, s— -^-rr—7—;- 

Length of pipe 


. . . , 


which is observed at the velocity of “ steady flow." For velocities which exceed 
that of steady flow, the loss of head is very well represented by the equation : 

Loss of head for a mixture of sand and water = Loss of head for pure water 
at the same velocity + a constant x percentage of sand. 

For sands which are carefully sifted so as to consist of grains which are all 
approximately equal in size, this law ceases to hold at velocities which are but 
slightly greater than that at which steady flow begins ; but for sands with 
grains of varying sizes, such as occur in Nature, the law holds up to the 
velocities given in Column 5 of the table below. For greater velocities, the 
resistance appears to be far in excess of that observed in the flow of pure 
water. This last result does not agree well with the experiments of Merczyng 
0 Comptes Rendus , 1907, p. 70), who finds only small differences between the 
resistances for pure water and water carrying n to 19 per cent, of sand in a 
clean, steel pipe 15 inches (0*38 metre) in diameter, at velocities ranging from 
io’5 to 127 feet per second. 

The following table is useful : 


Diameter 
of Pipe 
in Inches. 

Value of 
Constant 
when Pipe is 
1000 Feet 
long. 

Velocities in Feet per Second. 

When Flow begins 
but is often Blocked. 
Resistance = Resist¬ 
ance at Velocity 
in Column 4. 

When Flow is 
steady, Law 
begins to 
hold. 

When all Sand 
is in Suspension 
and Law ceases 
to hold. 

I 

9-6 feet 

I-25 

3*5 

8 to 9 

3 to 4 

3 j) 

2*5 

4 

Not observed. 

32 

1*2 „ 

6 to 7 

9 

14 

















































SAND WASHING 


54i 


The size of the sand is of importance. 

The above results refer to sand of about 0*33 to 0*50 mm. in effective size 
(say o’o22 to 0*034 inch mean diameter). Miss Blatch finds for graded sand 
moving in a smooth brass pipe one inch in diameter, that : 

I. For sand which passes a sieve of 20 meshes per lineal inch, and rests on 
one of 40 meshes per lineal inch, the constant given in Column 2 above is 
about 7*8 feet per 1000 feet. 

II. I< or sand that passes a 60-mesh sieve, but is retained by a 100-mesh 
sieve, the constant is approximately 2*6 feet per 1000 feet. 

Washing of the Sand. —There are many types of washer. As a general 
rule, the sand is lifted 3 or 4 feet, and is swept along a horizontal trough, where 
it drops and is collected. The water escapes, carrying the dirt with it. Thus, 
six or seven repetitions of the process are not unusual. The best method is 
that adopted at Washington, by Hardy iut supra). In this case the actual 
washing of the sand is effected in hoppers, about 3 feet square at the top, and 
6 inches at the bottom, with a vertical height of 2*3 feet. These have an 
ejector and auxiliary water supply bolted on to their bottom, and the auxiliary 
water supply is so adjusted that there is no downward flow of water in the 
hopper. The sand sinks through the water, and is carried away by the 
ejector, while the dirt is carried away by the overflow water. It is stated 
that one such washer cleans the sand, but two are provided. The mixture of 
water and cleaned sand is lifted by the last ejector into a bin, and the sand is 
deposited there. 

It would appear that the quantity of water used is about twelve times the 
volume of the sand washed, and about 75 per cent, is supplied at a pressure 
of 80 to 100 lb. per square inch. At Philadelphia the figures are sixteen times 
the volume of sand, and 70 lb. per square inch, but these figures must, I think, 
be considered as a minimum, as they are calculated from experimental results. 

Actual working results are given as 1 of sand, to 20, or 30 volumes of water, 
in most cases. In some places, 1 to 14 or 15 is attained with a pressure of 55 
to 60 lb. And with a pressure of 80 to 90 lb. a ratio of 1 of sand, to n or 12 
of water is stated to be obtained, although these latter figures do not appear to 
include the water used in the lifting ejector. 

It will be seen that even the minima results contrast unfavourably with the 
1 to 7 or 8 attained in ordinary work with drum or trough washers, although it 
would appear that such results could be approached at Washington provided 
that the lifting ejector was not used. 

In all calculations respecting the strength of sand bins it appears advisable 
to assume that pressures equivalent to those produced by a fluid weighing 120 
to 125 lb. per cube foot may occur when the sand begins to settle out from the 
water. The weight of the mixed fluid travelling in the pipes does not 
materially exceed 80 to 85 lb. per cube foot. 

Washing of Raw Sand .—In applying the above results to the washing of 
sand in mechanical filters, or to the cleansing of natural sand from dirt, it must 
always be remembered that sand from a slow sand filter is coated with Zooglea, 
and that even when this has dried up a certain amount of gummy matter still 
remains on each individual grain. Thus, the washing of sand which has not 
been used in a slow sand filter is a far more simple process, and where raw 
sand is cheaply procurable, and the filter beds have been so designed that a 
thickness of sand can be placed in them sufficient to compensate for the 


CONTROL OF WATER 


542 

relative inefficiency of raw sand (as compared with ripe sand), such elaborate 
arrangements are unnecessary. 

I give a sketch (No. 143) of the apparatus used at Washington for washing 
an ordinary raw sand mixed with clay, so as to free it from clay down to o'2 or 
o ; i per cent, by weight. The raw material is washed through a screen of say 
o* 16 inch to o'2o inch mesh, and the mixture falls into a box 16 feet long 
by 24 inches wide, by 16 inches deep at one end, and 4 feet 2 inches 
at the other. In the bottom of this four perforated pipes were laid, and 
by means of these about 1 cube foot of water per square foot per minute 
was passed upwards, and overflowed as shown. The sand was drawn off at 
the lower end of the box, and was washed at a rate approximately equal to 
1 cube yard per square foot per hour. 

The expenditure of water was about five to six times the volume of sand 
washed. 

Washing of Filters. —Certain special methods of filter washing 
(they can hardly be termed sand washing methods) deserve consideration. 

At Long Island the filter is washed by turning water into a trough running 
along one side of the filter bed, with its lip at the level of the sand, so that a 
thin stream of water flows over the bed, and is drawn off by a similar trough 
on the other side of the bed. The top layer of the sand is then raked and 
broken up, so as to loosen the Schmutzdecke and dirt, and this is continued 
until all the dirt has been carried away by the flowing water, and a clean 
surface is secured. i; J. : j, 

The method is essentially that employed for cleaning the early mechanical 
filters, and the fact that the water flows over the sand in place of rising 
up through it would appear to render the cleaning still less effective. 

No systematic report of the working of filters washed in this manner has 
yet been published, but th® method seems hardly likely to produce consistently 
satisfactory results, except in cases where the raw water is neither highly 
polluted nor very turbid. If, however, it is regarded as an expedient for 
rapidly and temporarily restoring the efficiency of a filter during hot seasons 
when the growth of organisms in the Schmutzdecke is so rapid as to clog the 
filters long before the top layer of the sand is really dirty, it appears to be a 
valuable process, provided that it does not lead to an undue neglect of sand 
washing later on. A similar process of raking under water is occasionally 
adopted in the summer in London. Bacterial investigations have not been 
published, and seem desirable. 

At Ivry, where the Anderson process (see p. 547) is applied, the pre-filters 
are scraped under water every day, and about 3 mm. of sand (say £th of an 
inch) is removed by means of a flat nozzle, provided with a guard in order to 
prevent more than the desired thickness being removed, and connected with a 
centrifugal pump. This method permits a steady and systematic scraping to 
take place without stopping filtration, and I am informed that the bacterial 
results are excellent. 

I regret that as the inventor has not yet published any drawings, I cannot 
give a sketch, as it seems to be a process which is well worth adoption in all 
cases. It must be remembered that this process is at present only applied to 
pre-filters, and bacterial tests when used on ordinary single filters (where, if no 
coagulant is used, the scrapings would hardly require to be so frequent) are 
greatly to be desired. 


FILTER WASHING 


543 


In some cases, the filters are washed by agitating the whole sand bed by 
means of compressed air and water, introduced into the under-drains, as is 
usual in mechanical filters. The difficulties of obtaining an equable distri¬ 
bution over a bed of large area are obvious. Judging from experience of 
mechanical filters, we may expect that after a few washings the sand will 
become stratified, and that the upper layers will contain a large proportion of 
finer grains, so that the washing will require to be frequently repeated, or the 
sand employed must be graded to a uniform size before use. The system 
therefore promises to be costly not only in maintenance, but in first outlay, and 
its advantages are open to doubt. 

The Torresdale (Philadelphia) pre-filters may be taken as an example. 

These are 60 feet by 20 feet 3 inches in area, and consist of 12 inches of 
sand, varying from 0*032 to 0*04 inch in diameter, resting on the following 
layers of gravel : 

8 inches of a size varying from £ to j inch. 

3 » >> t jj 2 inch. 

4 jj >) ?» F » ircch. 

15 „ „ „ 2 to 3 inches. 

The grading is very carefully adjusted, and the gravel depth (2 feet 6 inches) 
is larger than would be required were the washing effected in the ordinary 
manner. 



Sketch No. 144.—Bag-Scraper used at Hamburg. 

Cleaning in Frosty Weather .—Sketch No. 144 shows a grab scraper 
used for scraping the sand of the Hamburg filters when the water is covered 
with ice. 

As a rule, the adoption of covered filters renders such methods unnecessary. 
Where frosts occur which are not sufficiently intense to render covered 
filters absolutely necessary, but which are hard enough to form thin ice on the 
water, the following process suffices to keep the filters in regular working 
order. 

Shortly before the advent of the cold weather, the surface of the sand is 
formed into regular waves about 9 inches high, and 3 feet from crest to crest, 
so that when the water is drawn down to the sand level the ice is fractured 
and can be removed. The height and size of the waves must depend on 
the thickness of ice expected, and any undue delay in scraping may prove 
disastrous. 

Preliminary Filtration Processes. —Preliminary processes of filtration 
vary greatly in character. Filters of coke, brickbats, compressed sponge, etc., 


































544 


CONTROL OF WATER 


have been employed. The general idea is to strain out the coarser particles by 
means of a filter which can be easily cleaned so as to permit the sand filters 
to run without cleaning for a longer period. The general ignorance of the 
principles involved is best illustrated by the fact that it is still open to doubt 
whether these coarse filters do not remove a greater portion of the finer particles 
than of the coarse particles. As has already been stated, bacteria, and the 
particles which cause turbidity and which cannot be rapidly removed by 
sedimentation, are all far smaller than the passages between the grains of even 
the finest sand. Thus, at first sight, coarse filters should have no influence 
upon substances which are difficult to deal with by means of sand filters. As a 
matter of fact, it may be suspected that coarse filters are usually effective not as 
filters, but as aerators. The principles are best illustrated by a description of 
the degroisseurs of Peuch-Chabal. 

Degroisseurs or Roughing Filters. —In principle, degroisseurs are 
filters of coarse gravel. The theoretical rationale of such filters is at present 
uncertain. Kemna (. Etudes sur Filtration , see also Engmeermg News, 26th 
March 1908) suggests that the action resembles the retention of small 
particles by the slimy layer of mud that forms on each individual stone of the 
gravel. Contact action has also been put forward as an explanation, but such 
terms are merely polite expressions of ignorance. 

The most systematic method of pre-filtration is that introduced by Messrs. 
Peuch and Chabal, under the term “degroisseurs.” The installation at 
Suresnes {Trans. Assoc, of Waterworks' Engineers , vol. 12, p. 200) treats 
7,700,000 imperial gallons per 24 hours, and consists of the following : 

(i) A fall in a thin sheet of water through about 2 feet, for the purpose of 
aeration. One set of strainers of 1571 square feet (146 square metres) area, 
composed of 12 inches (0*30 metre) of pebbles, ranging from 1*2 inch to o*8 inch 
in diameter (0*03 to 0*02 metre), and passing the water at a filtration velocity 
of 790 feet per day ; or, if one-quarter of the area is being cleaned, at about 
1040 feet per day. Then aeration produced by a fall of 4 inches, followed by a 
strainer of 2648 square feet (246 square metres) area, with 14 inches (0*35 
metre) of pebbles, ranging from 0*4 inch to o*6 inch in diameter (0*01 to 0*015 
metre), with a filtration velocity of approximately 464 feet per 24 hours. This 
is followed by aeration as before, and treatment in a strainer of 4810 square 
feet (447 square metres) area, composed of 16 inches (0*40 metre) of pebbles, 
ranging from 0*28 inch to 0*4 inch in diameter (0*007 to o*oio metre), at a 
filtration velocity of 255 feet per 24 hours. Followed by four falls of about 2 inches 
each, and a fourth strainer of 7972 square feet (741 square metres) composed of 
16 inches (0*40 metre) of pebbles, ranging from 0*16 inch to 0*20 inch in 
diameter (0*004 to 0*007 metre), at a filtration velocity of 154 feet per 24 hours. 

It may be suspected that the aeration is not without influence on the working 
of the system. The water is exceptionally polluted, being drawn from the 
Seine below Paris. 

(ii) The further treatment consists of a double filtration as follows : 

{a) Through 2 feet of coarse sand at a rate of 65 feet daily. 

{&) . 1, 3 jj fine „ 10*7 „ 

The bacterial results are excellent, being considerably better than those 
yielded by the Anderson process at Ivry (see p. 547), and the final filters 
appear to require cleaning at the most twice a year. The first sand filters are 


D&GROISSEURS 


545 

cleaned about once every six weeks. During floods the d^groisseurs are 
cleansed almost continuously. 

From personal inspection, I feel it safe to state that without the aid of 
degroisseurs, or an unusually lengthy period of sedimentation, combined with 
coagulation, it would be impossible to work the filters at all ; I also doubt if 
equally good bacterial results could be obtained from the raw water by any 
other process of filtration (as distinguished from chemical disinfection). 

The system is usually applied to waters similar to those at Suresnes, but has 
been introduced at the Bamford filters, which treat a moorland reservoir water 
but little exposed to pollution. In this case the strainers are three in number, 
as follows : 

(i) 12 inches of gravel, from 0*42 inch to o'62 inch in diameter, working 

at a rate of 343 feet per 24 hours. 

(ii) 14 inches of gravel, from 0*30 inch to 0*42 inch in diameter, working 

at 264 feet per 24 hours. 

(iii) 16 inches of gravel, from o'18 inch to 0^30 inch in diameter, working 

at 103 feet per 24 hours. 

Aeration appears to be unprovided for, and the further treatment consists 
of a slow sand filter with 2 feet of sand (reduced by scraping to 1 foot), working 
at a rate of 12 feet per 24 hours (see p. 530). 

Our present information does not permit the variations in the process 
necessitated by different qualities of raw water being discussed. The Peuch- 
Chabal degroisseur is by no means the only type that can be used, and very 
good results may be obtained by one filtration through ordinary stone broken 
to about £-inch size. A typical case exists at Shanghai, where a very turbid 
and polluted river water, which had to receive at least two days’ sedimentation 
previous to slow sand filtration, is now turned direct into a strainer consisting of 
3 feet of ^-inch stone, working with a filtration velocity approximately equal to 
100 feet per 24 hours ; then slightly aerated, and passed at once to the filters. 
At present, the process is experimental, but the average life of a filter between 
cleanings appears to be increased from 14 days to 6 weeks. 

Double Filtration .—In some cases the water is filtered twice through slow 
sand filters. The circumstances which necessitate double filtration are dis¬ 
cussed by Goetze {Trans. Am. Soc. of C.E ., vol. 53, p. 210). The water of the 
river Weser at Bremen in times of flood is turbid, and when it arrives at the 
filters frequently contains over 10,000 bacteria per c.c. (by Koch’s test). It is 
then found that even with such low filtration velocities as 4^9 feet per 24 hours 
(63 mm. per hour) a bacterially satisfactory effluent cannot be obtained, and 
the effluent is also liable to be turbid. Under these circumstances, Goetze 
filters the water twice, at velocities ranging (according to the bacterial content 
and turbidity) from 8, to 16 feet (even 20 feet has been used) per 24 hours, and 
obtains a final filtrate which contains only 20 to 40 bacteria per c.c. In addition, 
the effluent from a freshly cleaned filter can be turned on to an old, ripe filter, 
and a satisfactory final filtrate is produced. 

The advantages are obvious, and it is equally plain that a preliminary 
sedimentation or coagulation would allow a fairly clear water containing less 
than 10,000 bacteria per c.c. to be delivered to the filters. Thus, while double 
filtration can produce a satisfactory effluent from a very bad water, it is extremely 
doubtful whether it is the best, and it is certainly not the only possible process, 

35 


1 


CONTROL OF WATER 


546 

The process is, in my opinion, somewhat in the nature of a makeshift, and has 
no real advantage except that the second filters require cleaning at long 
intervals only, so that during a short period of bad water the full capacity of 
the filter area can be utilised. In considering the rates of filtration to be 
adopted, the figures for Ivry (see p. 547), and Suresnes (see p. 545) are typical ; 
and, since the water dealt with at these places is unusually polluted, these 
velocities will, as a general rule, be found to produce satisfactory results with 
double filtration without any preliminary treatment. 

No rules can be given, and local experience alone permits a satisfactory 
system to be arrived at. It may be suspected that either the typical system of 
degroisseurs, or the rough modification used at Shanghai, is usually preferable 
to double filtration through two sand filters. The Shanghai water is about as 
bad as is likely to be usually dealt with, and the results are excellent. 

Degroisseurs are believed to have more effect on coloured water, or on 
waters with odours and tastes, than a sand filter. Double filtration should only 
be adopted when it is quite clear that it possesses advantages over the simpler 
method of degroisseurs and single sand filtration, or coagulation and sand 
filtration. 

Flood Waters. —Most engineers are adverse to passing water drawn from a 
river in high flood direct to slow sand filters, as the filters are liable to become 
rapidly clogged, and the necessary cleaning is laborious. Flood water, however, 
is not in itself objectionable if sufficient sedimentation is provided. 

Certainly, the first washings of a catchment area, as carried down by a flood, 
may be highly polluted, when regarded from a chemist’s point of view. It is 
somewhat doubtful whether such water generally contains far more than the 
normal quantity of pathogenic bacteria, and being turbid, it is certainly 
proportionately more improved by sedimentation than are the clearer, normal 
waters. 

If the sedimentation is incomplete, the filters will require frequent cleaning, 
but this fact may be regarded as an assurance that an engineer will not filter 
unsedimented flood water if it can be avoided. The water of a flood succeeding 
a previous flood at a short interval is probably (except for its turbidity) the best 
of the year. 

Flood waters of even such highly cultivated and thickly populated catchment 
areas as the Thames, and Lea valleys, will produce satisfactory filtrates. Thus, 
during October 1898 (a month of high and continuous floods) the following 
figures were obtained : 

Raw water,—average 1719 microbes per c.c. : filtered water,—average of 
26 samples, 13 microbes per c.c. 

These particular results were obtained with very little sedimentation, and it 
may be inferred that careful slow sand filtration is capable of producing satis¬ 
factory filtrates from flood waters. If previous sedimentation can be effected, 
the circumstances are even more favourable ; and, if sedimentation is impossible, 
coagulation is not only an allowable, but even an advantageous, temporary 
measure. 

Processes Supplementary to Slow-Sand Filtration.— A mere enumeration of 
the various processes adopted to render water better adapted for purification 
by slow-sand filters would fill several pages. 

Preliminary treatment by roughing filters has already been discussed. 

It is now proposed to discuss several processes of a chemical character 


ANDERSON PROCESS 


547 

before discussing such methods as sedimentation or coagulation, which are 
more or less dependent on the turbidity of the water. 

The arrangement is illogical, and has merely been adopted because sedi¬ 
mentation and coagulation processes form an integral portion of the American, 
or mechanical filtration, processes. As already stated, however, sedimentation, 
either in special basins or storage reservoirs, is a very important preliminary 
portion of the slow sand filtration process when applied to turbid waters (see 
pp. 534 and 552). 

Preliminary Chemical Treatments .—(i) Treatment with Metallic 
Iron .—The typical iron process is the Anderson process, in which the raw 
water is exposed to the action of scrap iron in revolving drums. This treatment 
is usually applied to turbid waters, and especially to those which are both 
heavily polluted and turbid. It forms a very powerful means of ameliorating 
the condition of the water. As a rule, the turbidity is considerably reduced, 
and settles down more rapidly in the sedimentation basins, and is more easily 
removed by slow sand and other filters. In fact, the process produces a 
coagulation. 

In addition, many waters of the type referred to contain colloidal (glue¬ 
like) substances, which are not easily filtered. Any classification of these 
substances is at present impossible, but as a matter of experimental knowledge, 
the Anderson process usually causes colloidal substances to assume a form in 
which they are easily removed by filtration. The process therefore constitutes 
a very efficient preliminary to filtration, and while special experiments must be 
made in all cases, it is usually found that when the water is of a kind which is 
adapted to the process, the area of the filters can be reduced to about one-half 
of that which would be required to filter the same quantity of untreated water, 
and the interval between cleanings is greatly increased. 

The most scientifically arranged installation is found at Ivry (near Paris), 
and supplies a large portion of the water used in Paris. The drums are 
26 feet 3 inches by 5 feet 9 inches in diameter (8 metres x 175 metres). These 
each contain 3! tons of metallic iron in small fragments, and make 15 revolu¬ 
tions per minute. The water passes through the drums at a rate of about 
12 cubic feet per minute per drum, and is thoroughly mixed with the iron. The 
drums are provided with internal shelves which lift the iron and allow it to 
drop through the water. The water consequently takes up a small quantity 
of iron, the consumption being about 660 lb. per drum per month. 

On leaving the drums, the water passes into a “ sedimentation basin,” 
through which it travels in six hours. The after-treatment consists of filtration 
through 2 feet of coarse sand (all the sand passes through an ^-inch 
(3 mm.) hole, and is retained on a 0^04 inch (1 mm.) sieve). These pre-filters 
are cleaned every day by pumping the top o’2, to 0*4 inch of sand away by 
means of a suction scraper worked by a small centrifugal pump (p. 542). The 
“sedimentation” basin is only cleaned once a month. Hence, it may be 
inferred that the “ sedimentation ” basin is in reality a coagulation tank, 
and that the pre-filter removes the sediment. The slow sand filters are shown 
in Sketch No. 139, are worked at a rate of 13*1 feet daily, and are cleaned every 
six months. Before the installation of the pre-filters, however, these filters were 
cleaned every 15 days in summer, and every month in winter. 

The process described is admirably adapted to the water of the Seine, as 
found at Ivry. It is not precisely a typical Anderson process, that usually 


CONTROL OF WATER 


548 

consisting of treatment in revolving drums, followed by 12, to 24 hours’ 
sedimentation (sometimes less than 12 hours), and slow sand filtration at the 
rates later indicated. 

As will be seen from the figures given on pages 547 and 588, each cubic foot of 
water subjected to the Anderson process dissolves about 0*9 grains of iron. The 
coagulation effect thus induced is approximately equal to that produced by 
4'5 grains of crystallised ferrous sulphate, or 6'6 grains of crystallised aluminium 
sulphate, though some portion of the iron may become combined with the colloidal 
substances without producing coagulation, and is obtained without any increase 
in the hardness of the water. Thus, in waters which are adapted to this process 
the coagulation is very favourably effected. The power required to rotate the 
cylinders, and the fact that the supervisor has no control over the process, 
must be taken into account when balancing the advantages of the Anderson 
and other methods of coagulation. The process does not appear to be well 
adapted to turbid waters which are not polluted (either by products of animal 
or vegetable decomposition), and the typical coagulation process should be 
employed in such cases. 

Occasionally the Anderson process is employed as a preliminary to 
mechanical filtration, but I understand that this is not recommended by the 
inventor. 

(ii) Polarite, Oxidium , and other processes. —These are proprietary articles, 
consisting principally of iron and lime salts, which are placed in layers buried 
in the sand of the filters. They appear to permit a higher rate of filtration 
to be used than would otherwise be found satisfactory. 

The published results indicate very satisfactory working, but (like all 
proprietary articles) full information is difficult to obtain, and it may be 
suspected that the process has sometimes been applied to waters to which it 
is not well adapted. 

(iii) Ozone. —This process has been applied to several waters after filtration. 
Its efficacy,—which is undeniable,—lies in completely destroying all bacilli 
when properly carried out. 

At present, however, all installations appear to be so costly in power that 
the process is not economically justifiable. If anything approaching the 
theoretical yield of ozone per horse-power hour could be obtained, the process 
would prove economically practicable ; and it may be hoped that the advance 
of electro-chemistry will equip waterworks’ engineers with a very efficacious 
method. 

(iv) Sterilisation by Heat. —In this process the water is first raised to a 
temperature sufficient to destroy all organisms, and is then cooled. It is 
obviously costly, even when the heating is produced by a “ multiple effect ” 
heater, and is thus hardly suitable for general use. I would, nevertheless, 
strongly recommend such an installation in all cities where infection from 
cholera is likely. 

The localities where cholera is endemic are well known, and in view of the 
enormous loss of life and depreciation to property caused by an outbreak of 
cholera, the expenditure entailed by a plant which will ensure absolute safety 
during the periods when infection may be apprehended, is thoroughly justified. 

(v) Chemical Sterilisation .—The practice of chemically sterilising water is 
making rapid advance, but the question is one for the chemist and physician, 
rather than for the engineer. 


STERILISA TION 


549 

Sterilisation is usually affected by chlorine, produced by adding bleaching 
power (“ chloride of lime ”), or hypochlorite of soda to the water. 

At Reading (Mass.), ( Engineering Record , 9th Oct. 1909), water containing 
from 120,000 to 1360 bacteria per c.c. (27,127 per c.c. on the average) was 
treated with quantities of bleaching powder varying from o'93 to 7*5 grains 
per cube foot. 1 he “ percentages of bacteria removed ” varied from 99*5 to 99‘8, 
and the action was apparently complete in five minutes, for after 60 minutes the 
increase in the percentage of removal never exceeded o'2 per cent. It will be 
plain that even the highest percentage of removal will not produce a satisfactory 
effluent when the bacterial content of the raw water exceeds 50,000. The 
bleaching powder contained 41*5 per cent, of free chlorine, and if more than 2’5 
grains per cube foot was added to the water, a slight odour of chlorine was 
noticed. Bacillus coll was “entirely destroyed,” and no free chlorine could be 
detected in the effluent. 

The process is simple. The requisite quantity of free chlorine, or the 
chemical containing it, is added to the water after as long a sedimentation as 
can be obtained ; or just before filtration, if that process is employed. Engineers 
must consider it as a very useful means of tiding over temporary emergencies 
such as abnormal pollution, or threatened outbreaks of cholera and typhoid. It 
is doubtful whether popular prejudice at present permits an extensive and 
systematic application of disinfection methods, and (judging from personal 
experience) most engineers are far more disposed to employ the treatment, 
than to publish their results. 

So far as I am aware, the chemicals, other than bleaching powder, used in 
sterilisation processes are hypochlorite of soda (producing chlorine), perman¬ 
ganate of potash (producing oxygen), and sulphur dioxide. The chemical 
action is probably essentially an oxidisation in every case. 

(vi) Neutralisation. —Several preliminary treatments for special purposes 
such as the neutralisation of acid waters, have already been referred to. The 
principles are purely chemical, and the details of their application depend 
so exclusively upon local circumstances that no general rules can be given. 
Thus, the neutralisation of acid waters has been effected by the following 
means : 

(a) By pouring each hour a weighed quantity of powdered chalk into the 
aqueduct. 

(b) By passing the watep through special filters of coarsely powdered limestone. 

(c) By mixing powdered limstone with the sand of the filter beds. 

(vii) Straining. —Similarly, the figures relating to the process of straining 
water through fine copper, or brass sieves, are very conflicting. Thus ( P.I.C.E ., 
vol. 126, p. 8), in two cases in the North of England, sieves of 900 and 14,400 
meshes per square inch were adopted. The circumstances under which the 
two types of sieves were used were very similar, and, so far as differences 
exist, the 900-mesh sieve is used under the less favourable conditions. 

The effects (other than the removal of visible impurities) of straining- 
through fine wire sieves are not well known. The process obviously prevents 
the entrance of fish spawn, or other large organisms, into the mains ; but 
it is doubtful if it has any permanent effect in preventing the development 
of algas or slime (see p. 438). In cases where it is the only treatment which 
is given to the water, such fine gauze as 14,400 meshes per square inch may be 
useful; but, if the water is later subjected to any other effective process of 


55 o CONTROL OF WATER 

purification, even a 900 mesh per square inch screen seems to be unnecessarily 
fine. 

Removal of Visible Impurities from Water. — As a matter of 
historical record, the first attempts to purify water were entirely directed with 
a view to removing visible particles from the water. Even at the present date, 
engineers are accustomed to obtain a rough idea of the effectiveness of any 
purification process by pouring the purified water into long tubes, and examining 
the colour and transparency of a 2 feet, 3 feet, or 4 feet layer of water. The 
test is unscientific, but in experienced hands the relative results afford a very 
valuable preliminary indication of irregularities in the working of the process. 
Regarding the question from this point of view, the visible impurities (mud, 
slime, etc.) in water can be wholly or partially removed by straining or 
sedimentation. 

Straining is effected by passing the water through orifices which are 
sufficiently small to retain the visible impurities. Such orifices are afforded by 
the pores of a sand layer, or by the meshes of wire gauze. The details have 
already been discussed. 

Sedimentation is a convenient term for the slow deposition of the visible 
impurities which takes place under the action of gravity. This action can be 
assisted by various mechanical or chemical processes. The term coagulation 
may be applied to this assisted sedimentation. 

As will appear later, sedimentation produces other, and generally, far more 
important effects on the water than are indicated by the mere diminution in 
turbidity produced by the process. 

Sedimentation. —This process is best applied to turbid waters, since the 
deposition of the suspended matter not only clears the water, but bacteria are 
mechanically entangled and are carried down to the bottom, thus producing a 
material purification. 

The following figures show that at least 75 per cent, of bacterial purification 
may be obtained in suitable waters, merely by 24 hours’ storage in a sedimenta¬ 
tion tank. 

At Louisville, Kentucky, in 24 hours, 75 per cent, reduction. 

At Kansas City, in 24 hours, 83 per cent, reduction. 

On the other hand, some waters contain very finely divided particles of clay, 
as small as o’ooooi inch in diameter {i.e. practically of bacterial size), and in 
such cases, unless a coagulant is added, sedimentation has comparatively little 
effect. For example, at New Orleans, we find the following results : 


Time of Subsidence. 

Turbidity in Parts per 
Million. 

Percentage Reduction of 
Tuibidity. 

Initial 

650 

0 

12 hours 

435 

33 

24 „ 

360 

45 

48 „ 

3 °° 

54 

72 „ 

265 

59 

















SEDIMENTA TION 5 51 

This comparatively high rate of reduction, followed by a rapid decrease, may be 
considered as characteristic of all sedimentation. If in the average state of the 
water the reduction in turbidity is less than 60 to 70 per cent, after 24 hours’ 
sedimentation, storage in a large and well-designed sedimentation basin for at 
least a week, or some coagulation process, is advisable, either regularly, or at 
certain seasons only. 

The effect of sedimentation on bacterial content is not entirely mechanical. 
It appears that the mere fact of storage causes a reduction in the number of 
bacteria existing in an initially polluted water, even though this water is quite 
clear. The reasons are obscure, and it is not yet certain whether the bacteria 
are mechanically deposited and sink to the bottom of the water, or whether the 
available nutriment contained in the pollution existing in the water is exhausted, 
and the bacteria are starved, but the balance of evidence seems to favour the 
latter supposition (see p. 552). 

In cases where a heavy and rapidly falling precipitate is produced in the 
water ( e.g . in Clark’s process for softening water, where a pulverulent precipi¬ 
tate of calcium carbonate, “ precipitated chalk ” is formed), the bacterial 
reduction may be so great as to render filtration unnecessary. As examples, 
the following reductions have been secured merely by applying Clark’s process 
(see p. 590) : 

Reduction of bacteria from 322 to 4 per c.c. 

Reduction of bacteria from 182 to 4 „ „ 

Where coagulants producing a gelatinous precipitate are used, as in the 
aluminium sulphate, or, better still, the ferrous sulphate and lime process, 
many American cities are content with the results obtained by such assisted 
sedimentation only. As for example, St. Louis, where the average results 
show a bacterial reduction from 65,100 to 200 per c.c. 

Sedimentation is usually regarded as a preliminary to filtration, and from 
this point of view it has merely been considered as a means of removing the 
larger suspended particles, and so increasing the period during which the 
filters run without cleaning, the bactericidal effect, until lately, not being recog¬ 
nised. Hence, the period of sedimentation allowed in practice, is very variable. 

Taking typical cases :—It has been proposed to allow a 56 days’ storage for 
Thames water, not so much for sedimentation, as to avoid the use of turbid 
flood water. This may be regarded as a counsel of perfection ; and, actually, 
the periods of sedimentation (or storage) allowed, varied in 1894, from 15 days 
for the East London Water Co. (using Lea River water principally), and 12, for 
the Chelsea Water Co., down to 3^3 for the Grand Junction Co. The storage 
capacities have since been largely increased (roughly doubled), and in view of 
the “ Reports on Bacterial Results ” by Houston (Reports to the London Water 
Board) the expenditure appears to be justified. 

The circumstances in London are peculiar. The raw water is heavily 
polluted, and, except in flood time, is not very turbid. Also the quantity 
supplied is now growing very close to the amount that may be drawn from the 
river in the months when its flow is least. An increase in storage capacity is 
therefore necessary, if only to ensure against shortage of supply. Houston’s 
investigations have probably produced the construction and use of reservoirs as 
sedimentation basins but a few years previous to their inception for storage 
requirements only. Indeed, it may be doubted whether an engineer accustomed 


CONTROL OF WATER 


552 

to such turbidity as occurs in America or India would consider the London 
Water Board reservoirs to be correctly termed sedimentation basins. Some 
sedimentation does occur in these reservoirs, and as far as possible no water 
is delivered to the filters which has not been passed through the reservoirs. A 
study of Houston’s reports will show that the reduction in bacterial content 
which occurs in the reservoirs is attributed to storage rather than sedimentation. 
The distinction is not of great practical importance, as even should it be proved 
that the duration of the storage is the only factor effective in destroying the 
bacteria, it is highly improbable that any engineer will build reservoirs to store 
clear water for this purpose alone. Where, however, turbidity or shortage of 
supply enforces the use of sedimentation reservoirs, Houston’s researches show 
that under favourable circumstances a marked diminution of the bacterial 
content may be expected even when the water is initially free from turbidity. 

Houston (“Third Report on Storage of River Water antecedent to Filtration ”) 
suggests 30 days’ storage previous to filtration, as the best period for Thames 
water, and it may be inferred that a shorter period would in most cases (other 
than the Thames) suffice to secure all the advantages anticipated from storage. 

The usual figures in British practice are two to three days’ sedimentation ; 
or, where the rejection of the turbid water which comes down with floods is desired, 
10 or 12 days’ storage suffices. Thus, in ordinary circumstances, 10 or 12 days’ 
sedimentation is procured. American engineers are usually satisfied with one 
day’s sedimentation, but the more modern installations are provided with 
sedimentation basins of two or even three days’ capacity. 

German practice is usually satisfied with 24 hours’ sedimentation, but it 
must be remembered that the working of filters in Germany is a matter of 
official regulation, and that the maximum permissible filtration velocity is 
somewhat low when compared with that usual in other countries. Thus, it is 
quite possible that, were greater latitude given to German engineers, they 
would find a longer period of sedimentation economically justified. 

Where polluted or turbid water occurs at definite seasons, a storage 
reservoir of sufficient capacity to allow of the rejection of this bad water, is a 
very useful adjunct, and can be used as a sedimentation basin at other periods. 
In the Nile, for example, during the first rise of the flood each year the river is 
heavily charged with faecal matter washed from the newly covered banks. 
Since 12 days’ storage would permit an entire rejection of this polluted water, 
and since the normal Nile water is but slightly polluted, it is plain that this 
amount of storage would permit a far less efficient filtration plant than is now 
required to secure good results throughout the year. 

A consideration of these figures shows that when coagulation processes are 
not applied about 24 hours’ sedimentation may be taken as the minimum 
period, and that we may then expect to secure a deposition of 25 to 50 per 
cent, of the suspended matter in unfavourable, and 90 to 99 per cent, in 
favourable cases. The accompanying diminution in bacterial content is some¬ 
what less variable, and may be taken as ranging between 60 and 95 per cent, 
if the water is markedly turbid. In clear waters, however, it is doubtful 
whether 24 hours’ sedimentation has any noticeable effect on the number of 
bacteria. 

An increased period of sedimentation is indicated in the case of muddy 
and heavily polluted waters, such as are found at Shanghai, where two 
days’ sedimentation is allowed, and more would be advantageous. For very 


SEDIMENT A TION 


553 

clear waters, particularly those that have already been stored, special sedi¬ 
mentation appears to be quite useless. 

A scientific investigation of the subject would treat the construction of the 
filters and the period of sedimentation as mutually dependent, but the requisite 
statistics are not available. The general principles, however, are plain. The 
finer the filter sand, and the thicker the layers, the shorter the period of 
sedimentation required to produce good bacterial results, although it must 
always be understood that filters of fine sand need more frequent cleansing, 
and are therefore more easily worked with ample sedimentation. 

The question is intimately connected with the value of land, and where land 
is cheap the present practice (which is the outcome of experience in localities 
where land is generally dear) should not be too closely followed, and at least 
twice the usual sedimentation can be given with advantage. 



Sketch No. 145.—Albany Sedimentation Basin. 


Construction of Sedimentation Basins .—Depth seems to have but little in¬ 
fluence on the efficiency of a sedimentation basin. Thus, a deep basin is 
indicated. Since pollution by the subsoil water can usually be regarded with 
equanimity, careful precautions against leakage from the outside, such as are 
provided in filters, or service reservoirs, are unnecessary. 

The best design is a tank with sloping sides, say 2 to 1, or 3 to 1, according 
to the character of the soil, paved with slabs of concrete of the type used at 
Staines (see p. 331). 

The bottom of the basin should be covered with 6 inches to 1 foot of con¬ 
crete, laid at a slope of 1 in 100, and smoothly rendered. It is then found that 
the deposited silt is very easily and rapidly removed with squeegees, assisted 
by a stream of water from a hose (Sketch No. 145). 

The action on bacteria in sedimentation is entirely different from that pro¬ 
duced by a long storage of fairly clear water, or slow-sand filtration. In the 
latter methods the bacteria are destroyed. In sedimentation, however, the 






































CONTROL OF WATER 


554 

bacteria accumulate in the silt deposit, and although individual species may 
die, the general result is a rapid increase in numbers, and, if the silt deposit is 
disturbed, they may again be distributed throughout the water. We are not, as 
yet, precisely aware how coagulation alone, or coagulation followed by rapid 
filtration, affects bacteria. In certain cases it is believed that they are partly 
destroyed, but, as a rule, we must assume that the bacteria are not destroyed in 
these processes, but accumulate in the wash water, or silt deposits. The matter 
is not so frightful as the idea of a concentrated deposit of bacteria might at first 
sight appear. Disease-producing germs are not highly resistant forms of life, 
probably the majority die very rapidly ; and, moreover, no one is likely to drink 
a semi-liquid mud. The real importance lies in the indication that systematic 
cleaning of the sedimentation basins is necessary, and that the present practice 


inlet 



of cleaning when you “must, 5 ’ should be superseded by routine cleanings at 
stated intervals. 

The velocity with which the water passes through a sedimentation basin 
should not exceed four or five inches per minute when reckoned on the quantity 
of water passing per minute divided by the area of the cross-section of the basin 
normal to the general direction of flow. In practice these velocities are rarely 
exceeded, and about \\ inch per minute represents the average velocity. Both 
the inlet and outlet to the basin should be of such a character that localised 
currents are prevented. Sketch No. 146 shows a typical method, and also the 
provision necessary to prevent differences in temperature from influencing the 
working of the basin. 

In the hot weather, when the entering water is cooler than that in the sedi¬ 
mentation basin, the outlet screen is let down on to the floor of the basin, so 
that the outlet draws from the warmer upper layers of water which are those 





















COAGULATION 


555 


which have been longest in the basin. In the winter, the warmer incoming 
water tends to float on the colder layers, and sedimentation is therefore less 
efficient. This is partially cured by raising the outlet screen, so that the outlet 
draws from the bottom of the basin. The width between the screen and the 
wall should be so calculated that the velocity of the rising water is not 
sufficiently great to lift up the silt deposits. 

Clay particles of equal size probably fall more slowly than quartz, and special 
experiments must be made before the final design of the basin can be deter¬ 
mined. Wiley states that d= 0*031^ 2 , where d , is the diameter of a particle 
in millimetres, and 7/, is its velocity of fall in millimetres per second. The 
experiments were made on particles of soil between 0*012 mm. (0*00048 
inches) and 0*075 mm. (0*003 inches) diameter, i.e. particles which settle in 
a reasonable period. The formula is incorrect for markedly smaller particles. 
If d, be expressed in hundredths of an inch and v, in inches per second we get 
d = o*969vi 7 T. 

The constructional details of a sedimentation basin are very similar to those 
of a storage reservoir (see p. 618). Except in very cold climates the arched 
covering is not required. It might also be inferred that since leakage is less 
detrimental the walls and sides might with safety be made thinner. In practice 
this is not generally the case. The reason is intimately connected with the 
function of the two works. Service reservoirs are placed on hilltops, and there¬ 
fore in well-drained soils, while sedimentation basins are placed in low-lying 
situations, and are therefore exposed to external ground water pressure. 

Hazen {Trans. Am. Soc. of C.E., vol. 53, p. 40) has endeavoured to treat the 
question of the size of sedimentation basins in a logical manner. The whole 
argument is rendered defective by the fact that he considers each particle as 
falling independently, and does not allow for the action of the larger particles 
in dragging down the smaller ones. For this reason I consider that his views 
concerning the advantages of shallow, as opposed to deep, basins are not 
entirely correct. The principle laid down, however, that the time which the 
water takes to pass through the basin should be some multiple of the time which 
the sediment takes to settle through a space equal to the depth of the basin is 
correct, provided that for the depth of the basin we substitute the space which 
the particles fall through before they have clotted together into relatively large 
masses. Allowing for this modification, it would appear that successful 
American practice agrees very fairly well with the rule: The capacity of 
the sedimentation basin = 25 to 50 times the period of clotting together 
of the particles, as ascertained experimentally in tubes of 6 to 8 feet vertical 
height. 

The rule is rough, as no particulars are given of the relative efficiency of the 
basins ; but it has the practical advantage that if the turbidity is of such a 
character that a 6 or 8 foot fall through still water does not produce any marked 
clotting, plain sedimentation is almost useless, and coagulation, or some other 
method, must be employed to deal with the turbidity. 

Coagulation.— Sedimentation does not produce any very great improve¬ 
ment in a water unless it contains a sufficient proportion of rapidly falling- 
particles to carry down a large proportion of the small particles which are detri¬ 
mental to filters, and which fall very slowly by themselves. In waters where 
the larger particles are deficient, ordinary sedimentation has but little effect. 
Consequently, in such waters it is necessary to produce a rapid fall of the small 


556 CONTROL OF WATER 

particles by artificial means. The most usual method is to introduce into the 
water a gummy, adhesive substance, which collects in flocks, to which the 
particles adhere, and then falls more or less rapidly to the bottom of the sedi¬ 
mentation basin or coagulating tank. The process may, in fact, be regarded as 
passing a filter through the water, in place of passing the water through a filter. 
The gummy, adhesive substance is produced by chemical reactions which aie 
set up in the water by the addition of various salts. The added salt is usually 
termed the coagulant, and the flocky precipitate, or falling substance, is lefened 
to as the coagulating substance. 

The coagulating substance is produced by the reaction of the coagulant with 
certain dissolved substances contained in the raw water, and the chemistry of 
this reaction requires consideration. 

The chemical reactions are separately discussed under each coagulation 
process, and in each case it will be found that the “ alkalinity 55 of the raw water 
is, chemically considered, the most important factor in the reaction. 

In practice, coagulation is usually only a portion of the complete process of 
water purification, being a preliminary to filtration either by slow-sand or 
mechanical filters, and it is only occasionally that coagulation alone is considered 
to produce a satisfactory water. 

Thus, the details of coagulation processes will be found to be largely influ¬ 
enced by the treatment which the water afterwards undergoes, and'the consequent 
differences in the methods adopted will be indicated as exactly as our present 
knowledge permits. 

Alkalinity. —The alkalinity of a water is a convenient term for that portion 
of the temporary hardness which reacts with a coagulant such as aluminium, or 
ferrous sulphate, or with slaked lime, in a period that is sufficiently short to be 
practically useful in the coagulating or water-softening process. 

The chemical process (usually referred to as Hehner’s process) generally 
employed by chemists in ascertaining the hardness of water determines the 
temporary hardness (reported as alkalinity, if this term is used by the chemist) 
as so many parts of calcium carbonate per 100,000. The alkalinity, however, 
may exist in the following forms: 

(i) CaC 0 3 (not more than three parts per 100,000). 

(ii) Ca(HC 0 3 ), i.e. carbonate and “bicarbonate ” of lime. 

(iii) MgC 0 3 . 

(iv) Mg(HC 0 3 ) 2 , i.e. carbonate and bicarbonate of magnesia. 

(v) Na 2 C 0 3 , carbonate of soda. 

If this last exists, there can be no permanent hardness in the water. 

From the point of view of an engineer engaged in coagulating or softening 
the water, the magnesia salts are unfavourable. The reactions producing water 
softening, or coagulation, do occur with magnesia alkalinity, but they take time, 
and in practice it may be stated that the alkalinity produced by magnesia is 
only about one-half as effective as the same weight of alkalinity produced by 
lime or soda. The statement is a rough one, as a great deal depends on the 
size of the coagulation and sedimentation basins. 

Taking the case of lime alkalinity, we have as follows: 

[a) With alumina sulphate : 

A/ 2 (S 0 4 ) 3 + 3Ca(HC0 3 ) 2 = A/ 2 (H 0 ) 6 d 3CaS0 4 -f6C0 2 


ALKALINITY 


557 


(/>) With ferrous sulphate : 

FeS 0 4 + Ca(HC 0 3 ) 2 = Fe(H 0 ) 2 + CaS 0 4 + 2C0 2 
Similar reactions occur with magnesia alkalinity, but take time. 

(c) With lime : 

Ca( 0 H) 2 + Ca(HC 0 3 ) 2 = 2CaC0 3 + 2H 2 0 

With magnesia alkalinity the above reaction occurs slowly, and then the 
reaction * 

Mg(C 0 3 ) + Ca( 0 H) 2 = CaC 0 3 + Mg( 0 H) 2 

occurs. 

Thus, remembering that alkalinity is reported in parts per 100,000 of CaC 0 3 , 
we obtain the following table for lime alkalinity: 


ONE PART OF LIME ALKALINITY PER 100,000 REACTS WITH 

PARTS PER 100,000 OF 


Alumina Sulphate. 

Ferrous Sulphate. 

Lime. 

Dry Salt. 

Crystallised Salt. 

Dry Salt. 

Crystallised Salt. 

Caustic Lime. 

Slaked Lime. 

I ' I 4 

2*22 

1 ' 5 2 

00 

N 

0*56 

074 


Grains per Cube Foot of Water. 



, j • ;; , 

4-99 

972 

6 '66 

12*16 

2 '45 

3’ 2 4 


Similarly, if time were given, the magnesia alkalinity would react in the 
same proportions, except that the quantities of lime would be doubled. 

More definite information concerning the complications produced by finely- 
divided turbid matter, etc., is given when the various processes are discussed. 

As a rule, however, any further information must be obtained by special 
experiment on the water considered. If the problem is put before a chemist, 
the proportion of the magnesia alkalinity that reacts in 1 hour, 2 hours, 3 hours, 
etc., can be ascertained, but it is necessary to check these determinations by 
large scale (say 200 gallons of water) experiments. 

Although the chemically determined alkalinity of a river usually varies from 
day to day, the ratio of the lime and magnesia salts does not vary to anything 
like so marked a degree. 

Thus, let us assume that a water contains 10 parts per 100,000 of alkalinity, 
of which 4 parts are in reality produced by magnesia. 

The water softening reaction (c) can be calculated as follows : 

Temporary hardness, 10 parts, equivalent to . 5’6o parts of caustic lime 

Additional for 4 parts of magnesia hardness . 2-24 „ „ 

Total reaction equivalent . . . 7*84 „ ,, 































CONTROL OF WATER 


558 

Thus, the complete precipitation of the 10 parts of temporary hardness re¬ 
quires 7*84 parts per 100,000, or 34*3 grains of lime per cube foot, and the correct 
dose of caustic lime maybe anything from (6xo’56x 4*375) — 147 grains, to 
34‘3 grains per cube foot, according to the size of the softening basin, the first 
figure corresponding to the removal of all the lime, and no magnesia, temporary 
hardness (which would be produced almost instantaneously), and the last figure 
to the total removal of all temporary hardness (which would probably not be 
attained in less than 48 hours). If the coagulation basin were of say 6 hours’ 
capacity, it is probable that 23 to 26 grains per cube foot would be a correct 
dose, but once the exact figure, say 25 grains, is ascertained, we may rest 
assured that for this particular water, and for this particular size of coagulation 
basin, the rule, 2*5 grains of caustic lime per cube foot per part of alkalinity per 
100,000, will never be very far wrong, and that variations in the temperature 
of the water will probably have more effect in altering the correct dose of lime, 
than any variation in the chemical composition of the alkalinity. 

For the coagulation processes ( a ), and (A), the question is not so acute. We 
do not usually wish to remove all the alkalinity, but merely wish to employ a 
certain portion in order to produce a coagulating precipitate. Also, if the 
alkalinity is deficient, lime can always be added. Thus, the distinction between 
lime and magnesia alkalinity is by no means so important, and, judging by 
certain experiments of my own, the reactions of the coagulants with magnesia 
alkalinity usually proceed with sufficient rapidity for practical purposes. 
Exceptions do occur in very cold water (say under 40 degrees Fahr.) where 
only magnesia alkalinity is present. I was then unable to produce a satisfactory 
coagulating precipitate with alumina sulphate in less than two hours, but, as the 
lime alkalinity had been specially removed, the fact is not likely to cause 
trouble in practice. 

Sulphate of Alumina Process.—The typical coagulant is sulphate of alumina. 
This chemical, when added to a water containing lime or magnesia alkalinity, 
breaks up into sulphuric acid (which unites with the lime) and aluminum 
hydrate. The hydrate collects in gelatinous, flocculent masses, and gathers up 
the particles suspended in the water. The sticky film thus formed adheres to 
the top layer of sand in the filter, and there makes an artificial Schmutzdecke. 

The details of the reaction require consideration. In the first place, there 
must be sufficient alkalinity in the water to decompose the alumina sulphate, 
and form an adequate amount of precipitate. Secondly, clay particles appear 
to unite with a certain quantity of aluminum hydrate and deprive it of coagulat¬ 
ing properties. Thus, in turbid waters, a larger quantity of coagulant is 
required to produce the same quantity of coagulating precipitate than in clear 
waters. In very turbid water, containing but little alkalinity, it may be necessary 
to add lime in order to provide a sufficient degree of “ alkalinity,” to decompose 
the total quantity of sulphate required both to unite with the clay particles and 
to furnish the quantity of coagulating precipitate required to carry down the 
turbidity. 

The relation between the turbidity and quantity of sulphate of alumina 
required to produce effective coagulation depends considerably on the physical 
character of the turbidity, the amount of sedimentation previous to coagulation, 
and the method of filtration afterwards adopted. 

As an example, I give the three methods experimented with at Cincinnati, 
andjthe two at New Orleans : 


5 UL PH A TE OF AL UMINA 


559 


Turbid¬ 
ity Parts 
per 

Million. 

Grains of Alumina Sulphate per Cube Foot. 

Cincinnati. 

New Orleans. 

Kansas City. 

Raw Water after¬ 
wards treated 
by Slow - Sand 
Filters. 

Sedimented 
Water approxi¬ 
mately 2 hours 
afterwards,Slow- 
Sand Filters. 

] 

10 Hours after¬ 

wards, Mechan¬ 
ical Filters. 

Rapid Filters. 

No after¬ 
filtration. 

Approxi¬ 

mately 

7 Hours’ 
Sediment¬ 
ation. 

No Sedi¬ 
mentation. 

* 

IO 



5*6 




2 5 

... 

... 

9*4 

• • • 


• • • 

5 ° 

. . . 

• • • 

I 1*2 

12*8 


• • • 

75 

• • • 

9-8 

14 ’6. 

13*9 


• • • 

IOO 

11*2 

12 '0 

16 '5 

I 5’7 


375 

I2 5 

I 2*0 

x 3'5 

18*4 

17*2 


• • • 

* 5 ° 

12*8 

15*0 

i 9‘9 

18*4 

22 'S 

7'5 

x 75 

I 3’5 

15-8 

2 1*4 

19*5 

23-6 

• • • 

200 

14-6 

16*5 

22*5 

20*2 

24*8 

I I *2 

3 °° 

16 *9 

18-4 

28*5 

2 5’5 

2 9'7 

18*0 

400 

18*8 

206 

33 ‘° 

3 °* 7 

34‘9 

2 5’5 

5 °° 

2 I 'O 

... 

... 

... 

42*4 

32-2 

600 

22*9 

... 

• • • 

... 

47*2 

397 

75 ° 

2 5’5 

... 

... 


52-9 


1000 

3 °-° 

... 

... 

... 

76*0 

. . . 

1200 

35‘6 

• • • 

• • • 

... 

• • • 

... 


Turbidity in Parts 
per Million. 

Hazen’s 

Values. 

Ordinary Average. 

Favourable. 

5°. 

7*6 

37 

100 . 

10*0 

5 * 8 

150. 

12*1 

7*6 

200 .... 

137 

87 

300 . 

l 6*3 

I I *2 

400 .... 

17 *6 

13*1 

500 . 

18 *6 

147 

600 .... 

20*0 

16*0 

75°. 

22*5 

r8*o 

1000. 

247 

20*0 


In view of these figures, the principles are fairly obvious. A mechanical 
filter needs more coagulant for proper working than a sand filter, and previous 
sedimentation produces a certain economy in coagulant, although, in some 





















































CONTROL OF WATER 


560 

cases (when sedimentation has removed a portion of the turbidity) the water 
may require more coagulant than a raw water which has not been allowed 
to deposit any portion of its turbidity, and is as turbid as the sedimented 
water becomes after sedimentation. 

The efficiency of pre-sedimentation is most marked in clay-bearing waters, 
containing a large proportion of their turbidity in the form of very small 
particles (say under 0^0005 inches in diameter). Such waters are capable of 
decomposing alumina sulphate, with, it is believed, the formation of alumina 
silicate, which is useless as a coagulant. The advantage gained by pre¬ 
sedimentation in such cases is well illustrated by the figures for New Orleans. 
In Cincinnati, the improvement is less marked, since, although the turbidity has 
been reduced by sedimentation, the portion which is still in suspension plainly 
decomposes the coagulant to a far greater degree. 

It will also be clear that both the time allowed, and the precautions taken to 
ensure a good coagulation, are of great importance. The figures given may be 
taken as covering the most unfavourable cases that are likely to occur, and 
economy both in chemicals, and time required for coagulation, can be secured 
by adding the coagulant in two doses, as later explained. 

The figures given in Hazen’s schedule (Column No. 2) (Engineering Record, 
June 27, 1908) should be attained under ordinary working, when the operator 
becomes accustomed to local peculiarities ; although on individual days 
variations of 30 to 40 per cent, may occur. Those figures given as “ Favour¬ 
able” (Column No. 3) should be considered as attainable by good working 
under average conditions (see p. 575). 

It must be remembered that economy in chemicals can be carried so far as 
to cause the filters to require cleaning more frequently than is desirable, and a 
cautious increase in the quantity of coagulant added, up to as much as 10 per 
cent, in excess of the figures given by Hazen, will frequently cause a mechanical 
filter to run from 15 to 20 per cent, longer without requiring cleaning. 

The above results are nearly all drawn from American practice. 

The work of Schreiber at Berlin, and of Bitter at Alexandria, indicate that 
turbid waters can be treated with quantities of chemical equal to those given by 
Hazen’s rule, the variations observed being well within the extreme results of 
good American practice. 

When applied to clear waters, however, large increases may be necessary in 
order to obtain the best bacterial results, and no rule can be given other than 
that the presence of algae is unfavourable to an economy in coagulant. 

The maximum quantity of aluminium sulphate that can theoretically be 
usefully added in order to produce coagulation is determined by the alkalinity 
in the water ; and when (which is very rarely the case) the above tables show 
a deficiency in alkalinity, lime must be specially added. 

The reaction is represented by the equation: 

A/ 2 (S 0 4 ) 3 + 3Ca(HC0 3 ) 2 = 3CaS0 4 -f- A/ 2 (HO) c T 6 C 0 2 

i.e. temporary hardness is changed into permanent hardness, and 342 parts of 
alumina sulphate react with 300 parts of carbonate of lime as bicarbonate, or, 
with 132 parts of semi-free carbonic acid. 

As a matter of fact, commercial alumina sulphate contains nearly 50 per 
cent, of water, the theoretical formula for the crystallised salt being: 

A/ 2 (S 0 4 ) 3 +i 8 H 2 0 


DOSE OF ALUMINA 561 

Consequently, approximately 666 parts react with 300 parts of carbonate, as 
bicarbonate, etc., or roughly, 2‘2 parts per part of alkalinity. 

Hence, we find that, corresponding to an alkalinity of one part per 100,000 
(assumed as entirely lime alkalinity), about 97 grains of alumina sulphate per 
cube foot is the maximum quantity that can be decomposed. 

In practice, owing to decomposition by clay particles, the theoretical quantity 
is almost invariably exceeded. 

Allowing for the fact that commercial alumina sulphate may contain slightly 
more than the theoretical quantity of the dry salt, it may be stated that even 
the very clearest water can decompose 9*0 grains of commercial salt per cube 
foot of water for every part of alkalinity per 100,000 which the water contains. 
The figure 9*0 becomes 10, or even 11 in more turbid waters. Practically, 
however, owing to difficulties in securing complete mixture and the time taken 
to complete the reaction, it does not appear advisable to reckon on decompos¬ 
ing much more than 80 per cent, of the quantity given by these figures. There¬ 
fore, if we wish to ascertain the amount of precipitate in a coagulating state, it 
is best to calculate it as corresponding to 8'o grains of coagulant, or r8 to i'9 
grains of aluminium hydrate per cubic foot of water per 1 part of alkalinity per 
1 co,000 in the water. 

The final result of the process is that temporary hardness (or “ alkalinity ”) 
is replaced by permanent hardness, and carbonic acid is set free in the water. 
The water produced is therefore relatively more pleasant to drink, and is more 
palatable than would be the case were the same natural water treated by a non¬ 
chemical process of purification (such as slow sand filtration), but is less suitable 
for use in boilers, or for most trade purposes. It is also more likely to attack 
and corrode unprotected metals, although this defect can be easily removed by 
treatment with lime, if considered advisable. 

In any given case, the alkalinity should be measured, and the quantity of 
coagulant decomposed should be ascertained by experiment. Allowances for 
variations in the lime-magnesia ratio can then be made if necessary. 

The necessity, or otherwise, for the addition of lime can thus be ascertained. 

The coagulant being added, the process should be directed more with a view 
to the removal of bacteria, than to that of turbidity. In comparatively clear 
waters (as at Cincinnati), the period of coagulation appears to have little effect ; 
while, in turbid waters, time is important, and increasing the period from a 
half to six hours, or even longer, promotes the removal both of bacteria and 
turbidity. 

The crucial point of the method is not so much the time of subsidence or 
coagulation: these are quite minor matters compared with the care taken in 
correctly adjusting the quantity of coagulant. 

Broadly speaking, it would appear that the following is the most efficient 
method. Add one-half to three-quarters of the amount of coagulant required ; 
allow the precipitate to subside for a period varying from half an hour, for 
waters of say 10 parts per 1,000,000 turbidity, up to six hours for 500 parts per 
1,000,000 ; then add the remainder of the coagulant, and filter. 

It will therefore be evident that the consulting engineer has less control over 
the process than the supervisor. The best that the engineer can do when 
designing for a water the characteristics of which are not well known, is to give 
the man who works it as much power to alter conditions as is consistent with 
economy, and to insist on the services of a highly efficient supervisor. 

36 


CONTROL OF WATER 


562 

The method in which the water is coagulated, i.e. the character of the motion 
forced on the water in the coagulating basins, is of importance. So far as my 
experience goes, the best results are not obtained by absolutely quiet water, nor 
by a turbulent motion over weirs or cross walls, but by a quiet swirling motion, 
just sufficient to bring the particles of precipitate into contact ; but not suffici¬ 
ently violent to destroy the flocks when formed. Motion of this character is 
best obtained by causing the water to move with a velocity of approximately 
3 inches per minute. This should be quickened up to say 2 feet per minute 
about six times in the whole coagulation period, by means of cross walls with 
submerged apertures. Very good results are also obtained by circulation in 
spiral channels the depth of which increases towards the exit. 

It will be noticed that the weak point in the alumina sulphate coagulation 
process is the possibility of the water not containing sufficient alkalinity to 
decompose the quantity of aluminium sulphate required to produce adequate 
precipitation, and so to properly coagulate, and collect the turbid matter. 
Such a deficiency of alkalinity should not give bad results, as a careful 
supervisor should be able to recognise the defect, and should supplement it 
by the addition of lime, or carbonate of soda. 

The designer should, however, arrange the piping systems so as to permit 
the addition being made without special arrangements having to be resorted to. 
The necessity will probably arise without any warning, and the supervisor’s 
attention should not be distracted by the provision of some temporary 
makeshift. 

This consideration is even more urgent in cases where the primary object of 
coagulation is the removal of colour, rather than turbidity. Coloured waters 
are frequently deficient in alkalinity. The complete precipitation of the colour¬ 
ing matter by aluminium hydrate, may consequently require far more hydrate 
than the untreated water can produce. Thus, the addition of lime may become 
a normal feature of the treatment (in the case of the removal of turbidity it is 
doubtful whether the addition of lime will be required for more than 30 days in 
each year). In such cases aluminium chloride—which is stated to decompose 
into aluminium hydroxide more readily than the sulphate—has sometimes 
proved a useful coagulant. As a rule, however, ferrous sulphate and lime form 
the best coagulant when the natural alkalinity is deficient, although conditions 
exist where aluminium hydrate forms a better precipitant of colouring matter 
than ferrous hydrate ; but it is believed that these are very rare. Usually the 
failures of either process in removing colouring matter may be considered to be 
due to the chemical reactions not being properly considered ; either the 
necessity for extra lime is not realised, or the water is not sufficiently turbid to 
produce nuclei for the coagulant to adhere to, which can easily be provided 
against by the addition of powdered clay. 

The chemical principles underlying the question of adding lime, or replacing 
aluminium sulphate by aluminium chloride, are very well illustrated by 
Whipple (Use of non-basic alum in connection with Mechanical Filtration) who 
has very clearly shown that an aluminium sulphate possessing theoretical 
constitution, A 1 2 (S 0 4 ) 3 .1 8 H 2 0 , is inferior, as a coagulant, to what is commercially 
known as basic alum. 

A salt possessing the above constitution contains 15*32 per cent, by 
weight of A 1 2 0 3 , and 36 per cent, of S 0 4 . 

In the “basic alum” the first quantity is increased, and the second is 


SEE CIFICA TION 


5 6 3 

diminished, so that a certain amount of A 1 2 0 3 , is not combined with the S 0 3 , 
thus justifying the term “basic.” 

Whipple recommends the following as a useful buying specification : 

The basic sulphate shall contain at least 17 per cent, of A 1 2 0 3 , soluble in 
water, and at least 5 per cent, of this shall be in excess of the quantity 
theoretically necessary to combine with the S 0 3 , present. 

This specification defines a salt which will produce the quantity of 
aluminium hydrate required for coagulation, with the least possible consumption 
of alkalinity existing in the water. 

The addition of lime, or the substitution of aluminium chloride for aluminium 
sulphate, are now plainly seen to merely be further applications of the same 
principle. 

Practical Details. —Aluminium sulphate being easily soluble, its 
solution in water causes but little difficulty. It is usual to employ some 
mechanical stirring arrangement, in order to prevent variations in the con¬ 
centration of the solution. Very good results are also obtained by permitting 
the water to enter the bottom of the solution chamber, and flow out at the top, 
thus rising through a layer of sulphate resting on a grating. In such cases, it 
is necessary to add (about twice every hour) the quantity of salt that will be 
consumed in the next half-hour, and the total- quantity of undissolved salt in the 
chamber should not be less than about 2 hours’ consumption. The water supply 
should therefore be adjusted so that the water leaving the chamber is almost a 
saturated solution of aluminium sulphate. 

In very large plants, constant mechanical feeding of the sulphate into the 
dissolving tank is sometimes adopted, but the complication seems hardly 
necessary. 

A combination of the upward flow method with a second mixing tank 
containing approximately the quantity of solution used in one hour’s working, 
will evidently prevent any sudden variations in the amount of salt delivered. 
In practice, except in very large or very small (one filter) plants, the supervisor 
is usually able to keep the quantity of salt delivered to the water sufficiently 
under control by adjusting the taps regulating the supply of water to the 
dissolving tank, and any extra tanks or stirrers appear to be unnecessary. 

Owing to the action of the solution on iron, all pipes and metal exposed to 
the concentrated solution are usually of brass. 

It will be found in practice that the best place for the addition of the 
coagulating solution depends to a large extent upon the temperature of the 
water and air, and possibly on the amount of dissolved substances in the water 
and the solution. The final location of the delivery pipe should therefore be 
left for the supervisor to ascertain by experience. At first, it is usually 
sufficient to deliver the solution through a pipe opening into the centre of the 
entry channel of the coagulating basin. 

In two very successful installations the centre of the coagulating basin was 
the location finally fixed upon. Distribution was effected by a fountain in one 
case, and by a small Barker’s mill in the other. 

In my opinion, most of the present installations are insufficiently provided 
with sedimentation tanks before the addition of coagulant, as also with 
coagulating basins in which the coagulating process occurs. 

The general rules when clarification rather than bacterial purification is 
the main object of the process, are as follows : 24 hours’ sedimentation 


564 CONTROL OF WATER 

before the addition of coagulant, and a coagulating basin of {5, to 6 hours’ 
capacity. 

Such an installation may be regarded as throwing an undue share of work 
on the filters. These, being patentable articles, have been developed and 
improved, so as to afford satisfactory results with even less capacity than that 
stated above. I believe that 4 hours’ sedimentation and half an hour’s 
coagulation is too hard for any filter, although 6 hours, and one hour appears 
to be quite a usual design. Obviously much depends on the raw water, and 
on the popular standard of a satisfactory filtrate. 

Any economy in first outlay is plainly secured at the cost of an extra 
expenditure in washing the filters, and it is even possible that additional 
filters may be required in extreme cases. And, for this reason, the advice of 
filter makers, as opposed to consulting engineers, should not be too readily 
followed. 

My own belief is that an engineer should consider 48 hours’ pre-sedimenta¬ 
tion, and 12, to 15 hours’ coagulation (in which should be included not only the 
capacity of the coagulating basin, but also that of the water in the filters) as 
justifiable, in places where land is cheap, and the power and labour used in 
washing the filters is costly. From this high standard we can work down to 
say 8 hours’ sedimentation, and 2 hours’ coagulation, which forms a limit 
below which it is undesirable to go, unless unsatisfactory results may occasion¬ 
ally be permitted in order to secure a diminution in cost. It will be plain that 
where the filters are washed mechanically, and where the power for such washing 
is cheaply obtained, the 12 hours and 6 hours stated as common are probably 
justified by economical considerations. 

Where slow sand filters, cleansed by hand, are employed, and the water is 
initially very turbid, the 48 hours and 15 hours may require to be exceeded. 
Engineers contemplating the combination of slow sand filters with coagulation, 
should consider all mechanical filter installations as insufficiently provided 
with sedimentation and coagulation capacity. It is also necessary when 
considering the adoption of any proprietary filters or processes to allow very 
carefully for the fact that, until late years, the success of all processes was 
judged almost entirely by the physical appearance of the filtrate. This method 
of judgment is by no means entirely obsolete, and while bacterial tests are 
probably more systematically employed in America than in England, there is 
little doubt that an engineer who copies even modern American practice 
blindly in an Asiatic installation will not obtain as great a decrease in water¬ 
borne death-rate as he expects. This statement must not be construed as 
adverse to the adoption of American methods when carefully adapted to local 
conditions. Three of the five Oriental cities that I consider have best solved 
the local filtration problems use more or less modified American processes, and 
none of the five relys exclusively on purely British methods. 

Ferrous Sulphate Process. —This differs from the alumina sulphate 
process in that ferrous sulphate is employed instead of alumina. Except in 
very alkaline waters, such as are rarely used for human consumption, it is 
necessary to add lime or other substances, as well as the ferrous sulphate, in 
order to procure a coagulating action within a reasonable period. 

The infrequent use of ferrous sulphate (as compared with alumina sulphate), 
may be attributed to the difficulty of handling the two chemicals. As already 
stated, coagulation by alumina sulphate requires considerable care. When 


FERROUS SULPHATE PROCESS 


5^5 

therefore the supervisor of the coagulation process is generously allowed two 
chemicals (i.e. lime, and ferrous sulphate), in place of one, to make mistakes 
with, it is hardly a matter of astonishment if the one chemical process is found 
to work more easily and regularly, and is consequently preferred. 

This is somewhat unfortunate ; as, when the ferrous sulphate process is 
correctly worked, it produces a precipitate which is in every way better 
adapted for coagulation. Being heavier, it collects in larger flocks, and more 
rapidly. It also appears to be totally unaffected in its coagulating properties 
by clay, or other turbid substances. It is brown in colour, whereas aluminium 
hydrate is white, and while I do not profess to explain the reason, it is never¬ 
theless a fact that a brown-coloured precipitate (probably since it resembles 
dirt) causes less fear of wholesale poisoning in Oriental and other unscientific 
minds than a white one. 

So also, the medical profession appears to consider a “ little iron and lime 
in the water” as less likely to affect public health than “an excess of alum.” 

In view of the fact that, when properly worked, neither process permits any 
undecomposed coagulant to pass the filters, and both usually produce an 
increase in permanent hardness, the reasoning of both parties is, to my mind, 
equally logical, but the waterworks’ engineer should respect such prejudices. 

Before this process can be satisfactorily applied to a water even more 
careful and systematic preliminary experiments must be made than are needed 
for an aluminium sulphate process. Our present knowledge hardly justifies its 
application to heavily polluted waters, except on so large a scale that the 
salary required to secure a first-class supervisor forms but a small portion of 
the running expenses. 

The reaction occurring in the ferrous sulphate process is a very complex 
one. The chief practical difference between this reaction and the one which 
occurs when aluminium sulphate is used as a coagulant lies in the fact that the 
reactions which occur in the ferrous sulphate process are only completed after 
a certain time, while the aluminium sulphate reaction (see p. 556) is practically 
instantaneous. 

Broadly speaking, if the ferrous sulphate is added to the water before the 
lime, we have : 

FeS0 4 + CaH 2 (C0 3 ) 2 = FeH 2 (C0 3 ) 2 + CaS0 4 (1) 

The ferrous bicarbonate is soluble, and will only slowly decompose into 
carbonic acid gas and ferric hydroxide. Thus, lime is added to hasten the 
reaction, and the following reactions occur : 

Fe(HC0 3 ) 2 + 2Ca(0H) 2 = Fe(0H) 2 + 2CaC0 3 +2H 2 0 . . (2) 

FeS0 4 + Ca(0H) 2 = Fe(0H) 2 + CaS0 4 .(3) 

That is to say, both the ferrous bicarbonate resulting from the first reaction, 
and any excess of ferrous sulphate, are decomposed, and produce ferrous 
hydroxide. 

This last very rapidly oxidises to ferric hydroxide, which is the precipitate : 

2Fe(OH) 2 + H 2 Ofi-O = Fe 2 (OH) 0 . . . (4) 

In addition, however, the lime reacts with any bicarbonates of lime, and 
magnesia, which have not been previously decomposed by the ferrous sulphate 
in the manner indicated in equation (1), and therefore the reactions above 


566 CONTROL OF WATER 

discussed occur simultaneously with the various reactions employed in Clarks 
water softening process, such as : 

Ca(H 0 ) 2 + C 0 2 = CaC 0 3 + H 2 0 '» 

Ca(H 0) 2 + Ca(HC 0 3 ) 2 = 2 CaC 0 3 + 2 H 2 0 . . (5) 

MgH 2 (C0 s ) 2 + 2 Ca( 0 H 2 ) = Mg( 0 H) 2 CaC 0 3 + 2 H 3 QJ 

The normal calcium carbonate thus produced is insoluble, and rapidly 
precipitates. The magnesia hydrate is less rapidly precipitated, and re¬ 
dissolves as the water absorbs carbonic acid from the air. T he magnesia 
hydrate is therefore only removed under favourable circumstances. 

Thus, it will be evident that the two processes of coagulation and water 
softening cannot be separated, and calculations which are based on the 
coagulation process only do not indicate the whole circumstances. 

Broadly speaking, when a water of ordinary composition is considered, the 
Calculations are as follows : 

(i) Ascertain the amount of temporary hardness, and calculate from 
equations (1), to (4), inclusive, the quantity of iron sulphate and lime necessary 
to cause the reactions. If this is likely to produce a sufficient quantity of 
precipitate to satisfactorily coagulate the turbidity, and form an efficient 
Schmutzdecke, we must experimentally ascertain whether the quantity of lime 
given by equation No. (2), is sufficient, or whether reactions of the type given 
by equation No. (5), also occur, with the corresponding amount of water 
softening. 

(ii) If, however, the amount of precipitate thus produced is insufficient, 
we must in addition calculate from equation No. (3), the necessary 
quantity of lime and ferrous sulphate required to produce the extra amount 
of precipitate in accordance with reaction (No. 3), and also experimentally 
ascertain whether any excess of lime is required for reactions of type 
No. (5). 

The crux of the process is whether reactions of type Nos. (2), and (3), occur 
before, or after those of type No. (5). This question can only be answered by 
experiment, as the results depend upon the relative concentrations (z>. the 
number of parts per 100,000) of each of the salts considered, which occur in 
the water. 

It will be evident that the process hitherto considered consists of a coagula¬ 
tion, combined with the transformation of a part, or, possibly, nearly all, the 
temporary hardness into permanent hardness, as per equation No. (1). This 
is the process most generally employed. 

Let us, however, consider the reverse process, where the lime is first added. 
We then have reaction No. (5) occurring, and the temporary hardness is entirely, * 
or, nearly entirely, precipitated, just as in Clark’s process. 

On adding ferrous sulphate, reactions No. (1), and No. (2), do not occur ; but 
No. (3) does, if an excess of lime remains. By suitably proportioning this excess, 
we can obtain a sufficient quantity of coagulating precipitate. 

This second method has the advantage that we not only coagulate the 
water, but can also partly soften it if the process is carefully conducted. Thus, 
the second method is preferable in waters containing a large amount of 
temporary hardness. It has, however, the disadvantage that the heavy pre¬ 
cipitate of calcium carbonate (which in the first, or usual process, forms 
simultaneously with the precipitate of ferric hydrate, and loads the flocks and 


CHEMICAL DETAILS 567 

materially increases the rate of subsidence) is now formed, and falls separately. 
Hence, the subsidence is less efficient, and, broadly speaking, a larger 
subsiding and coagulating basin will be required. Also, the consumption of 
lime, will probably be largely increased. Where the turbidity is great, the 
first, or usual process, should be adopted. A careful supervisor will, of course, 
change over from one process to the other, according as temporary hardness or 
turbidity is the most important factor. It may be noted that since the more 
turbid waters are those drawn from the river when in high flood, they are 
usually less alkaline than the normal waters, so that the change in method has 
practical advantages. 

It will be evident that any arithmetical rule, even if only as approximate as 
that given in considering the alumina sulphate process, is so liable to mislead 
as to be useless. 

On the other hand, the above investigation shows that the process is a very 
powerful one. I believe that if the details are correctly planned, it is applicable 
to a greater number of varieties of water than the alumina sulphate process, and 
can be made to produce better results. 

At St. Louis, Mo. ( Trans . Am. Soc. of C. E., vol. 60, p. 170), for instance, a 
fairly satisfactory water (from the bacteriological point of view) is produced by 
coagulation and sedimentation only, from a very turbid and somewhat polluted 
river water. Although I consider that the process, as at present adopted in the 
above-mentioned city, is merely educative, and will rapidly lead to a popular 
demand for an even better water, I doubt whether any such rough process with 
alumina sulphate as coagulant would prove satisfactory, even as a temporary 
measure. 

Therefore, as knowledge advances, I expect that this process will largely 
supersede the aluminium sulphate process. Even at the present date, if soften¬ 
ing by Clark’s, or a similar process, is desired, and a coagulation process (other 
than the slight coagulating effect obtained by the deposition of the calcium 
carbonate precipitate on particles of suspended matter), is also required, ferrous 
sulphate should be adopted rather than aluminium sulphate, since, where lime 
is added for softening, the extra complication of two chemicals has to be faced 
in any case. 

A modified ferrous sulphate process has lately been introduced, in which 
lime is not employed, live steam being injected into the water after the addition 
of the requisite quantity of ferrous sulphate. Details, however, have not as yet 
been published. 

Certain small scale experiments of my own indicate that reaction No. (1) 
occurs, and that the steam then causes the ferrous bicarbonate to rapidly 
decompose into ferrous hydroxide, and free carbonic acid. It will consequently 
be plain that the natural water must contain enough alkalinity (as calculated 
by the first equation) to produce sufficient coagulating precipitate. 

The modified process is therefore subject to the possibility of troubles 
caused by deficient alkalinity in just the same manner as the aluminium 
sulphate process. This defect, however, is known to be practically of little 
significance in turbid waters, and cases entailing the addition of some lime for 
the production of reaction No. (3), are likely to be almost entirely confined to 
coloured waters, where the object of coagulation is to remove colouring sub* 
stances or odours. 

The process certainly deserves the fullest consideration, since it will be 


CONTROL OF WATER 


568 

plain that the addition of an excess of live steam has no such adverse effect on 
the quality of the water as that produced by an excess of lime. 

I am unable to state definitely whether the live steam required is less costly 
than the lime which it replaces, but the general belief is that the lime process is 
the more economical. I therefore infer that the question really depends upon 
whether a supply of live steam is already available {eg. from the pumping 
station attached to the filter plant). In small installations, where steam would 
have to be specially generated, owing to the extra superintendence thus 
required the lime process may prove cheaper. 

My own experiments also lead me to believe that the pressure of the steam 
has little effect on the reaction, and that the best numerical results are obtained 
with 12 lbs. per square inch gauge pressure. 

The water produced by the ordinary ferrous sulphate process is relatively 
less palatable, and less pleasing to the eye than that which is produced from 
the same raw water by an aluminium sulphate or a simple filtration process. A 
consideration of the chemical reactions will show that the lime deprives the 
water of the dissolved carbonic acid, which remains in the water in the 
aluminium sulphate process. It will, however, be plain that when the process 
is carefully worked, and advantage is taken of the alternatives produced by the 
two methods of adding the chemicals, a water can be produced which does not 
attack metals, and which is well suited for use in boilers. Thus, the advantages 
of the aluminium sulphate process can be over-rated, and in considering this 
question an engineer should remember that the American standard of a 
“ palatable ” water is higher than that which is usual in Europe. The fact is 
curious, although it in some respects explains the relatively lower standard of 
“ healthy ” waters which undoubtedly prevails in America. 

The above discussion of the various reactions which occur when ferrous 
sulphate and lime are added to a water shows that a table of the quantities of 
chemicals per cube foot of water, similar to that given for aluminium sulphate, 
is useless. If attention is confined solely to the coagulation portion of the 
process, the following rule will be found to be approximately true provided that 
the water is not unusually‘alkaline. 

Add of crystallised ferrous sulphate two-thirds, and of slaked lime one-fifth, 
of the weight of aluminium sulphate which is found to produce satisfactory 
coagulation. The coagulation thus induced will generally prove equally 
effective, and in the case of very turbid waters will probably be even more so. 
If the water contains a large amount of temporary hardness (alkalinity), some 
amount of softening will generally occur, and the lime should be increased. In 
such cases it is advisable to ascertain by experiment whether the dose of ferrous 
sulphate cannot be diminished, since the additional amount of calcium carbonate 
which is produced in the water-softening reaction will probably load the 
coagulating precipitate, and produce a more rapid fall of the turbidity. Ferrous 
sulphate is more costly than lime, and each grain added produces an increase 
in the permanent hardness, so that a blind adherence to any rule is unadvisable. 

The following figures are the average of the results of each month as 
obtained in actual working at Cincinnati. 

The water is sedimented for 40 to 48 hours, and is then treated with sulphate 
of iron. After being thoroughly mixed, lime is added ; and coagulation for 1 to 
8 hours is allowed. The filters are each 1400 square feet in area, and treat 
4 million U.S. gallons per 24 hours, say 380 feet vertical, or, allowing for 


DOSE OF FERROUS SULPHATE 569 

cleaning and rejection of effluents after cleaning, work at a rate of about 400 
feet vertical per 24 hours. 

I he working head of a clean filter is 2 feet, and the filters are washed when 
the head is 12 feet. The wash water is used at a rate of r8 to 27 cubic feet per 
minute per square foot of filter, and the wash water is 3-8 per cent, of the total 
quantity filtered during the year. 

1 he following table shows the monthly average results obtained during one 
year’s working : 


Average Turbidity in Parts 
per Million. 

Average Grains applied per 
Cube Foot of Water. 

Average Interval 
between Wash¬ 
ings of Filters 
in Hours. 

. 

Raw Water. 

Water after 
Sedimentation. 

Ferrous 

Sulphate. 

Lime. 

7 

6 

9’2 

6 '3 

11 -6o 

11 

9 

y6 

5*2 

i4*45 

5° 

3i 

117 

6*9 

i4‘34 

93 

33 

11 ‘9 

67 

12*26 

145 

85 

lO’O 

6*o 

16-44 

Not recorded. 

8S 

8-5 

5 *° 

15-09 

190 

90 

8-5 

5'9 

13-00 

255 

* 5 ° 

*5'° 

8-o 

15' 16 

270 

12 5 

t 3 ' 1 

7*o 

21-39 

410 

220 

1 7*3 

9*° 

11 *i 1 

43° 

to 

O.) 

O 

15-2 

8-6 

11-72 


It must be noted that where the water is coloured by vegetable matter, 
aluminium sulphate is usually found to give better results than ferrous sulphate. 
This cannot, however, be taken as an invariable rule. The chemical facts 
underlying the question appear to be that some varieties of vegetable colouring 
matter combine readily with iron, and in most cases this combination is less 
easily dealt with than the uncombined colour. I have, nevertheless, met with 
coloured water (usually accompanied by a history of pollution by animal matter, 
and therefore possibly entirely of animal origin), which, when treated with ferrous 
sulphate, produced a bulky, rapidly settling precipitate, very easily removed 
by sedimentation alone, and for such waters the ferrous sulphate process is 
invaluable. 

Under this head it is as well to refer to the old method in which a dilute 
solution of mixed ferrous and ferric sulphates and sulphites is produced by 
passing the fumes of burning sulphur over metallic iron exposed to thin streams 
of falling water. The dilute solution thus obtained is added to the raw water. 

It is plain that the process amounts to an unregulated coagulation, 
accompanied by a possible disinfection from such sulphur dioxide as remains 
dissolved in the water, and uncombined with iron. The principle appears 
to be a good one, but in view of the fact that the supervisor has absolutely 
no control over the relative quantities added, and very little over the total 






























S7 o CONTROL OF WATER 

amount of mixed gases and salts, it is doubtful whether really regulai working 
can be obtained. 

Practical Details. —The practical details are very similar to those 
of the aluminium sulphate process. The capacities of the sedimentation 
and coagulating tanks are usually some io per cent, larger than in the case 
of the alum process, and, this addition being made, the reasoning theie set 
forth applies. 

The greatest difficulties, however, are connected with the addition of 
lime. If the lime is dissolved as lime water, the volume of lime solution is a 
very considerable fraction (as much as fth or gth in some cases) of the 
quantity of water treated. It is therefore customary to add the lime as milk 
of lime, containing about one-tenth its weight of hydrated lime. This milk 
of lime must be carefully strained, stirred, and kept in motion until added to 
the raw water. This is best effected by a screw propeller, working in the 
mixing tank, which should be placed as nearly as possible vertically over the 
point where the lime is delivered to the raw water. 

Troubles are frequently caused by deposits and incrustations of lime salts 
formed in the pipes. Such obstructions occur at the point where the 
lime is added to the raw water, or in the pipe systems of the filters. 

The first deposits seem to be almost entirely caused by the lime being 
added to the water when in violent motion, carrying air bubbles. This can 
usually be stopped by a change in the point where the lime is added. Some 
chemical action may also be suspected, since such incrustations rarely take 
place unless the lime is first added. The filter deposits appear to be mainly 
due to an excess of lime, and whenever the ratio : 


Weight of lime 
Weight of iron sulphate’ 


much exceeds o‘4 


such deposits may be considered as likely to occur. Occasional additions of 
lime, far in excess of the above value, have no ill effect, provided that such 
conditions are temporary, and are succeeded by periods during which the ratio 
is less than o’4. 

A quantity of lime in the treated water greatly exceeding 1*5 parts per 
100,000 of normal carbonates, if continually present, should be considered 
as unsatisfactory, since incrustation will sooner or later occur. 

Coagulation with Slow-Sand Filters. —The processes of coagulation already 
discussed are generally preparatory to mechanical filtration. There is, 
however, no difficulty in applying them as preliminaries to slow-sand filtration. 
The following discussion of the treatment adopted by Fuertes {Trans. Am. Soc. 
of C.E., vol. 66, p. 135) in the case of the Steelton (Pa.) water excellently 
illustrates the strong and weak points of the process. 

The water is frequently heavily polluted, is very turbid, and is also liable 
to become extremely acid owing to contamination by mine refuse. Altogether, 
the water is as variable as can well be imagined. The acidity is neutralised, 
and the necessary alkalinity is produced by the addition of lime in such 
quantities as to react with the required dose of alumina sulphate, and still 
leave about o'6 parts per 100,000 of alkalinity. The dose of alumina sulphate 
is entirely determined by the turbidity, and, when graphically plotted, the 
relation is represented by straight lines which can be laid down from the 
following particulars : 




I 


COAGULATION AND SLOW FILTERS 


Turbidity in Parts 

Grains of Alumina Sulphate per 

Cube Foot of Water. 

per Million. 

Falling 

Turbidity. 

Rising 

Turbidity. 

Summer 

Water. 

100 

4*7 

3 ’ 1 

2‘6 

1 

0 

0 

1 

r 3’3 

107 

8-2 


Twelve minutes’ “sedimentation” is then allowed, and the water is 
turned on to a roughing filter composed of 5 feet of anthracite coal screenings 
of an effective size of 1 mm. (0*04 inch), and with a uniformity coefficient 
of 2'4. 

The filtration takes place at the rate of 85 million U.S. gallons per acre 
per 24 hours, and the filter is washed by compressed air and water at the rate of 
1 cubic foot of air per square foot per minute, and 0*67 to 075 cubic foot of water 
per square foot per minute, as often as the filtration head becomes equal to 2*5 feet. 

1 his roughing filter evidently acts like a degroisseur, and the whole of the 
5 feet retains turbid matter. A large bacterial reduction (on the average 
60 to 70 per cent.) is also produced. Without any assistance from coagulation 
the roughing filter can reduce water containing turbidities of less then 25 parts 
per million to a state fit for the sand filters. 

These sand filters work at the rate of 3'62 million U.S. gallons per acre 
per 24 hours, and consist of: 

4 feet of sand, specified as follows : 

Not more than 5 per cent, under 0*24 mm. in diameter 

55 55 1° 55 0 “9 55 55 

,, less ,, 9® )j o So ,, ,, 

The effective size is 0*30 to 073 mm., and the uniformity coefficient is 
r6 to r8. 

The sand lies on 3. inches of crushed sandstone, between 4 to | inch in 
size. 

Then 3 inches of crushed sandstone, between f and \ inch size. 

Then 6 inches of crushed sandstone between 3 and § inches in size. 

The bacterial results at present obtained would not be considered satis¬ 
factory when the bacterial content of the raw water much exceeds 6000 per c.c., 
but there is a marked tendency towards increased bacterial efficiency, and after 
six months’ work the limit is nearer 10,000 per c.c. 

As is usual in American filters, the B. coli tests are relatively better 
than might be expected, so that the large number of bacteria in the raw 
water are not necessarily pathogenic (see p. 515). The filtrate is invariably 
clear. 

To a British engineer the mere idea of using raw water of such a character 
is abhorrent. In fact, Mr. Fuertes has to perform not only filtration operations, 
but a process of purification which should rightly be conducted, at the 
expense of the people who produce the pollution, before the polluted water is dis¬ 
charged into the river. Setting this legal problem aside (which an engineer as 






















572 CONTROL OF WATER 

a citizen ought not to do), the engineering problem is most excellently solved, 
and the only adverse remark that can be made is that the filtration velocities 
given above are only very rarely attained, and that it is doubtful if good 
bacterial results can be produced if the raw water is simultaneously highly 
polluted. The preliminary studies were very complete, and it is probable 
that a great demand for filtered water and heavy pollution will not occur 
simultaneously. The substitution of a small degroisseur for a large sedi¬ 
mentation and coagulation basin is especially noteworthy. 

Mechanical Filtration. —The various processes of mechanical filtra¬ 
tion are entirely the invention of engineers in America, and the method has not 
as yet been systematically adopted in other countries. Consequently, anything 
but American experience on this particular subject is unreliable, and it may be 
doubted whether the full advantages of mechanical filtration have yet been 
attained except in the United States. 

As a rule, American waters may be considered as less subject to pollution 
by pathogenic bacteria than are either German or English waters. On the 
other hand, turbidity of a troublesome character (combined with abnormal 
colorations, tastes, and odours) is more common than in Europe. At present, 
therefore, the mechanical filter is seen at its best when dealing with a turbid 
water, and its weak points are most manifest in the case of heavily polluted 
waters containing many bacteria. 

Auxiliary processes, such as disinfection and coagulation, are more easily 
applied in conjunction with mechanical filters, than in the case of slow-sand 
filters. We may consequently consider the following suggestions as applicable 
in modern practice : 

(a) For water with a turbidity after sedimentation frequently exceeding 50 
parts per million, and which contains a fair proportion of particles less than 
o’ooo5 i nc h approximate in diameter, mechanical filters are indicated. 

(b) For heavily polluted non-turbid water, slow-sand filters are better than 
mechanical filters. 

( c ) If a water is of such a character that it possesses two objectionable 
properties (eg. colour and turbidity, or odours and extreme hardness) each 
requiring a separate treatment, mechanical filters are usually desirable. Sand 
filters should be adopted if the water is heavily polluted, and the treatment for 
the other objectionable constituent does not assist in removing bacteria, so that 
the water as delivered to the filters frequently (say more than 20 days in the 
year) contains more than 2000 bacteria per cubic centimetre as ascertained by 
Koch’s test. 

This last statement is derived from a consideration of the bacterial results 
generally obtained by mechanical filtration. There is no doubt that in many 
cases skilled bacteriologists can treat a water containing more than the above 
number of bacteria per cubic centimetre by mechanical filtration, and can 
regularly produce a filtrate containing less than 100 bacteria per c.c. The 
average supervisor (whose working tests are based on the clearness of the 
filtrate), however, cannot with certainty reduce the bacterial count below this 
number by mechanical filters if the raw water contains a number of bacteria 
considerably greater than 1000 to 1500 per c.c. Thus, the above rule is a practical 
one, and, if anything, is too favourable to mechanical filters as they are usually 
handled. It must not, however, be regarded as an expression of opinion that 
systematic preliminary tests of mechanical filters when preparing a large scale 


MECHANICAL FILTERS 


573 


project for filtering polluted waters are useless, since it is believed that their 
adoption may prove economically advantageous when systematic supervision by 
a good bacteriologist can be obtained. A truly scientific solution of the 
problem could only be given if it were possible to state the conditions in terms 
of the number of pathogenic bacteria in a given volume of the raw water 
(see pp. 515 and 569). 

The above rules may be regarded as correct, provided that no consideration 
is given to the available capital and labour, and other local conditions. 

Mechanical filters are cheaper in first cost, but are more expensive to 
maintain and to supervise than the slow-sand type. As usually installed, they 
contain a good deal of metal work, but the masonry construction employed at 
Baroda shows that this can be avoided where iron and ironworkers are 
costly. 

On the other hand, machinery with its expensive supervision is always 
necessary, except in cases where a 40 to 50 feet head of water is available. In 
modern types, however, special machinery, other than pumps, is but a minor 
item. Also, the area occupied is small in comparison with slow-sand filters. 

The development of the rapid, or mechanical filter, arose from efforts to 
clarify very turbid water, and when the bacterial rationale of slow-sand filtra¬ 
tion first became generally known, rapid filters were viewed with suspicion. 

The modern aspect of the matter may be summed up as follows : Rapid 
filters [require more care, and a higher grade of supervision, in order that 
biological results equal to those given by slow-sand filters may be obtained. 
Their use, therefore, is at present mainly advisable in new and rapidly developing 
countries, where labour is dear, but intelligent, so that skilled supervision is 
relatively cheaper than manual labour. It is also as well to use mechanical 
filters where labour is markedly inefficient, and of uncleanly habits ; since, the 
cleaning being done by mechanical means, such outrages as defecation on the 
filter beds are prevented. 

In principle, the mechanical filter consists of about 30 inches of sand, resting 
on 6 inches of gravel, drained by a system of closely spaced strainers. Great 
care was taken in the early days of such filters to obtain a sand of large 
effective size (up to o'6o mm.), and small coefficient of uniformity (1*5, or even 
as low as 1 ‘2). Experience has shown that the expense thus entailed is un¬ 
necessary, and at present any sand suitable for slow-sand filters is used. It is 
also found that the numerous washings which the sand undergoes rapidly 
produce a suitable grade of filtering material. 

The rate of filtration is high, generally 80 to no million imperial gallons, 
or 100 to 125 million U.S. gallons, per acre per day of 24 hours. This entails 
washing at intervals, which rarely, if ever, exceed two days. The formation of 
a biological Schmutzdecke can therefore hardly occur, even though favoured by 
other circumstances. Its place is taken by an artificial Schmutzdecke, formed 
by the addition of a coagulant to the raw water. A coagulating basin and 
apparatus (consisting of valves and pipes for regulating not only the addition 
of the coagulant, but also the proportion of the mixture of coagulating pre¬ 
cipitate and turbid matter that reaches the filter) forms an essential portion 
of every installation ; and, if the water is not naturally turbid, the addition 
of artificial turbidity, usually in the form of powdered clay, may be found 
necessary. 

The principles of operation are simple. The addition of a coagulant to 


574 


CONTROL OF WATER 


the raw water, combined with the sojourn of the water in the coagulating 
tank, produces a flocky suspension of coagulant, and turbid matter in the 
water. On entering the filter, these flocks pack together on the surface of 
the sand, and form an effective barrier to the passage of bacteria. The 
biological action of the Schmutzdecke is greatly reduced, if not entirely 
arrested, so that the filtration is mechanical in a far more essential sense 
than that used by the inventor of the term “mechanical filter.” 

To use a somewhat broad simile,—a mechanical filter arrests bacteria 
mainly as close-mesh wire netting arrests the flight of birds. Whereas, the 
Schmutzdecke and sand of a slow-sand filter arrest bacteria-much as a loose 
heap of bird-limed twigs catches birds. 

The velocity of filtration is large (roughly, 400 feet in 24 hours, say 109 
million imperial gallons, or 131 million U.S. gallons per acre). Thus, the 
head forcing the water through the filter is high, and the deposit of coagulating 
precipitate and turbid matter that forms on the sand rapidly clogs the filter. 
Hence, the filter must be washed at frequent intervals, and in order to save 
time and labour these washings are effected mechanically. 

Since a rapid filter passes through a cycle of operation in 20 to 30 hours, 
it is obvious that we have to form a satisfactory Schmutzdecke about once a 
day, so that we should test the working of a rapid filter every hour in order to 
have the effluent under as close a supervision as that obtaining in a slow-sand 
filter subjected to daily tests. This is obviously impossible, and forms the 
greatest defect in rapid filters ; which, from a bacteriological point of view, are 
liable to be markedly irregular in their working. While great improvements 
have been made of late years in this respect, rapid filters are still largely 
inferior to the slow-sand type, simply because the filtrate of the period 
immediately after cleaning cannot be so accurately classed as either good or 
bad, from a bacterial point of view, as is the case with sand filters during the 
first day or two after cleaning. 

Therefore in considering the installation of a system of rapid filtration, an 
engineer must be prepared for very irregular bacterial results, especially during, 
say, the first six months of working, while the supervising staff are acquiring 
local experience. 

It is doubtful whether this defect will ever be entirely overcome, although 
the rapid improvements of late years are encouraging. 

As this defect is probably the factor which is most adverse to the adoption 
of mechanical filters by British engineers, it is as well to consider the manner 
in which it may be most rapidly minimised. 

The method is fairly simple. Reasoning on the analogy of slow-sand 
filters, we require to form our artificial Schmutzdecke as rapidly as possible. 
Once, however, it is formed, the thickness should not be allowed to increase 
at the same rate, since this would produce a rate of increase in the working 
head of the filter which would cause the filter to need cleaning far too 
frequently. 

It is consequently obvious that during, roughly, the first hour after washing 
the filter should be worked in a manner which differs from that which is 
advisable when it is running normally. This change in method does not, as 
yet, appear to have been explicitly recognised, although there is little doubt 
that supervisors of filters are well aware of its existence. 

The general outlines are clear. Until a satisfactory Schmutzdecke is 


WORKING OF MECHANICAL FILTERS 


575 

formed, the filter should be abundantly supplied with the precipitate produced 
by the coagulant. The Schmutzdecke being formed, as may be recognised 
by the working head of the filter increasing, say, two or three feet above the 
initial head, the working becomes normal, and as little of the precipitate as 
possible should be passed on to the filter. The rate of increase of the thickness 
of the Schmutzdecke is thus kept low during the period in which the filter 
delivers a satisfactory effluent. 

In practice, the effluent from a mechanical filter is usually considered to be 
satisfactory when it is free from turbidity. In waters of the American type, 
where a large proportion of the particles of turbidity are of bacterial size, this 
test is probably fairly effective in discriminating between effluents which are 
bacterially safe and unsafe, although it is believed that the filtrate becomes 
free from turbidity somewhat more rapidly than it becomes bacterially safe, 
if less than too bacteria per c.c. is taken as an absolute criterion of safety. 
The matter has been systematically investigated by bacterial methods at 
Cincinnati, Berlin, Alexandria (Egypt), and elsewhere, and it may be inferred 
that the effluent is usually bacterially safe when the working head of the filter 
exceeds 3 feet. When, however, mechanical filters are used to treat waters 
which do not carry a large quantity of particles which are of, or near to, 
bacterial size, systematic bacterial tests are required ; and it is quite plain that 
a great economy in working can be obtained by ascertaining the minimum 
head at which a bacterially satisfactory effluent is delivered. The supervisor 
can then systematically alter the method of working as above indicated, and 
is thus enabled to largely diminish the frequency of the filter washings. 

The importance of these preliminary bacterial investigations is very great, 
and, if they are systematically carried out, the mechanical filter can probably be 
made quite as effective in removing bacteria as the slow-sand filter. Even 
under such circumstances it will usually be found that when the water which 
reaches the filter contains more than 2000 bacteria per c.c. (as estimated by 
Koch’s test), the working head required to produce a satisfactory effluent 
becomes so great that slow-sand filters are generally preferable to mechanical 
filters. 

In practice, the above theory is more or less roughly followed. The 
following methods have been adopted : 

(а) The water for a newly washed filter is taken from the bottom of the 
sedimentation tank, and, when the head exceeds a certain value (details are not 
given), the supply is drawn from the top of the tank. 

( б ) An extra dosing of coagulant is given after washing. It will be obvious 
that this method cannot always be applied to the aluminium sulphate process, 
for, unless the water is sufficiently alkaline to decompose the extra amount in 
addition to that usually added, unchanged aluminium sulphate will pass through 
the filter. It is therefore most frequently adopted in the iron and lime process 
where the necessary alkalinity can always be obtained by the addition of lime. 

(c) An artificial Schmutzdecke is formed by adding powdered clay to the 
water, either before, or simultaneously with the addition of the coagulant. 

It is somewhat doubtful whether this last process has been designedly 
adopted for the purpose at present discussed. It is usually referred to in 
reports as being resorted to in cases where, for a few days at a time, the raw 
water was abnormally clear, and coagulation slow, or entirely arrested for want 
(apparently) of nuclei for the precipitate to form. on. 


CONTROL OF WATER 


57 6 

{d) In many cases it has been found advantageous to add one-half the 
necessary amount of coagulant,—to allow the reaction to complete itself,—and 
later to add the remaining quantity ; and after an interval (generally shorter 
than that permitted between the two dosings of coagulant) to pass the water to 
the filters. I am unable to state the exact rationale of this process, or the 
advantages derived, but it is quite plain that such a method lends itself ad¬ 
mirably to the rapid formation of a Schmutzdecke, by the addition, just after 
washing, of the whole of the coagulant at the point where the second half 
usually enters, and thus securing (for say the first hour) that the whole of the 
precipitate reaches the filter. Later, the filtration head having attained a 
satisfactory value, the double addition process can be carried out. 

The methods here suggested must be regarded as tentative, and it is to be 
hoped that systematic investigations may be undertaken, and that the results 
will be published. 

In any case, no consideration need be given to any Filter Company’s tender 
which does not explicitly deal with this question of irregular working, by 
guaranteeing that the daily results of bacterial counts will not exceed some 
maximum, more than a definite number of times per annum. A tenderer might 
reasonably request three to six months preliminary operation, before rigidly 
complying with his guarantee. 

Bacterial Tests of Coagulation as applied to Mechanical Filters. —The doses 
of aluminium sulphate or iron sulphate which produce the best effect in reducing 
turbidity have been discussed on pages 558 and 568. The figures there given are 
those which are usually adopted previous to mechanical filtration. It is, how- 
ever, very doubtful whether they are those which are best adapted to cause the 
maximum possible reduction in the number of bacteria during the whole process 
of coagulation and mechanical filtration. The only available information is 
furnished by the experiments of Schreiber at Berlin {Mitt. Kong. Preuss. 
Pruef ungsa71sta.lt flier Wasserversorgung , 1906). 

If the reduction in turbidity were alone employed to judge the efficiency of 
the process, Schreiber found that 10 grains of coagulant per cubic foot (23 
grammes per cubic metre) should be employed, while the best bacterial results 
were obtained with 18 grains per cubic foot (43 grammes per cubic metre). 
Thus, with aluminium sulphate dosing at a rate of 23 grammes per cubic metre, 
one hour usually elapsed between the washing of a filter and the delivery of a 
bacterially satisfactory (50 bacteria per c.c.) effluent. With a dose of 43 
grammes per cubic metre, the period never exceeded 30 minutes, and was 
usually far less. 

As the coagulating tank held only one hour’s supply, it is doubtful whether 
the advantage is inherent in the larger dose, or is only due to the fact that the 
larger dose causes the filtering film, or Schmutzdecke, to attain the requisite 
thickness more rapidly. If this supposition be true, the methods of working 
detailed on page 575 probably advantageous bacterially, as well as in reducing 
turbidity. As a preliminary rule it may be inferred that the filtrate should be 
v asted until the increase in the woiking head over that initially required to 
force the water through the clean filter is twice that which is necessary to 
produce a non-tuibid effluent. The water Schreiber used would hardly be 
considered very turbid in America, so that this rule is possibly over-stringent for 
markedly turbid raw waters. 

Cleaning Filters .—The frequency of the cleanings of a mechanical filter is 


BACTERIAL TESTS 


577 

affected not only by the dose of coagulant, but (contrary to what is found to 
hold good in slow-sand filters) also by the rate of filtration. Wernicke (ut 
supra , 1907) finds the following results in the case of Posen water coagulated 
by aluminium sulphate : 


Rate of Filtration in 
Feet per 24 Hours. 

-; , 

Cubic Feet of Water per Square Foot of Filter Area 
Filtered between Two Cleanings. 

13 "2 Grains of Sulphate 
per Cubic Foot of Water. 

22 Grains of Sulphate 
per Cubic Foot of Water. 

393 

66 

98 

360 

9 2 

124 

328 

118 

x 54 

296 

148 

181 

263 

i74 

206 

230 

200 

236 

1 91 

1 ~a- 

-.- 

230 

262 


i ' 1 

These, experiments of Schreiber and Wernicke were carried out on far clearer 
and, probably, more dangerously polluted waters than are usually dealt with by 
mechanical filtration. They form, however, almost the only series of experiments 
on mechanical filtration in which bacteriological standards were systematically 
employed to indicate the efficiency of the filtration. The figures are probably 
applicable only to the local circumstances under which they were obtained, but 
they are more interesting to the British engineer than the far more extensive 
American experiments (reports of Water Boards of Cincinnati, Louisville, New 
Orleans, etc.). In these, bacterial tests were usually considered as of secondary 
importance in comparison with the removal of turbidity. The American method 
is obviously the easiest, and, when applied to American waters, it probably 
secures a bacterially satisfactory effluent. When mechanical filtration is applied 
to waters which are highly polluted and are not turbid, bacterial tests must be 
used to investigate the conditions of working, and in view of the great field for 
mechanical filtration in tropical countries, should soon become standard. 

Practical Details. —The design of mechanical filters is mainly in the 
hands of patentees. The following matters require consideration by engineers 
when selecting filters: 

The drainage system consists of pipes and strainers, and the difficulties 
caused, in slow-sand filters, by unequal resistances to flow, occur in an 
accentuated form. 

As a rule, the total head lost in the filter when the sand is clean, is equivalent 
to about two-thirds of the depth of the sand (approximately r6 to 2 feet head), 
and the loss in the strainers (the area of which is about 0*4 square inches per 
square foot) should not exceed one-half this quantity (say o'8 foot to 1 foot head 
at most, and usually 0*5 to o'6 foot). So also, differences in frictional head in 
the pipe system (due to unequal lengths of piping) should not exceed about 
o*2 foot. This condition generally leads to the area commanded by one system 
of pipes being from 12 feet square, to 18x15 feet, and the individual filter is 

37 












CONTROL OF WATER 


578 

made up of four such units, z>., varies from about 600, to 1100 square feet. The 
area is arrived at by a compromise between expenditure in the brass pipe work, 
caused by the large pipes, required to minimise the differences of frictional resist¬ 
ance, and a desire for as large a filter unit as possible, in order to economise in 
the valves and piping connecting the individual filters. When the conditions 
affecting the rejection of the effluent after washing are better understood, 
satisfactory working may be hoped for when the individual filters and the 
pressure differences in the pipes are larger than are now usual. 

The design of the strainers is of the utmost importance. Any dead water 
spaces, such as existed in the earlier types, are objectionable, and should (if 
possible) be filled in with concrete. But the tendency of design is towards 
continuous lines of perforated brass plates, the upper surfaces of which are 
slightly sunk below the concrete bottom of the filters. 

As an example, at Cincinnati 3-inch wide plates are spaced at 12 inches from 


Sjud S' Grate) 



centre to centre, and are perforated with 64 holes, ^ of an inch in diameter, per 
foot run. (Sketch No. 147.) 

At Columbus, the strainers are 2^-inch circular brass plates, with j^-inch 
holes, spaced 8f inches from centre to centre, in both directions, and hence the 
distribution of the water flow is obviously less perfect. (Sketch No. 147.) 

The old-fashioned rose, slit cup, or perforated pipe (Sketch No. 148) strainers 
screwed into pipes, must be regarded as decidedly inferior. These were usually 
spaced about four to the square foot, although such figures as 2b per square foot 
occur, and as dead water spaces are then more easily filled up the wider spacing 
should be adopted if such strainers are used. 

All strainers (even if not so designed) should be sunk at least 2, to 3 inches 
(better, if possible, 5, or 6 inches) below the general surface of the concrete, and 
the pits thus formed should be filled in with gravel, which should extend at least 
3 inches (and preferably, if the strainer distribution is poor, 6 inches) above the 
top of the concrete. 

The gravel is usually sized into two layers, the lower one J, to \ an inch 
average diameter, and the upper one o’o5, to o'i inch. 





















































SAND SPECIFICATION 


579 


The sand is generally 070 to 0*40 mm. in effective size, and the uniformity 
coefficient should be low, preferably not more than 2 (after, say, three months it 
will be reduced to 1*5, and the loss should be provided for). In cases where 
the washing is not effected by raking, a brass wire screen is required to retain 
the gravel, 10 meshes per linear inch appearing usual. 

The Cincinnati filters may be regarded as good practice, although the 
advance in design is so rapid that any specification is liable to be obsolete. 
The sand layer is 31 inches thick, and, on the average, the effective size is 
o*33 mm., and the uniformity coefficient is 2'o, although the figures for the top 
layer are o’29 mm., and 1*35. 

The sand rests on 7 inches of gravel, which is kept in place by means of a 
brass screen with apertures o'o63 inch square. The gravel layers are as 
follows : 

4 inches of j^th inch to \ inch in diameter. 

2 inches of ^th inch to j inch in diameter. 

1 inch of j inch to inch in diameter. 

1 inch of ^ inch to 1 inch in diameter. 

It will be seen that no figures have been given concerning the loss of head 
in the filters. 

In practice, the working head varies from 1, to 1*5 foot at the commence¬ 
ment, and becomes at least 2*5 feet before a satisfactory effluent is delivered. 
If bacterial results alone are considered, the head when the filtrate is turned into 
the mains should be at least twice the initial head. The filters are usually 
washed as soon as the head exceeds 12 feet, although cases where 20, or even 
26 feet is employed are not infrequent. 

It appears that the depth of water above the sand and the vertical height of 
the clear water pipes must always be so adjusted that the absolute pressure 
at the strainers is at least equal to the atmospheric pressure. No reason 
can be given, but if this condition is not observed the results are less 
satisfactory. 

Broadly speaking, the rate of filtration is about 300 to 400 feet vertical (say 
100 to 130 million U.S. gallons, or 80 to 100 million imperial gallons per acre 
per 24 hours). The results of bacterial tests generally indicate that the lower 
rate should be preferred. The matter is influenced by the effective size and 
uniformity coefficient of the sand. As an illustration, the case of Exeter (Mass.) 
may be mentioned, where the effective size of the sand being 0*24 mm., and the 
uniformity coefficient i'5 2 > the “usual rate” of “ 125 million U.S. gallons is 
reduced to 75 million gallons per acre per day.” 

It may be inferred that the effect of an abnormal effective size or uniformity 
coefficient of the sand is very similar in character to that produced in a slow- 
sand filter. In view of the relatively small quantity of sand required for all but 
the very largest installations of mechanical filters, it appears advisable to pro¬ 
cure a sand of normal character. So far as our present knowledge goes’, an 
effective size of 075 to 0^45 mm. and a uniformity coefficient of 17 to 2*2 
specifies a good working sand, but each firm of filter makers has its own 
particular ideas, and the effect of a badly sized sand is so marked that the 
expense of procuring the size required by the makers appears to be 
justifiable. 

Washing of Sand in Mechanical Filters. —Washing is effected 


5 8o . CONTROL OF WATER 

by reversing the flow of the water. Pressure water enters by the strainers, ancl 
passes through the gravel, agitating the sand. 

In the earlier filters, the quantity of water forced through the sand was 
only sufficient to loosen it, and the dirt was therefore loosened and the sand 
stirred up by rakes hung from rotating - arms. The water was mainly relied 
on to carry away the dirt and impurities collected on the sand, and the raking 
loosened the dirt, and secured an even distribution of water. 

Of late, it has become usual to obtain a superior cleaning by forcing so 
much water through the sand that the whole bed is lifted bodily. The 
advantages over the old system are not very obvious, and appear mainly to 
consist in the suppression of the small, and therefore inefficient machinery, 
used to work the rakes. The rapid adoption of the practice in existing plants 
shows that it possesses appreciable advantages. 

If water alone is introduced through the older types of strainers, it is found 
that passages are readily formed through the sand, and the washing will then 
be incomplete. This action is prevented, and an even and regular distribution 
of water is secured over the whole sand bed by the introduction of air under 
pressure in order to loosen the dirt, and afterwards removing the loosened dirt 
by water. 

At Cincinnati, where washing by water alone is employed, the escape level 
is 31 inches above the top of the sand, when at rest; the effective size of the 
sand being o‘33 mm. Of the sand that was initially carried over, about 
96 per cent, was found to be less than 0*45 mm. in diameter, so that any 
smaller difference in elevation would, in the long run, cause the effective size 
of the sand to be increased through loss of the smaller grains. It may be 
noted that the sand used had been selected and graded to such an extent 
that 7000 cubic yards of material were worked over in order to secure 4000 
cubic yards of filter sand. 

The best results are obtained at Cincinnati by applying the wash water in 
the following manner: 

For the first minute, at a rate of 0*50, to 075 of a cubic foot per minute per 
square foot of filter area. This loosens the particles of dirt and mud, which are 
“ stored up ” in the whole depth of the sand. 

For two or three minutes, at a rate of 2, to 2*25 cubic feet per minute per 
square foot. Under this rate of washing it is found that a few grains of sand 
are carried up as high as 29 inches, but only a small quantity rises as high as 
u*5 inches, and the main body of the sand only rises 10*25 inches. The 
exact details are interesting, although (since they are obtained with different 
filters) we cannot assume that the sands are identical in size and grading. 


Cubic Feet per 
Square Foot. 

A Few Grains Rise 
to a Height of 

A Small 
Quantity Rises 

The Main Body 
Rises 

« 

2*00 

2*05 

2*08 

2*i8 

2*37 

12 25 to 29 inches. 

13*25 to 29 „ 

14*0 to 29 ,, 

15*0 to 30 „ 

23'75 tO 30 >5 

11*50 inches. 
n* 5 ° „ 

13*25 „ 

14*00 „ 

2 i* 5 ° » 

10*25 inches. 
10*25 „ 

12 *25 „ 

T 3* 2 5 „ 

18*00 

















WASHING OF FILTERS 5 8 i 

The Jesuits are somewhat irregular, but it seems fair to infer that a rate 
much in excess of 2’6 cubic feet per minute would cause the whole body of 
the sand to pass over. It is also as well to realise that each filter apparently 
possesses a definite rate of washing which produces the best results ; although, 
in practice, the valves controlling the wash water are arranged so as to 
pi event a greater delivery than 2 cubic feet per square foot per minute. 
The total pressure of the wash water is equivalent to a head of approximately 
40 feet. This system necessitates a special design of strainers, otherwise the 
pressuie at which the wash water is delivered becomes too high for economy 
(see p. 582). 

I he figures which relate to the systems in which compressed air or rakes 
die employed to loosen the dirt are somewhat discordant, as the wash water 
merely removes the dirt after loosening by air or rakes. 

The major portion of the work is not effected by the water ; and, con- 



Sketch No. 14S.—Strainer and Air Pipes for Mechanical Filters. 


sequently, the strainers are not usually designed so as to produce an efficient 
distribution of the wash water. As already shown, when the strainers are 
properly designed, air injection and raking are not required. Thus, the 
figures now quoted are in reality greatly dependent upon the design of the 
strainers. Better results could probably be obtained were the strainers 
designed so as to secure a more equable distribution of the water over the 
whole area of the filter. 

Compare the perforated pipe strainers in Sketch No. 148, with the 
Washington strainer or those in Sketch No. 147. 

The following figures may be noted as affording partial answers to questions 
that should be considered when selecting one or other of the various patented 
filters and strainers. 

The velocity of wash water which just raises the sand, and fits it for cleaning 
by rakes, is about 07 foot per minute reckoned on the gross filter area, for sand 
of the following effective size : 






































































582 CONTROL OF WATER 

0*42 mm., and a uniformity coefficient of r8 ; and 0*5 foot per minute 
for : 

0*22 mm., and a uniformity coefficient of 1*5: where no air is used. In the 
latter case, no appreciable loss of sand occurs when the escape is 10, to 12 
inches above the surface of the sand, which is about 4 feet deep. A velocity of 
0*625 foot causes some of the finer sand to be lost. 

The loss of head in the strainers when the flow is reversed is somewhat 
high in actual filters, being about 12 feet for 1*1 foot per minute in the above 
cases, and therefore about 5 feet and 2*5 feet at the velocities used in washing. 
During filtration at a rate of 100 million U.S. gallons per acre per day 
(z.e. about 0*2 foot per minute velocity through the sand), the loss is 
approximately o*8o, to 0*85 foot. The strainers experimented on were the old 
cup type, and the losses in the case of plate strainers of the type used at 
Cincinnati, are apparently about 60 per cent, of the above values. 

Similarly, the velocities employed in two other cases for washing by raking, 
were : 

o'9 to r 1 foot per minute, on sand with an effective size of 0*63 mm., and a 
uniformity coefficient of i*i, and 2*3 feet deep. Long-continued washing in 
this manner did not apparently cause any noticeable loss when the escape 
trough was 15 inches above the top of the sand. 

Similarly, when sand of an effective size of 0*36 mm. was washed by raking, 
with the escape trough 25 inches above the top of the sand, no sand escaped 
so long as the velocity of the wash water was restricted to one foot per minute. 
But when the escape was lowered to 15 inches above the top of the sand, 100 
washings at the above velocity were found to produce an increase in the 
effective size of the sand to 0*40 mm. 

It is therefore plain that when such filters are enquired for, a careful sizing 
test of the local sand should be furnished to the firms tendering. 

In the first of the above cases the velocity of 2 feet per minute, which is 
that suitable for washing by water alone, could only have been attained by 
delivering the wash water at a pressure of at least 17 lbs. per square inch 
(besides all other resistances). The strainer system is therefore quite un¬ 
suited for this method of washing. Thus, when either water washing, or 
water plus compressed air washing is contemplated, the tenderers should be 
asked to specify the necessary pressure of the wash water, or of the air and 
the water. 

Where the washing is by water alone, effective work is only possible when 
the strainers are of the perforated brass plate type, and are buried in pits with 
sloping sides as shown in Sketch No. 147. The head required to cause the 
sand to begin to lift is usually approximately equal to the depth of the sand. 
Russell (_ Journ . of Ass. of E?ig. Soc., vol. 42, p. 323) gives the following : 

H Ji g° - r w > feet 

IOO 

where H, is the head of water required to lift d feet of sand, of a specific 
gravity p, containing W per cent, of voids. The formula is only valid when 
applied to sands ranging from 0*30 to 0*50 mm. in effective size. Russell also 
finds that when the sand has been lifted, the following figures occur for 
the relation between H, and v, the velocity of the wash water in feet per 
minute. 



VOLUME OF WASHING WATER 583 


Thirty-one inches depth of sand of an effective size of 0^33 mm., and a 
uniformity coefficient of i'o. 


H = 1*58 feet. 

H = 2*6 i „ 

H = 2*20 „ 

With 30 inches of sand of an 
uniformity coefficient of 1*4 to 1*5 : 


v — 2’o6 feet per minute. 
7 / = 2-54 „ „ 

^ = 2*96 „ „ 

effective size of 0*37 to 0*40 mm., 


and a 


H = 2*o 5 feet. v — 2*08 feet per minute. 

H 2 54 )> V=2’Z j 2 ,, ,, 

H = 2- 33 „ ^ = 2*89 „ 

The last figure in each case shows the relation when the sand is thoroughly 
loosened. Since the head lost in the strainers in reversed flow is from 0*5 to 
°'6 foot, when v=2'oo feet per minute, it is plain that the total head given by 
Russell’s equation will suffice : 


(a) To start motion in the sand when no water flows through the system. 

(b) To pass the water through the lifted sand and the strainer system, at a 

rate of 2 to 2*5 feet per minute, according to the amount of loosening 
which the sand has experienced. 


Thus, the supervisor should be able to adjust the valves so as to reduce 
the pressure during the stage (b) slightly below that which is required to start 
the motion. 

The use of compressed air is evidently an additional complication, and 
appears to be inadvisable, unless some corresponding advantage in the 
economy of wash water is guaranteed. 

The velocity of the wash water (when compressed air is employed) appears 
to be about 1*5 foot per minute, with sand of an effective size of o’28 mm. to 
0*36 mm., and i’8 foot deep. 

The area of the exit holes from the air pipes must be carefully proportioned, 
in order to secure an equable distribution, and about 0*02 to 0*03 square inch 
per square foot of the filter area is usual (Sketch No. 148). 

The pressure of the air is usually from 3, to 5 lbs. per square inch, and can 
apparently be calculated from the static head of the water over the orifices (i.e. 
up to the escape level), together with an allowance 6f 0*25 lb. per square inch, 
which apparently represents the friction in the sand. 

The figures are ’clearly not in agreement, although the observations ard 
accurate. It may be inferred that the design of the strainers is capable of 
improvement in this connection, and that the older types are unsuited for 
washing otherwise than by raking. 

In every case the size of the escape troughs requires careful consideration, 
since the flow in these must be sufficiently rapid to remove the dirt, while the 
whole volume of clean water in the troughs is wasted as far as cleaning or 
filtration is concerned. 

The volume of wash water used is by no means Immaterial. Local circum¬ 
stances have a great effect { but, on the average, it is about 5 per cent, of the 
total water filtered, falling to 2, or 3 per cent, in very favourable circumstances. 
Values as high as 10 per cent, are reported, but with experience it is believed 
that 7 per cent, should not be exceeded. 

During periods of bad water, however, these values may occasionally be 
doubled. 


584 CONTROL OF WATER 

Let us assume a bad day, with 7 per cent, of wash water used. The rate of 
washing with rakes is about three times that of filtration, so that unless we have 
a storage tank, the pump supplying pressure water must be capable of deliver¬ 
ing at a rate of one-fifth of the volume dealt with by one filter. In the case of 
washing by suspension, the figure is 60 per cent. 

Thus, for a large filter delivering about three million U.S. gallons per 
24 hours, a pressure water supply at the rate of two millions U.S. gallons, or 
if million imperial gallons, per 24 hours, is required for washing alone, and 
the gross pressure may be considered as approximately 20 lbs. per square inch. 
For rake washing, the figures are about one-third of those given above, and a 
pressure of 12, to 15 lbs. suffices. This means 17 horse-power in one case, 
and 5 horse-power in the other, for washing alone ; and, in a plant containing 
few filters, an elevated storage tank may prove economical. 

The details as to the quantity of water that should be allowed to run to 
waste after each washing, before a satisfactory effluent is obtained, are not very 
well known. The question was not considered in the earlier types, a non-turbid 
effluent being held to be satisfactory. Later bacterial tests on such filters gave 
such values as 3, or 5 per cent, with a test by no means as exacting as Koch s ; 
but a mere comparison of these designs, and modern types, shows that these 
figures would now be overestimates. 

I am inclined to believe that a skilfully managed filter (every care being 
taken to establish a Schmutzdecke as rapidly as possible) should pass Koch’s 
tests with not more than 2 per cent, of waste. 

It was also customary to disinfect filters at intervals of six months, by soda 
lye, or steaming. This appears to be unnecessary in modern types, where dead 
water space does not exist. 

Deferrisation, or Enteisenung.—Many ground waters contain iron in various 
forms. Such waters, when exposed to air, usually deposit this iron as a 
precipitate, giving rise to turbidity in the originally clear water. 

In other cases, the iron causes trouble by depositing as iron mould on 
clothes, or interfering with cooking processes, or by encouraging the growth of 
slime in the water mains (see p. 437). 

Similar remarks apply to waters containing manganese. 

Processes for the amelioration of such conditions are nearly all of German 
origin, and the literature is almost exclusively so. The best information in 
English is found in a paper by Weston (Trans. Am. Soc. of C.E ., vol. 64, 
p. 112). 

We may divide ground waters containing iron into three classes : 

(1) Those which begin to precipitate the iron as soon as aerated, and 

which generally contain iron in the form of ferrous hydrate. 

(2) Those which will hold the iron in solution indefinitely, even when 

aerated. In these cases the iron is usually combined with some 

vegetable acid, and appears to be in a colloidal form. 

(3) Waters which contain iron in both the above forms, and therefore 

deposit part, but not all, of the iron content after aeration. 

The amount of iron that will cause trouble cannot be definitely stated. 

In waters of the first class, o’3 parts per million usually appear to be safe, 
and over o'5 give trouble, although Weston states that in certain cases o'i part 
per million causes difficulty. 


REMOVAL OF IRON SALTS 


585 

In water of the second class, quantities up to 0*9 parts per million do not 
generally require special treatment. It must, however, be remembered that in 
the process of time the water yielded by a well which is steadily pumped from, 
frequently changes its properties ; and experience indicates that, while hardness 
is likely to diminish, the liability to iron troubles increases. 

In waters of the first class, it may be said that the only trouble is to ensure 
that the iron is precipitated and removed before it enters the supply mains. The 
weight of oxygen required to deposit the iron is only one-seventh that of the 
iron, and this is generally so small a quantity that special precautions would be 
required in order to prevent the water from becoming sufficiently aerated by 
pumping only. Difficulties arise from the fact that the precipitate of ferric 
hydrate in some cases remains in a colloidal form, and the water cannot be 
filtered in a reasonable period. The time required after aeration, before the 
water is fit for filtration, in the sense.that a coarse sand or fine gravel filter will 
remove all the iron, depends on the chemical constitution of the water. Usually, 
the presence of sulphates is favourable, and little trouble is likely to occur when 
they are present. Chlorides and nitrates are unfavourable, but they also in¬ 
dicate a polluted water. The presence of carbonic acid is also unfavourable ; 
but this effect may be greatly minimised by passing the water during, or after 
aeration, through fine sand, or gravel. 

We may generally treat ferruginous waters of the first class by aeration,— 
either that obtained by leaky glands in pumps,—or, where carbonic acid or 
other detrimental substances are present, by trickling the water over a rough 
filter of gravel, sand, coke, or broken bricks, followed by a rough filtration in 
order to remove the precipitated iron. 

It will be evident that where the precipitation is slow, storage (after aeration) 
improves the efficiency of the process ; but I am not aware of any cases where 
special arrangements for storage have been found useful. In Germany, nearly 
all the waters contain sulphates, and precipitate readily. In America, those 
waters which precipitate more slowly are usually treated by chemical methods, 
as will be later explained. 

According to Weston, in the case of 21 German plants, 12 have brick or 
coke aerators, with sand filters. In 5 others, the aerators are wooden slats, 
which may be considered as easily cleaned substitutes for a coke or brick aerator 
(subject to the disadvantage of possibly fostering bacterial growths). 

In the four other cases, various special aerators are used, composed of wood 
shavings impregnated with tin oxide. 

The aerators appear to be worked so as to pass water at a velocity varying 
from 15, to 48 feet per hour, and there are indications that a speed much above 
48 feet per hour would require the installation of a “ sedimentation ” tank between 
the aerator and filters. So far as can be ascertained, the rate at which the water 
passes through the aerator bears no relation to the content of iron in the water, 
and is probably far more influenced by the other salts present. 

With 4 parts per million of iron in the water, coke aerators apparently require 
cleaning after passing about 200,000 cubic feet per square foot. 

The final filters are of gravel, the mean diameter of the finest layer being 
about o'20 inch, and work at a rate varying from 12 feet to 70 feet per day, 
the mean being about 50 feet daily. 

It will be evident that these filters are in the nature of degroisseurs, rather 
than sand filters, and that the iron deposits not only on the top, but also in the 


CONTROL OF WATER 


586 

interstices. A thickness of about 65 inches of material, graded from o'2o inch 
to 2 inches mean size, is usual. 

If the constitution of the water is such that the iron remains in a colloidal 
state after aeration, we have (to all intents and purposes) a water of the second 
class. Such waters, as also those of the third class, should, as far as our present 
knowledge goes, be treated in the following manner after aeration. 

The methods are all founded on the principle of encouraging the transforma¬ 
tion of the colloids into a precipitate, by forming a second precipitate in the 
water. Thus, where the factor preventing precipitation is an excess of carbonic 
acid, a precipitate of calcium carbonate is produced by the addition of lime. 

Where the disturbing factor is of vegetable origin, the presence of iron is 
usually combined with a coloured water. The Anderson process (see p. 547 ) h as 
been successfully applied, but the most practical method appears to be the 
addition of sulphate of alumina and clay ; the clay with the alum hydrate 
forming a rapidly settling precipitate, and removing the colour and iron. 

In such cases, special provision for aeration is probably unnecessary, and 
there is a certain amount of evidence to show r that aeration previous to coagula¬ 
tion is in some cases positively harmful as regards reduction of colour. 

The water at Reading (Mass.) may be taken as an example. It contains 
iron, and is coloured by vegetable humus, the quantity of iron and the coloration 
being variable between the limits 0*3 and io - 3 parts per million of iron and at 
least from 40 to 70 on the colour scale adopted. 

The treatment consists of the addition of about 7*5 grains of alumina sul¬ 
phate and 4 grains of powdered clay per cubic foot of water. So far as can be 
judged, neither the iron content nor the colour in any way influence the 
quantities of sulphate and clay required. The action is probably entirely 
mechanical. This statement is also confirmed by the experience in certain 
other cases recorded by Weston, where the formation of a precipitate of 
calcium carbonate with the primary object of softening the water (see p. 59°) 
is found to cause the iron and colouring matter to assume a filtrable form. 

The treatment after the iron has been rendered filtrable requires special ex¬ 
periments. As an example, coagulation with aluminium sulphate, as above, 
followed by 1^ hours’ sedimentation, followed by aeration in a trickling filter, 
has proved satisfactory, and has also removed odours which previously existed. 

The waters now considered are generally fairly free from bacteria. Conse¬ 
quently, the filters employed are usually of the mechanical type, with large¬ 
grained sand, but where clay is added to destroy the colloids by precipitation 
sand of an effective size less than 0*40 mm. should be used. Where slow-sand 
filters are adopted, 7*5 to 10 million gallons per acre per day is found to give 
satisfaction, the filtration being a rough straining rather than typical filtration. 

A peculiar example exists at Posen, which may serve as a useful hint. The 
town is supplied with water from two sources, from one of which an initially 
clear water is obtained which deposits iron on standing. The other water is 
dark coloured, contains humic acid, and, judging by the description, is heavily 
stained with peat. These waters are very difficult to treat separately, but when 
mixed are easily filtered. It appears that one part of iron reacts with the 
colouring substance in any ratio between 2*2 and 7 parts, so that any reason¬ 
able mixture of similar waters may be expected to react in a favourable manner. 

COLOURED Waters. —The occurrence of colour in water is usually produced 
by prolonged contact with decaying vegetation. The chemistry is therefore 


REMO VAL OF COLOUR 



somewhat complicated. When accompanied by iron salts, the removal of the 
iron should be the first thing attempted ; although, even in such cases, the 
possibility that the addition of more iron (either as ferrous sulphate, or by 
Anderson’s process) may upset the chemical balance, should not be forgotten. 

In Great Britain, the colour produced by peat is well known, although of 
late years, owing to the custom of cutting deep catch-water drains through all 
the peat-bogs existing on the catchment area, it has become rarer. But, even 
at the worst, such discoloration usually causes but little trouble, since the 
consumers do not generally regard it as a matter for complaint. 

Slight peat discoloration is easily removed by sand filtration,—or by aeration, 
followed by a rough filtration. When organic chemical standards of purity 
are seriously regarded, peat may give rise to indications which may possibly 
suggest pollution. 

In hot climates, where the life and decay of vegetation are more intense 
than in Temperate countries, the colour problem becomes more urgent ; and 
(unlike peat staining) waters so affected are usually injurious to health. Details 
of successful processes vary in nearly every case, but the general principles are 
mainly the same. It should be remembered that while colour is the obvious 
source of offence, the real success of the treatment depends upon the effect 
which the treated water has upon the health of the consumers. 

In the first place, the source of the colour is usually evident, and where this 
can be removed at small cost, it should be done. Such steps as denuding the 
banks of the reservoir of turf and vegetation (for say 20 feet below high-water 
level), and removing all dead trees, are obvious. The expense, however, may 
be too great, and such excessive caution as was displayed in the case of some 
of the New England reservoirs by stripping the whole of the reservoir site of all 
vegetable earth appears to be a waste of money, because a proper process of 
purification, including its running expenses, would have proved less costly. 

The methods of purification may be stated as, aeration followed by treatment 
with metallic iron, or other coagulant, followed by filtration. It is only rarely 
that the coloration is so obstinate as to require all three processes. 

I shall therefore describe the most complex method that I am acquainted 
with, and would remark that one or other of these three alone usually suffices 
for the removal of all coloration. 

Chadwick and Blount ( P.F.C.E ., vol. 156, p. 18) dealt with a Mauritius 
reservoir water of the following 

Total solids 
Chlorine 
Free ammonia . 

Albuminoid ammonia 
Oxygen absorbed 
Nitrogen as nitrates 
Nitrogen as nitrites 
Hardness 


position, 


7’6o parts per 100,000 
r81 
0'002 
o’obq 
0*42 


5 ) 

!> 

>> 

5 ) 


2*5 degrees 


>» 

>> 

5 ) 

55 


and proceed as follows ; 

The' reservoir was drawn down as far as possible, and all the trees and 
vegetation were removed from the low-water line to 10 feet above high water. 
The roots and stumps of all submerged vegetation were removed by a grab 
dredger. 




CONTROL OF WATER 


588 

The compensation sluice was also lowered, so that the compensation water 
was drawn from the deepest portion of the reservoir, instead of being taken 
from the top layers as previously ; and a regular system was adopted of 
discharging the excess water, as far as possible, through this lowered sluice, in 
place of over the escape weir. 

The water intended for town supply is first treated with iron in an Anderson 
revolving purifier, where it takes up about 20 lbs. of iron per million gallons. 
It is then aerated by being passed into a series of trays, 2 feetx 1 footx 1 foot, 
with bottoms of delta metal plates, jfths of an inch thick, pierced with 4584 
holes per tray, each hole being 0^04 inch in diameter, and discharging o'87 
gallon per hour, under 8 inches head. Thus, one tray deals with 3988 gallons 
per hour and fifteen with 1,000,000 imperial gallons per 24 hours (with allowance 
for cleaning). The water falls 6 feet, and is thus aerated to saturation, and is 
then filtered by slow-sand filters of the usual type. 

This question of aeration by small orifices is interesting. The authors state 
that unless the head on the orifice exceeds a certain value, which they term the 
“ critical head,” the small threads of water tend to coalesce, and good aeration 
is not secured. Above this value, jets that have actually coalesced, auto¬ 
matically separate when allowed to do so. 

They further give the following table : 


Diameter of Hole 

Critical Head 

Delivery per Hour under Critical Head. 

in Inches. 

in Feet. 

Cubic Feet. 

Imperial Gallons. 

0*040 

0*67 

0*14 

0*87 

0*036 

0*92 

0*13 

0*83 

0*032 

1 *oo 

0*11 

0*67 

0*028 

1 33 

0*083 

0*52 

0*024 

rs 3 

0*083 

0*52 


A similar process has been applied at Nairobi (Uganda), except that here, 
after aeration, aluminium sulphate (about 6*25 grains per cubic foot), and 
approximately 3 grains of lime per cubic foot are added, and the coagulation 
thus obtained permits mechanical filtration to be employed. 

These processes are obviously somewhat complicated, and, while quantities 
of 1,000,000 gallons per 24 hours are successfully handled, the method employed 
by Tomlinson at Singapore ( P.I.C.E ., vol. 156, p. 42) seems more practical 
when really large volumes are dealt with. At Singapore the water is somewhat 
unsystematically aerated by turning the filter supply pipes upwards, and the 
filters, which work at a rate of about 3*2 feet per 24 hours of actual work (say 
900,000 imperial gallons, or 1,080,000 U.S. gallons per acre per 24 hours), are 
cleaned every 4, to 14 days, according to the season, and are aerated for 12 hours 
after each cleaning. The raw water is very bad, and the rate of filtration (in view 
of the frequent cleanings and the time lost in aeration) is slow. A far greater 
speed could be attained by really systematic aeration of the water by means of 
fountains, or sprays ; and the time required for aeration of the filters could be 
reduced by embedding a layer (say 6 inches) of porous carbon, or charcoal, in 
the filter sand, as is done in the case of at least one English town, where the 
raw water is turbid and discoloured by peat, after rain. 

















REMOVAL OF ODOURS 


5 S 9 

Colour in water occasionally assumes a colloidal form. The question has 
been discussed under the removal of iron (see p. 586); and, in addition to the 
methods already described, the coagulation processes there discussed may be 
employed. The most effective process when applied only to remove colour, 
appears to be an addition of powdered clay followed by coagulation with 
ferrous sulphate. The after filtration cannot usually be satisfactorily effected 
at such high rates as are used when precipitated colloidal iron is strained out. 
The question depends entirely upon the bacterial content of the water, and 
must be settled by a bacterial examination. 

The removal of colour either by ferrous sulphate, or by aluminium 
sulphate, may occasionally be found to proceed badly, even although the colour 
itselfrapidly combines with the hydrates of iron 01-9 aluminium {t.e. the 
coagulating precipitate). The causes are obscure, but good practical results 
have been obtained by producing the hydrates in a concentrated form by 
precipitating a solution of the coagulant with lime or sodium carbonate in a 
special vessel, and then adding the precipitate of hydrates to the coloured 
water. Such cases require careful investigation. Sometimes the precipitate 
and the mother liquor can be thrown into the coagulating basin as soon as 
formed, but occasionally I have found that this method is useless, and 
that success was only attained when the coagulating precipitate was freed 
from the mother liquor by decantation before adding it to the coloured 
water. 

Odours and Tastes in Waters. —These are usually caused by the 
decay of plants or animals inhabiting the water. They are therefore most 
frequent in hot climates, and in more Temperate countries usually occur in the 
summer and autumn. 

Treatment generally consists in the destruction of the organisms, the decay 
of which gives rise to the odours and tastes. 

A very common method is the application of copper sulphate. This salt 
(in a dilute solution of one part per million or less) usually effects the destruc¬ 
tion of algae. It is best applied by placing the requisite quantity in a bag, 
which is moved about the reservoir so that the salt dissolves slowly and 
uniformly. It will be found that two consecutive applications of copper 
sulphate at, say, a week’s interval are more effective than one of the same 
total quantity. The process requires care, since the presence of an abundant 
growth of algae or other organisms generally produces growths of living 
plants in the mains, which live on the products of the original organisms. If 
these are killed by copper sulphate, or other treatment, the growths in the 
pipes will die, and may temporarily give rise to worse conditions than those 
originally prevailing. 

As processes less specially adapted to the removal of taste and odours, all 
those described under Colour in Water, are effective. Also, in the case of 
slow-sand filters, merely diminishing the usual rate of filtration is in most 
instances beneficial. So far as I am aware, all difficulties on record occurring 
when sand filters are used, have been successfully dealt with by aeration and 
double filtration. This process is no doubt simple, but obviously must be 
frequently quite impracticable, for want of filters. From personal experience, 
I have found that aeration and a dosing with alumina sulphate and powdered 
clay (the water was too clear to give a good fall of coagulated matter without 
this addition) was very effective. Towards the end of the season of bad water, 


CONTROL OF WATER 


59 ° 

aeration was not required. I considered the water extremely offensive, but in 
these matters there is no fixed standard to appeal to. 

The most complicated process I am aware of is that in use at Charleston 
(S.C.), where a very shallow reservoir water receives the following treat¬ 
ment : 

(1) Copper sulphate in the reservoir. 

(2) Aeration. 

(3) Coagulation and two days’ sedimentation. 

(4) Aeration. 

(5) Mechanical filtration. 

(6) Aeration. 

The process is complicated, and I believe that the following defects 
exist : 

(1) No clay, or other finely divided matter is added to “help the 

coagulation down.” 

(2) Mechanical filtration is certainly less suited to deal with tastes, and 

odours, than slow-sand filtration. 

It should be realised that these matters are essentially biological in 
character, and that the correct manner of dealing with them, after their first 
occurrence, is to study the life-history of the plants and animals. The 
remedies should also be applied not at the moment when the odours or tastes 
manifest themselves, but rather when the first generation of the organisms 
appears. Considerable assistance is afforded by encouraging frogs and fish in 
reservoirs, and where the water is filtered before consumption, the presence of 
such animals is quite unobjectionable. 

Cases arising from the presence of dissolved gases {eg. sulphuretted 
hydrogen) should be the subject of special investigation. As a general 
principle, however, these gases usually occur in ground waters, and it is only 
very rarely that any undesirable factor in a ground water is not greatly 
improved by aeration. 

Softening Processes. —In principle, these processes are founded on the 
method introduced by Dr. Clark in 1841. 

The hardness of water is due to two causes, and may be divided into two 
classes, temporary, and permanent. Temporary hardness consists of 
bicarbonates of lime and magnesia, which may be considered as simple 
carbonates of these elements held in solution by carbonic acid gas dissolved in 
water. When this carbonic acid gas is expelled (as by boiling), the carbonates 
become insoluble, and are precipitated. 

Clark’s process consists in adding to the water a sufficient amount of lime 
to combine with the dissolved carbonic acid, and thus produce a precipitate 
not only of the carbonates already existing in the water, but also of those 
formed by the combination of the added lime and the carbonic acid in the 
water. 

The reaction is expressed by : 

Ca(HC 0 3 ) ? + Ca(H0)2 = 2CaC0 3 -f 2H 2 0 

The water presumably being already saturated with all the calcium carbon¬ 
ate it can dissolve, when no carbonic acid is present, the whole of the temporary 
hardness is removed. 


CLARKS PROCESS 


59 * 

This equation indicates that for every 100 parts of calcium carbonate 
existing as bicarbonate, or for every 44 parts of carbonic acid, 56 parts of 
freshly burnt unslaked lime are required, and 200 parts of calcium carbonate 
are precipitated. 

If, however, magnesium also exists in the water, in the form of magnesium 
bicarbonate, the results are more complicated. In the first place, the equation 
similar to that given above, shows that : 

Eighty-four parts of magnesium carbonate, or 44 parts of carbonic acid as a 
bicarbonate, consume 56 parts of lime, and 184 parts of the mixed carbonates 
are deposited. But magnesium carbonate is fairly soluble, so that it is 
usually necessary to double the quantity of lime, producing the reaction : 

MgC 0 3 + Ca( 0 H) 2 = Mg( 0 H) 2 . CaC 0 3 
so that the final result is : 

Eighty-four parts of magnesium carbonate combine with 112 parts of lime, 
producing 258 parts of a mixed precipitate. 

Thus, a priori, any calculation from the quantity of the carbonic acid, or 
the total weight of the combined carbonates, is impossible. In a natural 
water, however, although the alkalinity may vary from day to day, it is 
unlikely that the ratio of the lime and magnesia salts will greatly alter. 
Thus, if we are aware that, as a rule, one part of alkalinity per 100,000 
requires—let us say—three grains of lime per cubic foot, for proper softening, 
it is unlikely that the ratio will alter greatly over the whole year, and one or 
two estimates of the weight required (covering as far as possbile the whole 
variation in alkalinity) will usually suffice to enable a calculation of the yearly 
weight of lime to be made. 

Permanent hardness principally consists of lime and magnesia salts in 
combinations other than those above discussed. The effect which an addition 
of softening chemical will have can only be stated in general terms. The usual 
reactions are ; 

(i) CaS 0 4 + Na 2 C 0 3 = Na 2 S 0 4 + CaC 0 3 

That is to say, soluble sulphate of lime is thrown down in the form of chalk, 
by the addition of carbonate of soda, and the less objectionable sulphate of 
soda remains in solution. 

(ii) CaCl 2 + NaCO s = 2NaCl + CaC 0 3 

This is the same principle, chalk being deposited, and common salt 
remaining in solution. 

Similar reactions occur with magnesium salts. These processes (and 
many others) are often used for the preparation of waters intended for use 
in steam boilers. Their application on a large scale to the purification of 
water intended for human consumption is unusual, but is growing more 
common. I cannot but consider that their systematic use must generally 
(excluding very arid regions) be considered as indicating a fundamental 
error in the selection of the source from which the water is drawn. 

The bacterial results of a water softening process are merely accidental, and 
resemble those of a long sedimentation (see p. 55 O- 

If any suspended matter is present in the water, the precipitate will generally 
form round the suspended particles, and these will be rapidly carried down. 


592 


CONTROL OF WATER 


On the other hand, the precipitates obtained consist mainly of calcium carbonate, 
which is a granular, pulverulent substance, has but poor coagulating properties, 
and does not form an efficient Schmutzdecke on a filter. However, practical 
experience has shown that water softening processes do not materially interfere 
with coagulation, and the two processes may, where necessary, be carried out 
simultaneously. 

Such combined processes have been largely introduced in America of late 
years. In England, the Porter-Clark process is frequently employed for 
softening waters drawn from chalk wells. Since such wells generally yield 
clear waters of great bacterial purity, coagulation, or sand filtration, is rarely 
necessary. 

Practical Details. —These have been discussed in connection with the 
ferrous sulphate process. The main difficulties (other than the mechanical ones 
connected with the addition of milk of lime) lie in the time required for the 
reactions given above to be fully completed. 

Delay is chiefly caused by the presence of magnesia, since the reaction ex¬ 
pressed by the last equation is not only slow in itself, but appears to exercise a 
prejudicial effect on the previous reactions. 

The determination of the size of the precipitation basin is consequently a 
somewhat complicated matter. If the basin is too small, incrustations in the 
filter drains and pipes will occur, or the full benefit of the reactions cannot be 
attained, and the effluent will contain a certain amount of hardness that could 
be removed. 

The problem is really therefore intimately connected with local opinion as to 
the amount of hardness that is permissible. Waters exist in which at least 12, 
to 15 hours would be required in order to remove the whole amount of hardness 
that it is possible to deposit. A settling basin of this size solely for the purpose 
of ameliorating the water is usually more expensive than the benefits gained 
justify (see p. 564). If the water also contains a large amount of permanent 
hardness, and either the entire removal of the temporary hardness, or the 
partial removal both of temporary and permanent hardness, is necessary to 
produce a satisfactory water, the cost of a large settling basin may be justified 
in view of the fact that the permanent hardness can only be removed by means 
of the relatively costly carbonate of soda. 

The largest basin in practical use appears to be at Winnipeg, and holds 
eight hours’ supply. 

The chalk waters of southern England contain comparatively little permanent 
hardness (on the average 2 or 3 degrees only), and a very large proportion (28 
degrees is reduced to 3^ degrees, and 18 degrees to 6 degrees) of the temporary 
hardness is removed by one, or at the most three hours’ settling. But these 
must be regarded as favourable cases, since the magnesia content is small. 

We may sum up the facts by stating that six hours may be considered as 
normal (although probably somewhat in excess of present-day practice) for 
waters containing about 20 per cent, of their temporary hardness in the form of 
magnesia, and accompanied by an amount of permanent hardness such that a 
reduction of the temporary portion to 5 degrees gives a satisfactory water. 

The size of the reaction basin may be increased in the case of waters con¬ 
taining more magnesia temporary hardness, or permanent hardness, and may 
be diminished in favourable examples of less magnesia and permanent hardness. 

Careful laboratory experiments should be made in any particular instance, 


REMOVAL OF MAGNESIA SALTS 


593 

and should be checked by a fairly large scale test—say 1500 gallons—before 
the final designs are drawn up. 

A certain decrease in sedimentation capacity can be obtained by re-carbon¬ 
ating the treated water by the injection of carbonic acid, usually produced by 
the combustion of coke. After-deposits in the filters or mains are thus prevented, 
and the water is rendered more pleasant as a beverage. So far as my experience 
goes, the advantages over the original Clark process are most marked in the 
case of waters that contain but little magnesia. 

The precipitate, in so. far as it consists of calcium carbonate, is very readily 
removed, and the cloth screens introduced by Atkins give great satisfaction in 
the treatment of chalk water. These screens are washed by reversing the flow, 
and it will therefore be plain that they are less well adapted to deal with pre¬ 
cipitates containing a large proportion of somewhat glutinous magnesia hydrate. 
Difficulties, however, are unlikely, provided that the above rules are followed in 
the determination of the sedimentation capacity. 

In cases where magnesia hardness is of importance, the completion of the 
reaction can be somewhat hastened by stirring up (usually by compressed air) 
the old precipitate, and mixing it with the newly dosed water. The falling pre¬ 
cipitate in some way encourages the completion of the reaction. The sedi¬ 
mentation capacity can then be reduced to about one-half of that stated above. 
This is not the only advantage. If a magnesia water is treated by lime a small 
quantity of magnesia hydrate (?) always remains in solution, and is only deposited 
on heating. This hydrate (?) is a gummy substance, and may rapidly clog the 
feed valves of a water heating apparatus. The precipitate stirring process re¬ 
moves this hydrate, and is therefore an almost indispensable addition to softening 
processes when applied to waters containing magnesia which are largely used 
for boiler feeding or other purposes entailing heating. 

Regulating Apparatus Employed in Filtration. —The necessity for 
some method of regulating the quantity of water filtered is obvious. The head 
required to force the water through a filter, at a given rate, varies according to 
the construction of the filter ; and also more markedly, from day to day, accord¬ 
ing to the condition of the Schmutzdecke. This factor alone is responsible for 
variations ranging from a few inches, up to 5, or 6 feet; or, in mechanical filters, 
from 2 feet, up to 15 or 20 feet. 

The original regulating apparatus was a valve in the discharge main from 
the under-drains, which was adjusted by hand to pass water at the required 
rate, and gradually opened as the head necessary to pass the desired quantity 
increased. 

This was a rough method, and entirely depended upon the care and judgment 
of the operator. Later, a weir was added in order to measure the quantity de¬ 
livered accurately, and with careful operation perfectly satisfactory results can 
be obtained. 

The more usual method, however, consists of a telescopic tube raised or 
lowered by a screw, and provided with a graduated scale to show the quantity 
of water taken in over the circular weir thus formed. Adjustment by means of 
the screw permits a given quantity to be delivered daily, and is superior to the 
method of valve and weir, but the necessity for constant supervision is equally 

great. 

The discharge can be automatically regulated if the telescopic tube be fixed 
to a float so that the top of the tube remains at a constant depth below the 

38 


594 


CONTROL OF WATER 


water surface. The Philadelphia modification is probably the most reliable 
form, since the discharge is through a series of deep slots, instead of over a 
long, circular weir. As is shown in the general discussion on Weirs, an error 
in the position of the sliding tube {e.g. due to sudden change in the water level, 
accompanied by a sticking of the tube in its guides) produces far less variation 
in discharge under these circumstances. 

Burton designed the regulator shown in Sketch No. 149, which is in effect a 
balanced valve, governed by a piston, and the difference of the pressure on the 
sides a , and b, of this piston is plainly the head required to force the quantity 
of water delivered through the orifice cd. We thus see that: 

If w, is the weight of the piston, valves, and their connecting stem, when 
weighed in water, and a , is the area of the piston in square inches : 

The pressure required to lift the valve is : 

/= — lbs. per square inch —2'3 — feet head of water. 
a a 



Sketch No. 149. —Automatic Diaphragm Regulating Valves. 

Now, if q, is the quantity of water passing in cubic feet per second, and 
A, is the area in square feet of the hole in the diaphragm cd, we have 

g=cA\l 2gp, where c, is the coefficient of discharge for the circular orifice ; and 
p, is expressed in feet head of water. Hence we get : 

?- cA \/ 2 ’3 = 7*9i A / w cusecs 
V a St a 

since c, can be taken as 0*65, in view of the suppression of contraction. 

The details of the non-coned valve and valve seats given by Burton 
{Water Supply of Towns , Fig. 114) should be carefully adhered to. Where 
(as in Weston’s design applied to the regulation of mechanical filters) coned 
valves and valve seats are desirable for practical reasons, oscillations and 
hammering of the valve will occur. Weston largely, but not entirely, prevents 
this effect by the insertion of a stilling device in the form of a diaphragm with 
























































































REGULATING APPARATUS 


595 

a small hole in it, between the valve and the balancing piston. (Sketch 
No. 149.) 

Fuertes ( Water Filtratioii Works , p. 171) gives a sketch of a regulator 
consisting essentially of a weir closed by a slide, which is governed by a float 
actuated by the water level in the clear water well. This seems less liable to 
give trouble through sticking, than sliding tubes, although I cannot say that my 
own experience with sliding tubes has been unfortunate in this respect, and 
I have rarely heard them complained of. 

On examining the working drawings of actual examples of such sliding tube 
regulators, it will appear that a good deal of ingenuity has been devoted to 
securing water-tightness at the sliding joint, where the telescopic tube enters 
its holder. This seems somewhat unnecessary, since leakage at this point 
(unless large) matters but little, for what we are concerned with is not the 
absolute magnitude, but rather the amount of variation in the quantity of water 
passing, as the water surface in the clear water well rises and falls with the 
variation in working head. 

As an example, let us assume a variation in working head of 5 feet (which 
is greater than that usually permitted), and that when the filter starts working, 
the effective head producing leakage through the joint is 1 foot. 

Assuming a joint 4 feet long, and ^\th of an inch wide, we have an area of 
075 square inch and the leakage does not exceed 0*025 t0 °’°3> or as a mean 
0*027 cusec, or about 15,000 gallons per 24 hours, and under a 6-foot head the 
leakage in the same period will be about 37,000 gallons. 

Such a regulator may be assumed as intended to pass at least 2,000,000 
gallons per 24 hours, so that even if no adjustment of the regulating screw is 
made during working, it would actually pass about 2,015,000 gallons when first 
started, and ‘about 2,037,000 gallons when working at maximum head. The 
variation, therefore, is at the most a little over 1 per cent. Thus, it would appear 
that a plain metal joint, such as can be constructed by any workman provided 
with a lathe, will suffice for quite as accurate regulation as is necessary. 

If, however, for any reason such variation is not permissible, it will be quite 
evident that any ordinary hat leather packing will give all the accuracy we 
can possibly require. Personally speaking, in view of the fact that if the 
tube sticks, the Schmutzdecke may be ruptured, and unfiltered water may be 
delivered into the mains, I consider that a tight joint or complicated packing, 
should be avoided. 

A pitfall exists in the design of the upper portion of a sliding tube. Let 
us consider the case already sketched out. A 4-foot weir without end con¬ 
tractions, with its sill 0*50 foot below the water surface, will discharge about 
3'33 X 4 X 0*36 = 4*8 cusecs, or roughly 2,600,000 gallons daily. 

The area of a circular pipe 4 feet in circumference, is about 1*29 square 
foot, or the mean velocity of the water when it enters the pipe should be about 
3*7 feet per second. The mean velocity over the weir, even if no shock occurs, 
is actually somewhat less than 2*4 feet per second, so that the upper end of the 
pipe will barely carry the weir discharge. Thus, for safety, a bellmouth, of the 
form indicated, is necessary. The extra length of weir thus obtained reduces 
the head required to discharge 2,600,000 gallons per day, and in this particular 
case we may enter the region of low heads, where Francis’ formula ceases to 
be accurate (see p. 106). 

In practice, it is simpler to design the weir so as to pass the required 


CONTROL OF WATER 


59^ 

quantity under a fairly low head, say o'4o foot, and to adjust it accurately by 
observing the rise in the clear water reservoir as soon as operations begin. 

Influence of Climate on Processes for Water Purification.— 
The effect of hot or cold weather on various processes has been referred to on 
several occasions (pp. 520, 532, 554, and 587). 

Generally speaking, the hotter the weather the more effective all chemical 
processes will be. It is often difficult to effect a satisfactory coagulation in 
very cold water (eg. water drawn from rivers covered with thick ice). 

The difficulties are not entirely due to the temperature, as the worst cases 
occur when fairly clear and very cold water has to be coagulated. Success can 
usually be obtained by adding sufficient powdered clay to form nuclei on which 
the coagulating precipitate can begin to form. 

The processes which are distinctly more biological than chemical in 
character, such as sand filtration and natural sedimentation or storage, are 
most effective at temperatures which range from 55 to 75 degrees Fahr. In 
colder waters the processes are not very markedly less effective, but a sand filter, 
or other biological machine, requires a far longer period to get into proper 
working order. In hotter climates the processes are (as a rule) less efficient, 
and while a sand filter gets into the best possible working order very rapidly, 
it is less efficient than at a lower temperature, and becomes useless ( i.e . 
requires cleaning) far more rapidly. 

Certain exceptions occur. The action of a degroisseur is probably 
essentially biological, but, nevertheless, in very cold waters a degroisseur works 
badly, and is probably far less effective than coagulation when applied to very 
cold waters which contain turbidity of the same character as that which occurs 
in the southern United States. 

The general principles are now fairly obvious. Slow-sand filters are most 
suitable for insular climates, and best of all for Temperate insular climates. 
Degroisseurs should probably be covered when used in conjunction with 
covered slow-sand filters, and are probably very efficient in Tropical climates. 

Chemical processes are less affected by cold weather than are filters or 
degroisseurs, but are most efficient in hot climates. 

In Tropical climates, therefore, it is advisable to effect the major portion of 
the purification by chemical methods, and (unless repairs are difficult owing to 
scarcity of skilled mechanics) mechanical filtration is preferable to the slow- 
sand process. 


CHAPTER XI 


PROBLEMS CONNECTED WITH TOWN WATER SUPPLY 

Consumption of Water. —Average daily consumption over the whole year—Maximum 
daily consumption—Maximum hourly consumption—Effect of waste—Values of the 
ratios 

Maximum daily supply Maximum hourly supply 
Mean daily supply ’ Mean hourly supply 

Temperate climates—Eight hours main—Baths—Gardens—Hotter climates—Future 
variations of the ratios. 

Average Absolute Quantity of Water Used. —Minimum possible — British 
values—German values—American values—Australian values—Values obtained for 
domestic use exclusively—European figures—Indian figures—House to house versus 
hydrant supplies—Chinese and Japanese figures—South African figures. 

Trade Supplies. —Effect of rates—Private trade supplies. 

Prevention of Waste of Water. —Inspection—Water meters—Preliminary work— 
Leakage from mains—From house fittings—Necessity for repeated measurements— 
Standard fittings—Reducing valves—Sale by meter. 

Water Meters —Requirements of accuracy. 

Town Water Supply.— Special pipes, special valves, air, scour, etc. 

Special Problems Relating to Mains. —Examples—Calculation of the pressure at 
any point. 

Service Reservoirs. —Capacity required — Practical conditions introduced by the 
various objects of a service reservoir. 

Details of Construction of a Service Reservoir. —Masonry or Concrete Service 
Reservoir—Puddle lined type—Cement rendered type—Bitumen or asphalte sheeted 
type—Roofing. 

POPULA TION S TA TIS TICS. 


Consumption of Water.— Units : gallons per head per day. — The average 
daily consumption over the whole year is important in the design of large works, 
such as storage reservoirs, or supply mains. For works of the second order, 
such as pumping stations, or filter beds, the chief factor is the maximum daily 
consumption, which usually occurs in the hottest season of the year. Works of 
the third order, such as town mains, and their minor reticulations, are designed 
for the maximum hourly requirements, plus an allowance for the extra demand 
that may be caused by fires. These quantities are usually expressed in gallons 
per head per day. 

The ratios of these figures depend on the climate, the habits of the popula¬ 
tion, its standard of living, and above all, on the waste of water. 

The importance of this last factor has frequently been overlooked, chiefly for 
two reasons:—Firstly, the amount is usually not accurately known, and when not 
approximately ascertained, is invariably underestimated. Secondly, since waste 

occurs every hour of the day at a fairly constant rate, its effect is to minimise the 

597 


V 





CONTROL OF WATER 


598 

percentage variations of the total consumption, and to produce an apparent con¬ 
stancy in demand. Consequently, I believe that many of the rough rules at 
present employed for dimensioning the minor works of a town supply are in¬ 
correct ; and by way of indicating my personal views on the importance of the 
matter, I propose to deal with it first of all. 

As an example, I select the figures for a German city in the month of August. 
These are very accurately ascertained, and refer to a period of maximum con¬ 
sumption, to a very well constructed system, the habits of the people also being 
such as to ensure that very little of the waste was wilful,—in fact, without wishing 
to depreciate the skill of the supervising engineers, they, and not the house¬ 
holders, must be held responsible for any waste. I consider that the figures do 
both parties great credit, as they were obtained without any special efforts being 
taken to prevent waste. 

We have (Sketch No. 150) in percentages of the total 24 hours’ supply:— 


A.M. 

I 2—1 

1-85 

A.M. 

6-7 • 

5-28 

p.m. 

12-1 

5' 8 3 

P.M. 

6-7 • 

1 

5’°4 

1-2 

179 

7-8 . 

5’ 2 5 

1-2 

577 

7-8 • 

4-69 

2-3 • 

i*8o 

8-9 . 

6*oo 

2-3 • 

5'48 

8-9 • 

3'59 

3-4 • 

178 

9—10 . 

6-31 

3-4 • 

5*55 

9-10 . 

2’93 

4-5 • 

1-83 

10-11 . 

5*95 

4-5 • 

5 ’ 16 

IO-II 

278 

5-6 • 

275 

11-12 . 

6’04 

5-6 • 

5 ‘ l8 

11-12 . 

176 


We see at once that the minimum, mean, and maximum hourly consumptions 
are: 

Per cent. Per cent. Per cent, 

176 : 4*17 : 671 or, as 072 : 1 : 1*51. 

Now, in this city there is very little consumption for hydraulic power, and 
the habits of the people are such as to render any great demand for water 
during the dead hours of the night improbable ; nevertheless, for the six hours 
11 p.m. to 5 a.m. we find an average consumption of r8o per cent. 

The period is too long for us to assume that the pump counters registered 
water that was actually consumed later, and there are few service reservoirs in 
which the excess could be stored. It is therefore very hard to avoid the conclu¬ 
sion that a large portion of this consumption is waste, and later (see Prevention 
of Waste) I shall produce evidence to confirm this view. 

Let us merely assume that in this city two-thirds is waste. It consequently 
appears that 24 x 1*20, or over 28 per cent, of the water pumped is wasted. This 
is a somewhat unfair estimate, since, during these dead hours the pressure in 
the mains is higher than during the period of intense consumption (although it 
must be remembered that being a pumping supply, large variations of pressure 
due to changes in demand such as occur in a gravity supply, are improbable). 
It seems just, therefore, to conclude that the loss during the other 18 hours is 
not less than 1 per cent, per hour. We may thus assume that if no waste 
took place, the correct figures would be (as percentages of the present supply) 
076 : 3*17 : 570, or as 0*18 : 1 : 1 *68, and the whole 24 hours’ supply would be 
about 74 to 80 per cent, of the present consumption. 

These figures are at first sight somewhat astonishing, but they are amply 



















CONSUMPTION PATIOS 


599 


confirmed by other examples ; and, as 1 have already stated, they were (water 
meters not being used) very creditable to the engineers responsible for the service. 
The real lesson to be drawn is that in a well-maintained system supplying a 
careful, and—according to other than German ideals—an over-regulated popu¬ 
lation, 25 per cent, of the maximum day’s delivery is wasted through leaks, and 
defective fittings. Consequently, no engineer who has not as yet measured the 
waste from house fittings and the leakage of his mains is entitled to assume a 
smaller quantity. 

It is therefore plain that the ratios: 

Maximum daily supply : Mean daily supply throughout the year, 

and 

Maximum hourly supply : Mean hourly supply throughout the 24 hours, 

are to a large extent dependent on the waste of water ; and that all figures given 
should be considered as liable to modification if waste is systematically checked. 


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Sketch'No. 150.— Diagram of Hourly Variations of Supply. 


Thus, it appears that in cases where the systematic prevention of waste is 
contemplated, a logical design will take into account the alteration produced in 
the usual values of the ratios under consideration. The method is obvious 
Having obtained the ratios as affected by leakage waste, and the leakage waste 
by measurement of the consumption during the dead hours, we can assume that 
the leakage waste in other hours varies as the square root of the pressure in the 
service mains j and the new ratios can then be calculated. The general effects 
are apparent, since all major works will be diminished, some of them by as 
much as 33 per cent, or more. The town mains and reticulations will probably 
not be very greatly affected, except in the case of the larger mains, where a 
diminution of 15 per cent, may be attained. 

On the other hand, the dimensions of all works which have the equalisation 
of supply as their purpose, such as service reservoirs, will certainly be increased 
relatively to the smaller supply for which they are to be calculated ; and it may 
happen that they will prove insufficient in size even when designed according to 
rules based on the absolute value of the uncorrected supply. 





















































6oo 


CONTROL OF WATER 


Subject to these remarks, it may be stated that in Temperate climates, the 
maximum day’s consumption is about 1*5 of the average daily consumption, and 
that the maximum hour’s demand is also about 1*5 of the average hourly con¬ 
sumption. We thus deduce that the maximum consumption of any hour of the 
year is about 2*25 of the average hourly consumption. These rules are obtained 
from experience of carefully maintained and well-constructed waterworks. 

“ Eight Hours Main.”—A very common practical rule is thus arrived at. 
The supply main in towns where large service reservoirs do not exist should be 
proportioned on an eight-hour basis. That is to say, the pumps and the supply 
main should be capable of delivering the average consumption of 24 hours in a 
period of 8 hours only. The assumption amounts to: 


Maximum consumption during 1 hour = 3 x average hourly consumption 
during the year. 



Sketch No. 151.—Diagram of Monthly Variations of Supply for Years 1909-1910 

at London. 


The rule plainly affords a certain excess capacity which is useful in case of 
fire or other abnormal demands. 

In cases where the greatest possible care is taken to prevent waste, it is 
probable that the ratios are as high as: 

Mean daily : Maximum daily : : 1 : 1*7 

Mean hourly : Maximum hourly : : 1 : 3 

but such values are only obtained by systematic and unremitting efforts to 
minimise waste. (Sketch No. 151 shows the variation in consumption by 
months and is therefore more applicable to such questions as the draught from 
storage reservoirs than to the variation of the daily ratios.) 

Where the waste is considerable, the ratios are greatly diminished, but actual 
figures are not available for such cases, since great losses by waste are almost 
invariably accompanied by a systematic neglect of all measurements. 

Besides waste, the habits of the people influence the above ratios. A 











































DAILY AND HOURLY VARLATLONS 


601 


population accustomed to a daily bath will evidently draw heavily from the 
mains in the early morning hours, and the standard of living being high, 
the house fittings may be expected to be of good quality, so that waste is 
consequently minimised, and both causes tend to produce a large hourly 
consumption ratio. 

On the other hand, where the town authorities permit the water supply to 
be utilised for gardening purposes, although we may expect a very high daily 
ratio ( e.g . at Rochester in Victoria where the average supply is 54 gallons 
per head per day, the maximum daily supply reaches 215 gallons per head 
per day, being mainly employed in watering fruit gardens), yet the hourly ratio 
is not likely to be large, as watering is usually done in the evening, when 
domestic consumption is small. 

If a considerable portion of the supply is utilised for trade purposes, we may 
expect both the hourly and daily variations to be reduced. 

In hotter climates, while the hourly variation is much the same as in 
Temperate countries, the daily variation is largely increased. The values for 
a series of Australian cities where garden watering is not permitted show a 
maximum value of 2*25 for the ratio ; 

Maximum daily supply 


Average daily supply 


, and an average value of i‘9o. While, for climates 


such as the Punjab, the dry zone of the United States, or South Africa, where 
a hot summer succeeds a cool winter, the average daily ratio may rise as 
high as 2*25, and maxima of 2*40, and 2*50 occur where irrigation is not 
permitted. 

In Insular Tropical climates where the changes in temperature are not 
very marked, the ratio is lower than usual. For instance, at Colombo the 
value of the daily ratio oscillates between no and 1*46 ; and since this city is 
not provided with water-closets, and is well looked after as regards waste, it 
appears that these values may be considered higher than those usually obtaining 
in Equable Tropical climates. 

In respect to the probable direction in which future variations of the ratio 
may be anticipated,—any increase in the standard of living, or in the trade of a 
town may be expected to reduce the daily variations, but will probably increase 
the hourly variations. 

Average Absolute Quantity of Water Used. — In a civilised 
community, there is an absolute minimum which has been fairly closely 
attained in many different countries. In several cities in the Midlands of 
England it is about 18 gallons (say 22 U.S. gallons) per head per day. This 
has only been reached by constant inspection, and has in a sense been forced 
on the population by the paucity of the available supply. While no discontent 
is expressed, and no inconvenience is felt, I cannot say that I think such a 
consumption is an ideal to aim at. Such cities are by no means popular 
residential places, and any community which contents itself with so small a 
provision may be considered unfortunate, in that it deliberately adopts a less 
high standard of life in reference to its water supply. 

I believe that a city is well supplied for the requirements of the British 
climate, which actually uses (abnormal waste apart) about 22, to 25 gallons 
(i.e. 26 to 30 U.S. gallons) per head per day; this, allowing for trade 
consumption, means that each citizen enjoys approximately 15 to 18 gallons 
per day. With a normal allowance for waste, this would work out at 30 to 35 



602 


CONTROL OF WATER 


gallons (36 to 42 U.S. gallons) per day, which is slightly less than the 
consumption of well-inspected residential quarters in London. 

It may be objected that I am here advising a larger supply than has 
frequently sufficed, but to this I would reply that in such cases the scarcity 
of water has induced a sparing use, and a standard of living (in the matter 
of water) has been produced which custom alone renders tolerable. 

I consider it an engineers duty, in so far as it lies in his power, to foster 
an advance in the general standard of living, and if I personally have any doubt 
as to whether the above standard is correct, it is only in regard to future 
sufficiency. 

It must also be remembered that an abundant supply of good water is 
no mean factor in a city’s equipment, from the point of view of competition 
in trade. 

Starting with this figure as a minimum, we may say that British cities are 
rarely, if ever, supplied with more than 50 gallons (60 U.S. gallons) per head 
per day. 

In German cities the present practice is to allow a somewhat smaller 
quantity than in Great Britain, but there is little doubt that an increase will be 
found advisable should the present advance in prosperity continue. The 
limits are 12, to 30 gallons (say 14, to 35 U.S. gallons), and the mean appears 
to be about 22 gallons (say 27 U.S. gallons) per head per day. These figures 
are for partly metered supplies, and for unmetered water an increase of 20 per 
cent, is recommended. 

In American cities the supply of water per person is on the average far 
larger than in Europe. Whilst it is a matter of notoriety that the pumps 
which form the water meters of many American cities are exceedingly leaky, 
and that waste from house fittings is in many cases regarded as of no 
importance ; there is no doubt that the population does use more water for 
legitimate purposes than a similarly situated European population. I am 
quite unable to consider that this greater consumption is in any way undesir¬ 
able. The standard of living amongst Americans is high, the daily bath is a 
widely spread habit ; and, while I fully agree that waste should be avoided, the 
large consumption per head in many cities, where waste has been cut down 
to a quantity comparing favourably with European practice, can only be 
regarded as a sign of a high civilisation. The larger figures, however, can 
only be explained on the assumption that continued and obvious waste is 
permitted. 

The statistics for hi cities with populations of over 25,000 are as 
follows : 

Maximum consumption 270 gallons (324 U.S. gallons) per head per day. 

Average „ 88 „ (105 „ ) 

Minimum „ 26 „ (31 „ ) 

/ . ! f t ? \ | ' \ . ' * j J , f ' V « { i ' 

For 76 cities, with a population less than 25,000, similar figures 
were : 

Maximum consumption 124 gallons (149 U.S. gallons) per head per day. 
Average „ 5 1 „ ( 61 „ ) 

Minimum „ 8*5 „ (10 „ ) „ 


PUREL V DOMESTIC CONSUMPTION 


603 

There is, of course, little doubt that in the higher figures waste, or extensive 
watering of gardens (frequently both), r must occur ; but in view of the habits 
of the people, it appears undesirable to design works for an American city to 
supply less than 50 gallons (60 U.S. gallons) per head. 

I am the more convinced of this, since in Australian cities, inhabited by a 
people as prosperous as the Americans, and where continued and obvious 
waste is as infrequent as in Europe, the average consumption of all towns 
where the water supply is plentiful is 48 gallons (58 U.S. gallons) per head. 
In smaller towns (some of which are not well supplied) the average is 
30 gallons (36 U.S. gallons), and in these places trade consumption is almost 
negligible. 

The following information is recorded not for any value attached to 
the absolute figures, but as a comparison enabling an engineer to test his 
own values. 

(i) Absolute Consumption of Water in purely Do?nestic Use. —Whitney at 
Newton, Mass., found that : 

(a) The consumption at the kitchen tap (average of five persons per 
house) was 5*5 imperial gallons (6^67 U.S. gallons) per head 
per day. 

Where a second tap existed, it consumed ri imperial gallon (i‘3 U.S. 
gallon) per head per day. 

ip) Water-closets. 

First closet. 5 imperial gallons (6 U.S. gallons) per head per day. 
Second „ 2*2 „ (2*6 „ ) „ 

(c) Baths. 

First bath. 4*1 imperial gallons (4-8 U.S. gallons) per head per day. 

♦ Second „ o-8 „ (ro ,, ) „ 

Thus, we arrive at 14 to 15 imperial gallons (17 to 18 U.S. gallons) as a 
fair minimum value for a population leading what may be considered as a 
comparatively comfortable existence, with no waste. 

This result is confirmed by Cooper {Trans. Am. Soc. of C.E. , vol. 55, p. 43 °)> 
who found that a small educated population, too addicted to the luxury of 
baths (from a popular point of view), consumed 20 imperial gallons (24 U.S. 
gallons) per head daily, and he believed that the purely domestic use was 
167 imperial gallons (20 U.S. gallons) per day. 

Hunter {P.I.C.E., vol. 137, p. 44 ) gives for domestic purposes, solely, in 
London (waste included) figures ranging from 55 imperial gallons (66 U.S. 
gallons), which includes stables and carriage washing, down to 14-3 imperial 
gallons (17 U.S. gallons) in a locality where daily baths are less frequent. 

Data for requirements, exclusive of trade supplies, are more easily obtained, 
and the following, which refer to the period about the years 1895-97, are given 
by Griffith ( P.I.C.E. , vol. 117, p. 190) subject to the annexed remarks : 

{a) The towns are notorious as possessing a large percentage of working- 
class people. 

{ b ) To my personal knowledge, the standard of comfort in several cases is 
below that of England as a whole, and the figures for London, although 


CONTROL OF WATER 


604 


swollen to some extent by waste (1 believe by about 15, to 20 per cent, on the 
average), may be considered as more applicable to residential cities. 


Derby 
Nottingham 
Liverpool. 
Leicester . 
Manchester 
Norwich . 

i U L 


. 13’ imperial gallons (15'6 U.S. gallons) per head per day. 


• 13-5 

55 

55 

(i6'2 

55 

) .. 

55 

• 15 

55 

55 

(18 

55 

) „ 

55 

. 14 

55 

55 

(16*8 

55 

) .. 

55 

• 13 

55 

55 

U ' 6 

55 

) .. 

55 

. 10-5 

55 

55 

(12 - 6 

55 

) .. 

55 


London Water Companies (now merged in the Water Board) : 


New River . 20*6 

Lambeth . -22*3 

Kent . . 2 2 *9 

West Middlesex 24*8 
Southwark and 
Vauxhall . 24*4 

East London . 25*5 

Chelsea . . 28*8 


Grand Junction 31’2 


imperial gallons (247 U.S. 
,, ,, (26 8 

» „ ( 2 7'5 

rt ( 2 9‘ 8 

» >, ( 2 9‘3 

» „ ( 3°‘ 6 

>> }) (34 5 


(3 7*5 


gallons) per head per day. 
) >> ” 

M ) JJ ” 

55 ) 55 ” 

55 ) 5 ) 55 

5 5 ) 5 5 55 

(waste occurs). 

„ ) per head per day. 

(more residential 
than others). 
„ ) per head per day. 


(ii) Total Consumption .—The following figures are not easily comparable, 
since they include trade consumption as well as domestic use. 

For British cities, for all purposes, the figures range from : 


* 


Consumption 

per Head per Day. 

f ■ 

Leicester . 

16 imperial gallons (19 U.S. gallons)) 

Wigan 

17 

55 

55 

(20 

V 

Sheffield 

22 

55 

55 

(26 

)\ 

Carlisle 

2 3 

55 

55 

hi 

„ ) 

Nottingham 

2 4 

55 

55 

(29 

.. ) 

Birmingham 

2 4 

55 

55 

(29 

„ ) 

Liverpool . 

2 5 

55 

55 

(3° 

>. )J 

Leeds 

43 

55 

j » 

(5 2 

” >1 

Brighton 

43 

55 

55 

(5 2 

„ ) 

! Aberdeen . 

43 

55 

n 

(5 2 

) l 

Plymouth . 

43 

55 

?> 

(5 2 

.. ) 

! Perth . 

* 

5° 

55 

5) 

(60 

.. ) 


Remarks. 


These must be 
considered too 
low. 

These are suffi¬ 
cient, but leave 
little margin for 
an enhanced 
standard of 
consumption. 

These are high, 
but two include 
supplies to ship¬ 
ping. 


The French figures range from : 

11 imperial gallons (13 U.S. gallons) to 170 imperial gallons (202 U.S. 
gallons), 


















DOMESTIC AND TRADE CONSUMPTION 


605 


but the consumption is apparently on the average somewhat higher than that 
in Great Britain, the difference probably being due to more systematic dis¬ 
couragement of private trade supplies. 

Other Continental cities range from : 


9 imperial gallons (11 U.S. 
17 „ (20 

to : 


gallons) at Venice, readily explained by 
the situation. 

,, ) at Amsterdam, also explained by 

the situation. 


50 imperial gallons (60 U.S. gallons) in the lake towns of Zurich and 
Geneva, 

and 200 imperial gallons (250 U.S. gallons) in Rome, 

which is really a legacy from the Imperial City, although the restoration of the 
aqueducts is a modern achievement. 

For Indian conditions the facts are more complicated. As a matter of 
experience, 6 imperial gallons (7*2 U.S. gallons) per head per day appear to 
be sufficient. Harriet ( P.I.CE ., vol. 143, p. 276) gives the following figures 
for Raipur : 

1893- 4 Average 4^4 imperial gallons per head per day. 

1894- 5 » 5' 8 

l8 95“6 ,,69 5 ) 5 ) 5 J 

1896— 7 ,,74 55 55 55 

1897- 8 „ 8-o „ „ 

The steady increase cannot be entirely regarded as extra consumption, and 
is probably more attributable to increased leakage. 

The general rule, however, is to design with a view to 8 or 10 imperial 
gallons (10 to 12 U.S. gallons) per head per day ; and this may be considered 
as the maximum day’s consumption, since the water of most Indian towns is 
pumped from wells or rivers. 

As examples, Simla with about 12 per cent. European population is supplied 
with 8 gallons. Amballa with 7 gallons, with an extra allowance for the gaol 
and barracks. 

The above figures refer to towns in which the water is not delivered from 
house to house, but drawn from street hydrants, and public fountains. Whereas, 
in Bombay, and less markedly so in Calcutta, the supply is from house to 
house. In the former town we find 35 imperial gallons (42 U.S. gallons), some 
of which is waste ; and in the latter 25 imperial gallons (30 U.S. gallons) almost 
entirely for domestic use. 

We may therefore assume that the 8 to 10 gallons usual in India is due to 
the poverty of the population. Nevertheless, the advantages gained by the 
introduction of a pure water, if acceptable to the population, are so great that 
I should personally be prepared to advocate even such small supplies as 3 or 4 
imperial gallons (say 4 to 5 U.S. gallons) per head per day, when money was 
scarce, as preferable to the usual city well with its abnormal pollution and 
consequent infection resulting in outbreaks of cholera. 

Following Indian experience, the present practice of English-speaking 
engineers is to consider 8 to 10 gallons as sufficient in China. But facts do not 
confirm this, since Hong-Kong is supplied with 17 to 18 imperial gallons (20 to 


6 o6 


CONTROL OF WATER 


23 U.S. gallons) ( P.I.C.E ., vol. 100, p. 247), and even this amount is apparently 
inadequate ; which, in the case of a town with no water-closets would be 
peculiar, were it not that the requirements of the shipping are relatively large. 

At Shanghai, with about 22 per cent, of Europeans, the figures are from 50 
to 70 imperial gallons (60 to 84 U.S. gallons) per head per day (Johnson, Trans. 
Am. Waterworks ’ Engineers Assn., 1907, p. 252). 

So also, Moore (P.I.C.E., vol. 180, p. 297) designed for 10 imperial gallons 
at Hankow, and was requested to provide 20 imperial gallons (24 U.S. gallons). 
Making every allowance for “ Chinese face, 5 ’ I cannot but agree with the 
Mandarins. 

The Japanese figures given by Johnson (ut supra) also seem to confirm the 
above. They are : 


("Average . 
Tokio A Maximum 
^Minimum 

('Average . 
Yokohama^ Maximum 
[Minimum 

{ Average . 
Maximum 
Minimum 

( Average . 
Maximum 
Minimum 


14 imperial gallons (17 U. S. gallons) per head per day. 


*9 

j ) 

)> 

( 2 3 

55 

) 

33 

33 

9 

• 

99 

>> 

(II 

55 

) 

33 

33 

20 

99 

33 

(24 

55 

) 

33 

33 

24 

99 

J) 

( 2 9 

55 

) 

33 

S3 

16 

99 

33 

(19 

55 

) 

33 

33 

2 5 

55 

33 

( 3 ° 

55 

) 

S3 

33 

33 

55 

5 ) 

(40 

55 

) 

33 

33 

17 

5 5 

S3 

(20 

55 

) 

33 

33 

2 3 

55 

33 

(28 

55 

) 

33 

33 

33 

55 

33 

(40 

55 

) 

33 

33 

12*5 

55 

33 

(i 5 

99 

) 

33 

33 


We may therefore conclude that Oriental communities should (where the 
money is available) be supplied with water on a scale but little inferior to a 
German population. Where funds are scarce, I consider that it is the engineer’s 
business to boldly ignore all rules, and to give the best possible supply, without 
regard to previous experience. 

South Africa.—The following figures, tabulated by Lindesay (P.I.C.E., 
vol. 158, p. 420), will make it perfectly plain that the principles deduced above 
have already been applied in South Africa. They may be regarded as very 
creditable to all concerned, whether engineers or town councillors. 


AVERAGE DAILY SUPPLY. 

Port Elizabeth . 9^5 imperial gallons (11*5 U.S. gallons) per head per day. 


Johannesburg . 

10 

33 

33 

( 12*7 

33 

„ ) 

33 

33 

Cape Town 

3 i 

33 

33 

( 37 

33 

>. ) 

S3 

33 

Pietermaritzburg 

5 ° 

33 

33 

( 60 

33 

„ ) 

33 

S3 

Durban 

62*5 

33 

33 

( 75 

33 

a ) 

33 

33 

Pretoria . 

87 

33 

33 

(101 

33 

» ) 

33 

33 


(includes gardens). 

Trade Supplies . —Except where otherwise stated the preceding figures 
include the consumption of water for manufacturing purposes. As already 
remarked, this fact renders any very close comparison of the figures impossible, 
and it will also partially explain the large variations in the consumptions per 
capita that appear in any tabulation of statistics of water supplies. 

The actual ratio between trade and domestic consumption must vary not 




WASTE OF WATER 


607 

only in different towns, but also in different years in the same town. The 
experience of the London Water Board when a uniform system of water rates 
and charges was introduced all over the London Water Supply area, to replace 
the varying charges of the old Water Companies, shows that a very slight rise 
in the charge for water suffices to cause large consumers (both for trade and 
domestic purposes) to instal private water supplies wherever local conditions 
are favourable. Statistics are very hard to obtain, but two cases are frequently 
quoted. The private (well) supplies in a certain district in South London are 
capable of yielding 5 per cent.(more than the gross capacity of the Waterworks 
Authority’s installation. At Liverpool a similar excess used to occur, but this 
has diminished since the introduction of a better water supply. 

In projects for town water supplies the engineer usually has some trade 
statistics to guide him. Nevertheless, a careful census of trade supplies should 
be taken, and in drawing up the final design the engineer should carefully 
consider whether it is advisable to endeavour to secure the custom of the trade 
consumers by low rates, or to let them shift for themselves. While the first 
course is obviously more preferable, the solution actually adopted must entirely 
depend upon local circumstances. 

Prevention of Waste of Water.—I have previously taken occasion to-express 
my views on the great importance of waste from leakage, and have referred 
to its possible prevention. 

The principal source of leakage is found in defective house fittings, such 
as taps and service-pipes. In good modern practice, leakage in mains laid 
down in the streets is infrequent, and, except in gravelly soils, is usually manifest 
soon after occurrence by subsidences in the roads, or by the appearance of water. 
An engineer who takes charge of a system laid previously to 1880, say, (even 
though under the best supervision of its date) will, however, be well advised 
to institute systematic search for leaky mains and open joints. 

The methods of detecting house leakage are two : 

(i) House to house inspection , combined with a systematic replacement of 
defective fittings. I consider this to be most undesirable. In the first place, 
the Waterworks’ Authorities cause trouble to all householders (whether careless 
or otherwise). Secondly, although this method when energetically carried out will 
reduce waste to its lowest point, the engineer is never exactly informed of the 
results obtained, and apart from his own personal curiosity on the matter, is un¬ 
provided with any accurate figures to justify his action when discontent is excited. 

It is also evident to any observant individual that the engineer is taking no 
steps to enquire whether “ his own fittings ” (i.e. the service mains) are leaky ; 
and since this must be regarded as a very practical objection to the method, 
I cannot recommend it except as a temporary expedient preliminary to the 
introduction of the second plan. 

(ii) The Water Meter System .—This necessitates more preliminary work, and 
also a fairly large outlay on plant. A sketch of the mains and piping of the district 
to be dealt with, showing all stop-cocks, is first prepared. The approximate 
supply is then estimated, and the locality is divided into isolated sub-districts 
(which may render some alteration of the mains necessary), so that the total 
water entering each can be measured by a meter of such a size that the maximum 
supply does not exceed the capacity of the instrument which it is proposed to use. 

All stop-cocks must then be made easily accessible, which, if the system 
is not laid out with a view to meter work, is often somewhat difficult. 


608 CONTROL OF WATER 

The meter is then fixed, and diagrams are taken to ascertain the initial 
consumption. 

Thereafter, the process is as follows : 

About midnight the meter is set to record the flow, and inspectors visit 
each stop-cock and listen with a stethoscope for the sound of flowing water, 
which is best heard when the cock is only partially open. Each “ sounding 
cock 55 is noted, and after testing, all are shut off, and remain so for half an 
hour. The record of this half-hour gives the leakage from the mains, and 
the houses supplied by all stop-cocks which gave a sound are inspected next 
day for defective fittings. 

Diagrams are taken off the meter daily until the district is in good order, 
and thereafter, say three times each month, so that any fresh leakage can be 
detected, and, if large enough, sought for. 

In well-constructed mains the leakage outside the houses is small, eg. in 
three cases recorded by Stewart ( P.LC.E ., vol. 66, p. 348) the minimum flows 
were 1,500 gallons, 2,000 gallons, and 2,000 gallons per hour, and the leakages 
from the mains o, 50, and 150 gallons. So that defective house-fittings were 
responsible for more than 90 per cent, of the leakage, even when the mains were 
in relatively bad order. 

In view of this fact, it is plain that no effective measures for the prevention 
of waste are possible, unless legal powers are obtained either to enforce the 
repair and renewal of faulty fittings, or to cut off supplies in cases of proven 
and continued waste. 

The sale of water by bulk through individual meters fixed in the pipes 
supplying each consumer is an obvious alternative, and is the most equitable 
method for trade supplies. The application of meters to domestic supplies is 
most objectionable, since any stint in the domestic use (not waste) of water 
is sooner or later likely to be visited by natural penalties far outweighing any 
private advantage that may possibly be derived. The legal provisions against 
sale by meter which occur in several American cities may be regarded (if 
rigidly restricted to domestic supplies) as founded on a high, even if merely 
instinctive, sense of rightful sacrifice for the advancement of public welfare. 
Opposition to the infliction of penalties for wilful or continuous waste appears 
less likely to be entirely caused by public spirit. Also, as a matter of finance, 
small meters are relatively costly and the interest on the investment entailed may 
easily exceed the value of the water which their use prevents being wasted. 

To those unacquainted with the usual amount of waste the results are 
surprising. In a city where fittings had been subject to regulation and inspec¬ 
tion for some two years, the following figures are typical for areas served by a 
single meter (ut supra). 


SUPPLY IN IMPERIAL GALLONS PER HEAD PER DAY. 


Before Starting the System. 

After Three Meter Inspections. 

Total Daily Rate. 

Night Rate. 

Total Daily Rate. 

Night Rate. 

81 *8 

64*0 

34 'i 

9‘9 

68-3 

457 

3 i *9 

I 5 *° 

41*6 

27*4 

27-4 

8*3 

61 *o 

55 '° 

47-2 

23*8 




















SALE BY METERS 609 

And, in the district as a whole, the consumption for all purposes was reduced 
from : 

Daily. Night Rate. Daily. Night Rate. 

49 377 to 32 17-5 

It must be remembered that the improvement thus obtained is essentially 
of a temporary nature, and that if inspection is neglected, the old rate will 
recur after a period measured only by months. 

The cheaper classes of house fittings, such as are usually supplied by 
builders, deteriorate very rapidly, and become leaky. In some cases, therefore, 
the waste inspectors are instructed to perform such minor repairs as the 
insertion of a washer, without troubling the householders. 

Where the pressure in the mains is great, some authorities have obtained 
legal powers either to enforce the installation of only such fittings as satisfy 
a certain standard of water-tightness, or to instal their own fittings at a fixed 
charge. 

Local conditions, and the views of the community on a proposal which may 
have obvious objections, must be considered before adopting either of these 
methods. 

There is also another method of minimising waste which deserves attention, 
especially in gravity supply systems. This consists in the introduction of 
reducing valves, so that the pressure in the mains can never exceed a fixed 

amount. 

These valves prove useful, especially in cases where the area supplied 
varies markedly in level. They then not only diminish waste in the lower lying 
districts, but also increase the available pressure in the higher, which frequently 
suffer from lack of water. 

The final results of measures for the prevention of waste, or metering of 
supplies, are very difficult to predict. The methods adopted in selecting the 
supplies to be metered or tested for waste have great influence on the results 
obtained. If consumers are metered or inspected at their special request 
only, no particular effect on the consumption can be expected until perhaps 
more than 50 per cent, of all householders have adopted the system. If, on 
the other hand, houses are first inspected, or metered, which are notoriously 
badly maintained, a considerable decrease in consumption may be anticipated 
almost immediately ; but the fixing of a meter is regarded in the light of a 
penalty, and the authorities become as popular as detectives. 

The best system is to endeavour to meter all trade supplies, and to sell this 
water by bulk, while water for domestic requirements is supplied at a fixed 
rate, independent of the quantity actually used, waste being checked by street 
meters measuring the total consumption of, say, 200 to 500 houses, as already 
described. 

Under such circumstances, the daily consumption per head may be 
decreased by 50 per cent, (even when the initial consumption was not very 
large, eg. 32 to 16 gallons, 01*42 to 21 gallons), when the system is in full swing, 
and about 20 per cent, of the total supply will then be unaccounted for. If every 
supply is metered, a further decrease of 10, to 15 per cent, may be anticipated, 
and not much more than 10 per cent, of the water will remain unaccounted for. 

The most modern information on the subject is found in reports on 
“ Waste of Water in New York, and its reduction by Meter and Inspection,” 

39 


6io 


CONTROL OF WATER 


principally the work of Fuertes, where the influence of conditions and variations 
in local policy is most ably discussed. 

Mr. Fuertes states that even in America waste through leaky street mains 
must be considered as unproved. I had previously come to the conclusion tha 
such wastage was non-existent in Europe, and it therefore appears that the 
enormous consumption recorded from many American cities should be regarded 
as arising almost entirely from house waste, and not from any appreciable 
leakage from street mains. 

The question of the accuracy of the records remains uninvestigated, 
although it may be remarked that the very large consumptions per head are 
usually recorded in cases where the supply is pumped ; and if a badly 
maintained pump is used as a water meter, it is quite possible that the recorded 
figures bear no particular relation to the quantity actually pumped. 

Water Meters. —It is quite impossible to describe all the types in 
existence, and their design is best left to specialists. What is really desired, 
from the point of view of a householder, is a meter which works noise¬ 
lessly (it must be remembered that water pipes are excellent conductors of 
sound). 

The requirements concerning accuracy of registration are variable. If the 
meter is used for selling water by bulk to private customers, a carefully 
calibrated and correctly registering instrument is necessary. If it is used solely 
for the detection of water waste, unimpeachable registration of the maximum 
flow is not very essential (since this only lasts a few minutes), but the meter 
must record the total quantity passed by a long continued small flow with 
certainty, accuracy in the rate of flow being less material. 

For example, in a meter for the measurement of the total water supplied to 
a large town, correct registration of even so large a flow as io gallons per 
minute is immaterial ; whereas, a waste detection meter should register the 
total quantity passed by a flow of cri gallon per minute, over a period of even 
ten minutes. 


SYMBOLS. 

Problems connected with town water supply. The ordinary units are used. 

d, with an appropriate suffix, denotes the diameter in feet of any pipe, d' is used when 
the diameter is measured in inches. 

D, is a general symbol for the total demand by domestic consumption, fires, etc., during 
any individual hour, expressed in cusecs. D„ ia . T and D e (see p. 616). 
h, is used for the total loss of head, in feet, in a main of varying diameter conveying a 
constant quantity of water. 

Ii, is used for the similar loss of head, when the main supplies water at various points 
along its length. 

/q, h , /i, (see p. 615). 

K, is a contraction for - 

ioooff s 

k, (see p. 616). 

/, is the length of a main, in feet, when the diameter is uniform throughout the length /. 

L, is used for t when we consider different portions of the length /. 

Q 0 , is the quantity of water, in cusecs, entering the length l or L. 

Q l5 or Q e is the quantity leaving the length 1 or L. 

q, is the quantity, in cusecs, drawn off from the main, per foot run. 

Thus ql — Q 0 — Qi, and yL = Q 0 - Q e . 

q x , (see p. 617). jj 

x, x v y, 2 (see p. 617). 

2 is the symbol for summation. 



PIPE BENDS AND SPECIALS 


611 


SUMMARY OF EQUATIONS. 

Uniform volume of water. 

64QV Q%/ 

= 2 5° ( L^^ .[Inches] 


More accurate formula. h ~ 

Variable volume of water. 

h = 


- -Q 2 2 .' 


1500 d b ‘ 6i 


L 


1000.# \ 
L 


fQo 2 + Q 0 Qe + Qe^ 

[ 3 /’ 


3000^° 


, 5 Qo~> if Qe — 


H = 


,Qo^Qi 


IOOO dj 5 


It is not proposed to enter into the details of construction and maintenance 
that form the principal duties of a town waterworks manager. Local 



conditions are so important that any general rules are almost useless. The 
designs of street water pipes and mains that are used in London are suited to 
Eondon conditions, but in my opinion have frequently been adopted, even in 
British cities, where a cheaper construction would have sufficed. 

Modern practice, however, tends towards leaving these matters mainly in 
the hands of the local manager, and since I consider this is advisable, I do 
not propose to obtrude my own (equally local) ideas. 

The dimensions of bends, tees, and other “ specials ” used in street mains 
may be ascertained from any pipe founder’s catalogue. Similarly, such matters 
as air valves, reflux valves, scour valves and automatic cut-off valves (to 













































































































































612 CONTROL OF WATER 


provide for possible breaks in the mains) are usually procured from and 
designed by specialists. 

The installation of these valves is advisable and the general principles of 
their location are obvious. Air valves are placed at the top of each crest in a 
large main and wherever a site near the crests of a small main which affords 
no possibility of contamination can be secured. Scour valves are placed at the 
bottom of valleys in those places where opportunities for discharging the 
surplus water into a drain or stream are easily secured. 

Personally I distrust automatic cut-off valves: breaks rarely occur in well- 
laid mains and therefore the “ automatic ” cut-off valve usually sticks when it 
should act. 

Special Problems Relating to Mains — The most convenient method 
of treating problems relating to pipe mains of variable diameter, or those which 
convey variable quantities of water, is to consider the total loss of head. 

Let the given main be made up of: 

A length of 4 feet, of diameter d L feet; a length 4 , of diameter d 2 feet; a 
length 4, of diameter <4 feet. 


v dP ' " 

Let O = 7 rdd— — 7 T— v 2 — etc., cusecs 
4 4 


be the quantity of water passing. 

Note.—i cusec = 22,500 imperial gallons per hour = 27,000 U.S. gallons per 
hour. 

Then we have: 

V\ = C* / ^Si, and if /z, is the total head lost: 
v 4 

/ i =2^=2^!4 =s _ 6 4Q^ feet 

C*d Vcv 5 


Now, as a fair approximation, we can put C = 80, and it 2 = 10. 
We thus get h 


Q 2 -P feet, 


1000 d h 

where /, and z/, are expressed in feet, or : 

h = 25oQ 2 2^ feet, . 


[Inches] 


where h , is in feet, and is in inches, and, if still greater accuracy is 
desired, the simplified Tutton formula gives : 

Q 2 / 

^ = 75oo 2 "a^3> w ^ th ^ = 100 ba< % incrusted pipes), 


and one-half this value may be assumed for clean pipes ; where C x = 140. 

Let us now consider the problem of a main of uniform diameter d, and length 
L, where Q 0 , cube feet per second enter at the initial point, and a supply q, per 
foot run is drawn off by service pipes, so that the quantity passing at a distance 


x, from the initial point is Q — ax , and the velocity at this distance is 

4 

Thus, the element of head dh , lost in the length dx, is: 

dh = g cgff 6 * a 

TT-d°C 2 - 









LOSS OF HEAD IN MAINS 


61 


3 


Integrating, since h — o, when x = o, the head lost in the length L, is 

64L 


h = 


C*d*n* 

L 


1000 d 5 

L 


(Qo 2 -?QoC+— 

3 (Qo 2 -Q.?l+^) 


(Q«! 


+ QoQ?+ Qe 


ioood 5 

L (Qo 2 ) 


) 


or, if we put Q 0 —^L=.Q e , 

We get, h — 

f 

and if O e = 0, h *= 

iooo<? 5 3 

From a combination of the two results given above, we get the following 
fairly accurate and easy method of obtaining the loss in a main of varying 
diameter, with branch mains leaving it at different points. 

Let a quantity Q 0 , enter the main, and let the first length be / l3 and its 
diameter also let Q l5 be the quantity flowing in the main when the diameter 
changes to d 2 . 

Let us assume that Qi = Q 0 (i —p\ where is small. Then the head lost 


O 2/ Q 2/ / 

in the length l x is not greater than — ~° \ nor less than j -r( 1 —/ + — ) 

& 1000 dF 1000 d } 5 \ 3 / 


Qo 2 A 


/ 2 


Thus, = _Nh(i~P), or, 


IOOO 

QoQ di 


1000 dN* rn 1000 d-I 

is a minimum value which does not probably differ more than f r0 m the 

3 

true value, and since the value of C, may vary as much as 10 per cent, in a 
short length of pipe, it is sufficiently correct to say that the total head lost is 
obtained from : 


H = 2 Hj= feet, 


IOOO 


dj 


where / x and d 1 are in feet. 

,Q<AQi 


Or, H = 2502 


d' 1 5 


[Inches] 


where d\ is in inches. 

Qo is the quantity entering the length / 1} and Q 1} the quantity that leaves 
it, and the order of the quantities in the summand suggests a regular and 
systematic method of calculation. 

If greater accuracy is required, the formulae : 

H = s Q ° 2 + QiQ<> ±Qi 8 _A_ for i ncrust ed pipes, 

, „ ^,Qo 2 + QiQo+Qi 2 h c \ 

and H = 2—--XL ■ for clean pipes, 

9000 ^i 5 - 33 r r 

may be used. 

These formulae may be applied in order to calculate the pressure that exists 
at any point of the main system. 

In actual practice, it would appear advisable to use the larger values of H, 
not so much because of incrustation in the pipes (which should rarely be allowed 
to reach a magnitude such as is indicated by C 1 = ioo, in Tutton’s formulae), 
but to allow for the intense and localised draught that may occur during fires. 
























614 


CONTROL OR WATER 


Very elaborate investigations of the pressures obtained at various points in 
a network of mains are given by Lueger (.Die Was serversorgung der Stddte). 
The formulae are too complex to be of practical use, even if the possibility of 
an outbreak of fire at any point in the network did not render the fundamental 
assumptions highly doubtful. 

In actual practice, such questions are best solved by trial and error. 

Thus, (Sketch No. 153) assume that a loop exists in the mains, which is 
represented by ABCD. Let Q x , reach A, by the pipe xA, and Q y , leave C, 
by the pipe C y . Also let a quantity be drawn off from the main ABC of a 
length equal to / x , between A, and C. Also a quantity q 2 , from the main ADC, 
the length of which is l 2 . 

Thus, Qz—Qy = ? l + ?2- 



Sketch No. 153.—Diagrams for Branched Mains and Terminal Reservoirs. 


Assume that Q*, divides at A, into Q 1} flowing in the main ABC, and into 
Q 2 , flowing in the main ADC. 

Then, assuming that /i, is the difference in pressure between A, and B, 
we have; 

Ji — Qi (Qi-g'i ) 4 __ Q2 (Q2 ^2) 4 

1000 dR 1000 dR 


Now putting Qi=zQ x and Q 2 = (i — z)Q x we obtain a quadratic equation for z 

which is independent of h and which enables us to determine the ratio Qi 

Q2 

when d 1 and d 2 are given. So also if Q l5 Q 2 and h are given we can determine 
di and d 2 . 

If, later, a third main of a length / 3 , is laid to C, from another point E, the 
excess of pressure at which, relative to the pressure at C, is h 3 , its discharge 
























SER VICE RE SER VO IRS 615 

Qsj say, (under the assumption that the pressure at C, is unaltered) can be 
obtained by the usual equations. 

The most probable supposition, however, is that the delivery Q y , remains 
constant. We can then determine the new pressure at C, as follows : 

The total delivery to C, under pressure differences h, and // 3 , is 

Q17W1 + Q2—■£ r 2 + Q3~£3 5 where q z is the supply drawn off from the 
main EC. 

Let us assume that the new pressure differences are h\ between A and C 
and // 3 , between E and C, where h\—h z —{h~h') so that the pressure at C 
exceeds the former pressure by h—h\ and calculate the new deliveries at C, 

which will be respectively, (Q.-q,) ^ 

where ^ 1} q 2 and q 3 are assumed to be small in comparison with Q x , Q 2 
and Q 3 . 

The sum of these should be equal to Q,,. We thus get on substituting for 
^ 3 a quadratic equation for ti, and the increase in pressure at C, is h—h'. 

The above example is taken from an actual case where it was desired to 
erect a public fountain at the point C, and serve e?i route (by means of the 
third main) a newly erected building. 

I suspect that more complicated problems require such detailed statistical 
information that it is but rarely that the equations will prove useful. 

Service Reservoirs. —Service reservoirs are required for two purposes. 
When placed between the storage reservoir and the town, at the lower end of a 
long supply main, they permit of the main being designed so as to deliver a full 
day’s supply in 24 hours, whereas if no such equalising reservoir existed, the 
main would have to be capable of delivering water at a rate corresponding with 
that of the maximum demand ; which, if only hours are considered, is about 
170 per cent, of the average demand per hour taken over the whole 24 hours 
of the day on which the maximum demand occurs. 

Similarly, in a pumping scheme, a service reservoir permits the pumps and 
connecting main to be designed for a uniform rate of delivery, in place of one 
varying with the demand, and if convenient (as in small schemes) we may 
arrange to run the pumps for say 8, 10, or 12 hours only per day, the reservoir 
storing up the surplus delivery for discharge during the hours when the pumps 
are idle. 

When used for this purpose, the theoretical volume of the reservoir is 
evidently that required to equalise the draught over the day on which maximum 
consumption occurs (or more accurately, the day of maximum variability of 
consumption). In some actual examples this would amount to about 60 per 
cent, of the average day’s consumption, or say 35 per cent, of the maximum 
day’s consumption. The precise calculations are not of great importance, 
however, as the condition which really determines the size of a service reservoir 
is not variability of draught, but rather the time during which the supply main 
is likely to be out of order, and this evidently depends on such local considera- 
ions as its length, construction, whether duplicate or not, etc. 

The question is determined by experience, and no accurate solution can be 
given, but the capacity of such equalisation of supply reservoirs rarely exceeds 
three days’ supply, unless the supply main crosses a river or other obstruction 
rendering repairs more than usually tedious. 

Similarly, in a pumping scheme we must not only consider the repairs to 



6i6 


CONTROL OF WATER 


the mains, but also those to the pumps, so that the type of pump installed and 
the surplus power must also be taken into account. 

It is evident that the most economical solution will largely depend on local 
circumstances, and in a flat country where no easily accessible sites for service 
reservoirs exist, it may be advisable to duplicate the main, and rest content 
with a very small service reservoir, if this has to take the form of a water tower 
or elevated tank, (see p. 944). 

Where favourable sites exist, service reservoirs are frequently placed at the 
side of the town farthest removed from the point where the water supply first 
enters the town. The ultimate object is as before, namely, to secure a saving 
in the cost of mains ; but here it is not only in the supply mains to the town that 
the saving is effected, but also in the larger distribution pipes in the town. 

It will be evident that in times of acute demand all mains near the service 
reservoir draw water from it, and in times of small demand the surplus water 
passes through the mains and refills the supply reservoir. 

To^accurately determine the size of such a supply reservoir (which I propose 
to call a terminal supply reservoir), is by no means easy, and the necessary 
information is also not always available. 

Let us assume that the supply main is of constant diameter and that the 
draught per unit length from it is constant along its length. At the time of 
maximum demand, we wish to have a certain minimum pressure at every point 
of the main. This minimum pressure may be taken as about 40 lbs. per square 
inch as this permits a fire jet being delivered at about 60 to 70 feet above the 
main. Local conditions must fix the exact value and, personally, if funds permit 
it, the manager of a big Fire Insurance Co. is the best person to consult 
provided the corresponding reduction in fire insurance rates is offered. 

Let D mux represent the demand from the whole length of the main during 
the hour of maximum demand, expressed in cusecs. Let L, be the total 
length of the main in feet. Then, referring to Sketch No. 153, let Q 1? 
cusecs enter at A, and supply a length L 1} feet of the main. Thus, Q x =^'L 1 . 
So also, Q 2 cusecs are drawn from the terminal supply reservoir, and Q 2 = ^L 2 , 
where L 1 + L 2 = L. 

Now, if the supply be “constant,” as should be the case in all good town 
supplies, the pressure at every point in the main AR, must not fall below a 
certain value, determined as above. For preliminary calculations we may 
take 100 feet of water. 


Setting up lines to a height equal to this minimum, we get : 


where K, is written for 


Ql * - ^ and Q 2 s = & 

, d, being the diameter of the main in feet. 


1oooff 5 


Thus, Q,» + Q,» = .^LfLr + ^fU = f (*,+*,) 


KLi 


and d, is to be a minimum subject to this equation, while q'L — D wax . 


Thus, Qi = Q 2 = —- nax , and thus d, can be determined bv 


d r > = 


D 3 


max 


Now, put D e - = where k = h x —h v 


12000 y(/q+/L) 







SERVICE RESERVOIRS 


617 

During all the hours in which the demand in cusecs is less than D c , the 
quantity entering the main at A, is not only adequate for the demand, but also 
permits the delivery of a quantity equal to x, cusecs into the reservoir where : 


a- 2 + D.r+ 


D 2 D 2 


where D, represents the demand in cusecs during the hour considered. 

x, can thus be calculated, and a volume of 3,6oo.r cubic feet is stored up 
in the reservoir R. The minimum possible volume of the reservoir is thus given 
by 3,6002.13 where the summation includes all the hours during which D, is 
less than D t >. 

Similarly, for the hours during which D, is greater than D c , but less than 
D ma;r , we have : 

y , cusecs enter the main at A, and supply a length of l Vi feet of the main, 
and Xi, cusecs leave the reservoir and supply 4 » feet of the main. The 
equations are of the same form as those given when considering the demand 


D 


D, /ia «, but K, is now known, and q , is no longer equal to —but is, say, 

1—4 

D 

^ L : 


We thus get: 

y 3 — xy = and y+x 1 = D. 

K 

Put pd = z, and we have : 

(1 — s') 3 — z 3 = J ff~D 3 
K 

This equation reduces to a quadratic, but is more rapidly solved by trial and 
error, using a table of cubes. Two places of decimals (i.e. z = o'8i say), is 
more than is really required. 

Now, the value of the total outflow from the reservoir is equal to 3,6002^, 
cube feet. If this be less than 3,6oo2.r, the reservoir is of sufficient volume, 
and d, can probably be slightly reduced if considered advisable. If, however, 
2 x x , is greater than Sx the supply main is not sufficiently large. A somewhat 
greater value of d, must therefore be selected, and the calculations of x, and x lf 
must be repeated with new values of K, and D e , until a balance between 2.r, 
and Sx lf is obtained. 

The above calculations are probably not very useful in determining the size 
of the supply reservoir, but they afford a good deal of valuable information 
when questions concerning the necessity for reducing valves, or small service 
reservoirs, on isolated hills, are considered ; and it is with that object in view 
that the subject has been considered in detail. 

In practical cases the problem is by no means so simple, but the principles 
to be followed are the same. The necessity of affording sufficient pressure at 
the hour of greatest demand permits us to determine the supply pipe, which is 
usually of uniform diameter. Then, for the hours of small demand, we can 
calculate the supply which reaches the terminal reservoir, and for the hours of 
more intense demand, the draught from the terminal reservoir, so that the 
supply pipe must if necessary be enlarged until the total influx is greater than 
the total draught. It is advisable to secure a greater influx than the calcula- 



618 


CONTROL OF WATER 


lions of draught indicate, as such an excess may form a very useful reserve in 
case of accidents to the main, or when fires occur during the hours of intense 
supply. 

In actual practice, it will usually be found that a terminal supply reservoir 
serves other purposes besides those which have been indicated here. Indeed, 
of eight cases where I am fully informed as to the reasons for their construction, 
only one is a purely balancing reservoir ; two are in addition employed to store 
a quantity of water as a reserve against fires occurring in a very valuable 
district ; three are also break pressure reservoirs ; while the last two are 
principally considered as reserve reservoirs to permit repairs to mains crossing 
a river. It will therefore be plain that the above calculations cannot as a rule 
be permitted to solely determine the size of a reservoir. On the other hand, 
they should be used as a check, since the more the reservoir exceeds the 
volume indicated by these calculations, the more the water contained in it is 





Combined Entry i Exit ripe 


Sketch No. 154.—Puddled Service Reservoir and Pipe Arrangements. 


likely to stagnate. The arrangement of pipes shown in Sketch No. 154 is 
advisable, since it partly prevents stagnation, and in a pumping scheme 
eliminates sudden variations of the head pumped against. 

Details of Construction of a Service Reservoir.— The necessary 
volume being determined as already described, we have to select the material. 
As a rule, service reservoirs are either made of masonry, or of concrete, and are 
located at the top of a convenient hill, or are built of steel plates, being then 
usually in the form of a water tower, or elevated tank (see p. 944). 

Masonry, or Concrete Type .—Usually this type is the cheapest, if a suitable 
site is obtainable. The proportions are very much a matter of experience, and 
it is as well to remember that typical examples are generally situated on sites 
where land is valuable, so that a shallower reservoir than usual may prove 
economical when land is cheap. 

The depths generally selected vary between 13 and 20 feet, although 











































































SEE VICE EE SEE VOIES 619 

examples as shallow as 8 feet and as deep as 40 feet exist; but the latter 

are liable to prove unsatisfactory unless circumstances are exceptionally 
favourable. 

The determining factors in design are : The means adopted to render the 
reservoir water-tight, and the quality of the foundations. 

The early examples are nearly all made water-tight by an outer skin of 
puddle. I consider that this is an undesirable method, and is a relic of the 
days when good Portland cement and hydraulic lime were not so readily 
procurable, as at present. There are, however, cases where the foundations at 
the only available site are of such a quality as to render a layer of puddle 
advisable as a precaution against possible cracking of the masonry, owing to 
settlement. It may also happen that good puddle clay is found at, or close to, 
the site, when considerations of cost indicate its use. 

When puddle is used the real difficulty is to prevent the angles of the 
masonry from fracturing the puddle lining, as it settles. This is best guarded 
against by having no portion of the puddle lining vertical, but laying it all 
either horizontally, or on a slope, and correspondingly sloping these portions of 
the foundations which are usually vertical. 

I append designs for a covered reservoir, which seem best suited for such 
a case (see Sketch No. 154). 

The other important points in the design are: 

(i) Vertical side walls (of the type shown in the second design) are to be 

avoided, since they generally give trouble, probably owing to the 
unequal intensity of pressure which must exist across their base, due 
to horizontal earth or water pressure. 

(ii) The pier foundations should be so proportioned as to produce the 

same intensity of pressure on the puddle as the water load and 

brick flooring combined, thus securing that all portions of the 

reservoir shall compress the puddle equally. 

The more usual, and I consider (except in the case of bad foundations, 

which should be avoided when possible) the more practical design is one in 

which water-tightness is secured by a cement rendering, or a coating of asphalte 
or bitumen. 

In such cases the chief difficulty is* to prevent cracking, and where the 
reservoir is exposed to great changes of temperature it seems doubtful whether 
construction in concrete alone will ever be really satisfactory unless some 
elastic lining, such as asphalte, is added to prevent the water leaking along the 
cracks. Brickwork or stone masonry appears to be less liable to cracking, and 
in many cases water-tightness has been secured merely by a facing of hard 
bricks (e.g. those known in England as blue bricks) laid in cement mortar. 

On the other hand, concrete has certain advantages, in that it can be 
rammed close up against the undisturbed sides of the excavation. 

The design (Sketch No. 155), which includes a |-inch rendering of Portland 
cement mortar, floated over with neat cement, seems to me to be the cheapest 
and most advantageous in good foundations. Where the foundations are not 
good it would appear better to thicken the walls 6 inches at the bottom, and to 
batter them at 1 in 8, where the earth seems likely to slip ; while in cases where 
settlement is apprehended, an internal layer of asphalte or bitumen sheeting 
will prevent leakage through cracks even |--inch wide. In the very worst cases 


620 CONTROL OF WATER 

a rounding of the internal corner as dotted has been found to add strength to 
the work. 

Roofing. —As shown in both designs service reservoirs are usually roofed 
over, and in the case of a filtered water, roofing of some sort may be considered 
imperative. The roofing is generally of brick arches, and should be kept as 
light as possible, as all it has usually to carry is about 12 inches of earth, 
(although in hot, dry climates it is often impossible to get plants to grow on so 
thin a layer of earth). The usual dimensions for such arches are 9 inches thick, 
up to 15 feet span. The drainage of the hollows above the springings of these 



Sketch No. 155.—Concrete Service Reservoir. 


arches should be carefully looked to, and for this reason I cannot recommend 
the adoption of vaulted arches, since although, qua strength they possess 
certain advantages, an undrained pocket is formed over the top of each column. 

It will be evident that reinforced concrete is well adapted to the construction 
of service reservoirs, and in view of the fact that reinforcement not only prevents 
cracking due to mechanical stress, but also a great deal of that caused by 
changes in temperature, it may with advantage be adopted where the changes 
in temperature are great, or the foundations are unusually bad. I must, how¬ 
ever, state that in ordinarily good earth the extra expense entailed by reinforce- 













































































POPULATION STATISTICS 


621 


ment appears (in such cases as I have personally investigated) to outweigh the 
economy secured by thinner walls. 

I have noted many cases where a local reinforcement has proved advantageous 
in dealing with a patch of bad foundation ; and I also believe that where, owing 
to local conditions, reservoirs of irregular form or of unusual depth have to be 
designed, it will prove a cheap method of construction. 

While the majority of existing service reservoirs are square or oblong, a 
circular form is evidently economical, as the outer walls are reduced in length 
(for the same surface area) and it will be found that both designs are adaptable 
to a circular form, the only disadvantage being that the centerings for the 
arches and the arches themselves are somewhat more complicated. 



'tin. OpenJointmuted when brickwork has set. 


Stretchers 

Stretchers 

I Header to I Stretcher 
Stretcher 

Stretcher 


Concrete 


Sketch No. 156.—Junction between Bitumen Sheeting and Brickwork. 


In considering the application of these designs to unusual conditions it is 
well to remember that service reservoirs are usually placed on top of a hill 
thus ground water pressure or even wet soil pressure does not exist. I should 
expect all these designs to fail or, at the best, to crack if located in a valley. 

Population Statistics. —Engineers when drawing up reports concerning 
the water supply of towns frequently prepare tables showing the expected future 
increase in the population. In any examples I have seen these are prepared 
on the following basis : 


Let Pj be the total population say in 1881. 
P 2 „ „ 1891. 

P 3 „ „ 1901. 

P 4 » . 33 1911- 




33 


33 


3 ? 


3 ) 







































































622 


CONTROL OF WATER 


Then put (i+A) = qr (i+A) = & (i+A) ” ?r 

*1 *2 r 3 

and put / = Pvth± h 

3 

Then P 5 , the expected population in 1921, is given by P 5 = (i+/)P 4 , 
or in some cases P 5 = (i+i^P-t- 

The deductions such as : 

Population in 1912 = (i+/)^P 4 = (1 
or, in logarithms t 

log (population in 1912) = log P4 + iVog (1+/) 

, -n . log P 4 —log P 3 

or = log P 4 + _ 5 — * - ° —9 

10 

are obvious. These may also be somewhat more accurate than the figures for 
P 5 , but do not happen to be of much use in the problem of determining when 
an extension of the waterworks will be required. 

The figures for the population are usually recited in legal investigations by 
the Town Clerk, and the only reason for the engineer’s interference appears to 
be a belief that Town Clerks cannot use logarithms. This I believe to be 
unfounded. In any case I expect that the figures of the 1911 census will put 
a stop to the practice in Great Britain. I record the formulae in case a Town 
Clerk should ask for the table. It is believed that expert statisticians can 
produce results which are better adapted to the ordinary individual’s powers of 
belief, but, I am not inclined to consider that an engineer should necessarily 
claim expert knowledge of all matters that can be reduced to figures. 




CHAPTER XII 


IRRIGATION 


Irrigation.— Definition — Influence of agricultural methods — General description of an 
irrigation canal—Other irrigation systems—Effect of silt. 

Terms used in Irrigation .—Perennial and flood, or basin irrigation—Flow and lift 
irrigation—Canal, well and reservoir irrigation—Duties of an engineer—Bibliography 
—Hot and cold weather crops—Quantity of water available—Importance of local 
knowledge. 

Quantity of Water Applied During the Growth of a Crop .—Depth of water 
used— Duty of water—Base of the duty—Place of measurement—Complete specifi¬ 
cation of duty—Conversion of duty figures into depth of water—Losses in the canal 
and branches—Capacity of channels in terms of duty—Factors affecting the value of 
the duty—Excessive irrigation—Effect of cultivation—Quality of soil—Climate—Pre¬ 
diction of duty—Example. 

Variations in the Value of the Duty.—Table of values—Values of duty as affected by 
the species of crop—Estimation of the duty—Number of waterings—Interval between 
waterings—Waterings of unusual depth—Experimental determination of the depth 
of a watering—Program of experiments—Seasonal variation in demand for water— 
Effect of area of the irrigated plots—Normal depth of a watering—Allowance for 
rainfall—Excessive irrigation—Rice—Marcite. 

Influence of the Rate at which Water is Applied to a Field on the 
Quantity of Water used in Irrigation. 

Inunda tion Irriga tion. 

Design of Irrigation Works.-— Enumeration of the structures on a large canal. 

Relationship between tpie Design of Hydraulic Works and their Mainten¬ 
ance.— Vortices — Smooth surfaces — Punjab fall — Overflow dam — Ogee fall — Bell’s 
dykes—Kanthak’s wide crested submerged weirs—Silting tanks—Profiles—Silt 
berms—Scour. 

Regime. — Regula tion. 

Headworks. —General—Regulator across canal head—Bar across river—Low dam, or 
weir across river—Typical headworks—Storage dams—Undersluices—“Afflux,” or 
flood conditions—Low-water conditions—Training works. 

Working of a River for Irrigation Purposes.—Disposal of surplus water and silt. 

Working of a River Carrying Sand only.—Sutlej, at Rupar. 

Working of Rivers Carrying Boulders, or Gravel.—Jumna, at Tajewala—Ravi, at 
Madhupur—Suggestions for future working—Site for a canal head—Constricted 
channel above a weir—Bell’s dykes. 

Working of Inundation Canals .—Selection of site for canal head—Temporary gates 
—Stone pitching. 

Weirs. —Types—Description. 

Type A .—American and Indian designs. 

Type B. — Kistna weir maintenance—Godaveri weir—Sand or clay foundations. 

Type C. —Description. 

Design of Weirs.—Errors of record plans—Aprons—Curtain walls—Talus—Imperme¬ 
able and permeable portions of a weir—Breadth of impermeable portions—Breadth 
of downstream apron and talus—Breadth of downstream apron—Thickness of apron 
—Thickness of dam wall—Reversed filter. 

623 


624 


CONTROL OF WATER 


Curtain Walls , or Cut-offs. —Steel piling—Wells. 

Ups trea m A pro ns. 

Groynes. 

Bars. 

Failure of Weirs.—Summary of weir design—Maintenance of weirs—Special pre¬ 
cautions in construction of weirs—Rules for ring banks—Springs—Well, or pile 
junctions. 

Undersluices. —Rules for apron and talus—Piers—Floor thickness—Discharge capacity 
—Bengal type. 

Canal Regulators. 

Head Regulators.— Design—Waterway area—Permissible velocities—Regulators in 
rivers carrying gravel—Example of Upper Chenab regulator—Advantages of Stoney 
gates. 

Failures of Regulators.—Wells versus sheet piling. 

Scouring Action of Escapes.—Theoretical investigation—Effect of silt deposits on 
roughness of canal—General rules. 

Auxiliary Escapes. —Escape reservoirs. 

Canal Drainage Works. 

( a ) Aqueducts. —Pitching at head and tail—Foundations—Velocity of the water. 

(b) Syphons .—Type design for continuous flow—Type for intermittent flow—Con¬ 
struction in brickwork—Depth of cover—Combined pressure syphon and deep 
level crossing. 

(c) Level Crossings. 

Bridges over Canals. 

Head regulators of branch canals—Exclusion of silt. 

Falls and Rapids. —General conditions—Selection of rapid, or fall—Erosion—Ogee 
fall—General principles—Needle fall—Punjab type of fall—Fall in somewhat firmer 
soil—Rapids—Maintenance of rapids—Rapids upstream of aqueducts or flumes. 

Prevention of Erosion below Falls and Rapids. —Chequer pitching. 

Notched Fall. —Regulation by raised sill—Notch fall regulation—Formulae. 

Design of Irrigation Channels. 

Location of Irrigation Channels. —“Command”—Bed slopes—Balancing depth— 
Section of banks—Temporary banks in small canals—Kennedy channels. 

Command. —Fall from large channels into branches—Relative levels of ground surface 
and full supply—Drop from canal into watercourses. 

Methods of Field Irrigation. —Sections of watercourse—Areas of irrigated holdings— 
Division of a holding into plots. 

Design of a Distributary. —Examples—Absorption—Final plans—Records—Calcu¬ 
lation of watercourse orifices. 

Modules. —Survey of an irrigated area—Absorption, or leakage, from channels and 
reservoirs—French navigation canals—Punjab irrigation canals—Influence of depth 
of the canal—General results for canals—Seepage into a canal—Effect of scour— 
Lining of canals. 

Leakage of Reservoirs. —Effect of percolation from surrounding strata— General rule 
—Local rules—Regulation. 

Alkaline Soils. —Chemistry of alkaline soils—Effect of chemical composition on re¬ 
clamation—Engineering classification of alkaline soils—Reclamation— Drainage _ 

Area reclaimed by one pump—Quantity of water required—Reclamation of Lake 

Aboukir—Spacing of drains—Quantity of salt removed—Tile drains—Flooding 

Cultivation after reclamation—Prevention of alkalinity—Drainage—Depth to subsoil 
water level—Punjab rules—Egyptian drainage—Deterioration in fertility of soil. 

Silt.— Definition—Bed silt—Turbid matter, or suspended silt—Original silt—Derived 
silt—Prevention of erosion—Example of Ibrahimiah Canal—Direction of the head 
reach of a canal—Egyptian practice—General rules for cases where bed silt is not 
important—Conditions existing in the Punjab—Kennedy’s rules—Necessity for 
careful inspection—Application in localities other than the Punjab. 

General Principles. —Rivers carrying fine silt—Rivers carrying coarse silt. 

Grading of Silt. —Silt classifier—Notation—Grade of detrimental silt. 

Silt Traps. —Extra loading of silt produced by disturbances at entry—Head reach 
deposits—Length of zone of silt deposit—Scouring operations—Sampling the lower 
layers of water—Escapes—Sand traps—Double head reaches—Decantation tubes. 

Physical Basis of Kennedy’s Rule. —Curve of velocity and silt per foot of bed width 
according to Kennedy’s rules—Seddon’s experiments. 


IRRIGA TION 


625 

Irrigation. —The term irrigation is used to describe the processes 
connected with the artificial application of water to land for agricultural 
purposes. 

There are probably few, if any, countries in which agriculture is practised 
where irrigation is entirely unknown. In this book, however, the practice is 
considered only under circumstances such that irrigation on a large scale 
forms a routine portion of the agricultural operations. The expression 
“routine” is employed in place of “essential,” since modern investigations 
have shown that satisfactory crops can be obtained by special methods of 
cultivation under circumstances which are usually held to render irrigation 
absolutely necessary. Similar processes are well known to Indian agri¬ 
culturists, but are employed only when local circumstances are highly 
favourable. 

The boundary between irrigation operations and the purely agricultural 
processes employed in cultivating the soil, is very indefinite. It may indeed 
be said that the purely agricultural processes have far more influence in 
determining the best methods of irrigation than the climate of the locality, or 
the character of the soil. Similarly, the method actually adopted in irrigating 
an area of land affects both the crops grown and the necessary agricultural 
operations to a considerable extent. 

A complete treatise on irrigation can therefore hardly be produced without 
the collaboration of an agriculturist, an engineer, and a lawyer. Such a 
treatise has not yet appeared, and would obviously either refer to an ideal 
state of affairs, or would merely be a handbook of little more than local 
interest. 

My object is to deal with the design of irrigation structures in general. 

I therefore refer to local conditions as rarely as is consistent with clearness* 
It will, however, be noticed that the effect of local conditions appears at 
every point. 

My own experience was acquired in the Punjab (Northern India), but has 
been supplemented by a personal study of the conditions occurring in Egypt, 
Ceylon, and the Californian irrigation districts, with a less detailed study of 
irrigation as practised in Lombardy. 

The general arrangement of the chapter corresponds to the conditions 
existing on a modern irrigation canal in the Punjab. These canals present the 
most complicated problems normally found in irrigation. 

The works consist of the following structures : 

(i) A low weir, or dam, thrown across a river, with the training works 
required to control the river, which is frequently torrential, and is always 
subject to heavy floods. 

(ii) The head works of the canal, which are mainly designed with a view to 
excluding silt. 

(iii) The main canal, which usually crosses several subsidiary drainage 
channels ; which necessitate syphons under, or aqueducts over the canal, 
for the disposal of the flood discharge of such drainages. Escapes are also 
required in order to dispose of surplus water, or to remove silt deposits. 

(iv) The distributary and minor canals from which irrigation is actually 

effected. 

(v) The field watercourses, by which the water is conveyed to the in¬ 
dividual fields in which the crops are grown. 

40 


626 


CONTROL OF WATER 


The problems arising in the design of such a canal include those which 
occur in the design of any normal irrigation system. The only two exceptions 
are as follows : 

(a) In Southern India (and of late years in the Western United States and 
Egypt) the flow of the river is not only diverted, but is stored up in large 
reservoirs for use during periods when the natural flow would not suffice for the 
requirements of the irrigation system. The design of such reservoirs and their 
outlet works is treated in Chapter VII. 

(b) In Egypt, and less markedly in Southern India, some portion of the 
irrigation is effected by rapidly flooding the land, and after the water has 
thoroughly soaked in, the surplus water is drained off. While the actual 
details of the methods adopted in such cases are extraordinarily complicated, 
and can only be satisfactorily treated by a long study of the local conditions 
(see p. 649), the principles of the design of the works are amply covered by 
a study of the sections on Escapes, Canal Regulators, and Syphons. 

As a rule, the problems are far more simple than those which exist 
in the Punjab. Where the water is directly derived from a clear water 
stream, or from a reservoir, silt problems do not exist, and the design of the 
canals is simpler. 

Practical experience, however, leads me to believe that this is by no means 
an unqualified advantage. An engineer accustomed to silty waters can 
always effect certain economies in construction and maintenance by skilful 
design, and it is by no means certain that these economies do not amply 
cover the expenditure in silt clearance which is required in a well-designed 
system. A clear water canal need not necessarily be provided with a head 
regulator, but it is doubtful if this economy is not generally attained at the 
cost of very inefficient working of the whole system, unless escapes are 
provided which are sufficiently powerful to act as regulators. 

Terms used in Irrigation. —It is absolutely impossible to give a 
glossary of the technical terms used by irrigators in various countries. The 
Urdu (Northern India) irrigation vocabulary contains more than 100 terms, 
each with a definite meaning, and it is still incomplete. The following 
English terms are selected from those which possess the most extended 
geographical currency, and are believed not to conflict with any local 
terminology. 

Irrigation is said to be perennial when water is applied to the land under 
crops at a fairly equable rate during the whole season of crop growth. When 
a large proportion of the irrigation water is secured by deeply flooding the 
land, and the crop growth is afterwards wholly or partially sustained by the 
moisture thus stored up in the saturated soil, the term “flood, basin,” or 
“ inundation ” irrigation, is employed. The terms “ perennial,” and “ flood,” 
are not necessarily mutually exclusive, although they are frequently so 
used, as in most cases flood irrigation is supplemented by minor waterings. 

The terms “flow,” and “lift” irrigation are used in order to specify 
whether the water level is such that it will naturally flow on to the land, or has 
to be lifted artificially by means of various types of machines. Flood irrigation 
must necessarily be by flow (i.e. from a river, or canal), although the supple¬ 
mentary waterings frequently assume the form of lift irrigation ; whereas, 
perennial irrigation may either be by lift, or by flow, and the same source of 
supply may obviously be used for either method. 


METHODS OF IRRIGATION 


627 

We may also divide perennial irrigation and the supplementary waterings 
which may or may not be required in flood irrigation, into classes specified by 
the source of the water. 

From this point of view three main classes exist : 

(i) Canal irrigation, where the water is drawn from a canal which takes out 
from a river. 

(ii) Well, or subsoil water irrigation. 

(iii) Reservoir, or tank irrigation, where the water is stored in reservoirs. 

Canal irrigation may either be by flow or by lift, but is usually by 

flow. 

Well irrigation is usually by lift, but irrigation by flow from artesian wells is 
sometimes possible. 

Tank irrigation is nearly always by flow, but occasionally a modified form 
of flood irrigation is obtained by cultivating the banks of the tank as the water 
level falls. In such cases, the crops usually receive one or more waterings by 
lift from the tank. 

The terminology is hopelessly confusing. This is illustrated by the present 
state of certain portions of Egypt which receive flood irrigation in August and 
September, supplemented by well irrigation until March. From March to July 
the land is perennially irrigated by lift from canals ; these, from March to April, 
are supplied by the natural flow of the Nile, which is supplemented during May, 
June and July in steadily increasing proportions by water which has been stored 
in the Assouan reservoir. In practice, however, there is usually but little doubt 
as to the manner in which any definite area of land is irrigated, and it will be 
found that the terms employed have a real application, since the various condi¬ 
tions thus specified produce very different methods of cultivation. 

In flood irrigation, the engineer is chiefly concerned with the clearing out 
of the canals before the flood, and with the prevention of breaches in the flood 
banks during the flood. He has but little responsibility in regard to the quantity 
of water supplied, as that principally depends upon the height to which the flood 
rises. After the flood has subsided his duties become very similar to those of 
an engineer in charge of perennnial irrigation. The Egyptian methods may 
be taken as standard, and reference may be made to Willcocks’ Egyptiati 
Irrigation , and to Barrois’ Les Irrigations eti Egypte. 

In perennial irrigation, the engineer is most concerned with the design and 
maintenance of the canals which distribute the water over the land, and he is 
responsible during the whole year for the provision of a supply of water sufficient 
to meet the demands of the agriculturists. The Indian methods may be taken 
as the standard in this case, and reference may be made to Buckley’s Irriga¬ 
tion Works in India , and also to Mullins’ Irrigation Manual. 

Italian methods are also good, but the available literature is small. Baird 
Smith’s Italian Irrigation , although fifty years old, is still quoted in Milan as a 
reliable book of reference. 

The works of Willcocks and Barrois (which is of later date) give a good idea 
of Egyptian methods of perennial irrigation ; but it must be remembered that 
Egyptian perennial irrigation is as yet young, and we can hardly be certain 
that the differences which exist between Egyptian and Indian methods will 
prove permanently advantageous. 

In reservoir irrigation, the engineer has to consider the design and mainten¬ 
ance of reservoirs. Here, the actual methods of irrigation differ but slightly 


628 


CONTROL OF WATER 


from those obtaining under perennial irrigation, and the books referred to 
above may be consulted with advantage. 

The main problems in lift irrigation are the mechanical difficulties connected 
with the design of pumps, and their maintenance in a high state of efficiency. 
The civil engineer is chiefly concerned with the location of the channels and 
the methods of preventing leakage from them. This portion of the process has 
been sadly neglected, and, since every drop of water has to be lifted at a certain 
cost, the question deserves more attention than it has as yet received. 

The Californian methods of thus economising water are standard, and the 
publications of the State Irrigation engineer, of the University of California, 
and of the United States Geological Survey, may be consulted. 

In the majority of countries where irrigation is practised, the climate is 
sufficiently hot to produce crops all the year round. Such a condition favours 
good financial returns, as the money invested in irrigation works can then earn 
interest during the major portion of the year ; whereas, if only one crop can be 
grown in the year, interest for twelve months has to be earned by six or perhaps 
eight months of cultivation. 

Putting aside special cultures such as fruit trees, meadows, or sugar cane, 
which occupy the land for the whole, or a very large portion of the year, and 
intermediate crops which are sown and harvested at special seasons, it will 
usually be found that two very different classes of crops are grown in a year. 
These may be called the cold weather crops (which consist of staples such as 
wheat, barley, vetches, and other temperate zone cultures), and the hot weather 
crops (which consist of the more pronouncedly sub-tropical cultures such as 
cotton, millet, maize, and rice). 

The varieties of crops vary from country to country, and localities exist 
where wheat and rice, or flax and cotton, are grown simultaneously. As a 
general rule, however, the distinction is well marked, and owing principally to 
the hotter temperature (the species of the crop does not appear to influence 
the question to any great degree, although rice and sugar cane always consume 
more water than the typical cold weather crops), the hot weather crops as a 
group consume far more water (roughly twice, or even three times the depth) 
than those grown during the cold weather. This fact gives the engineer ample 
opportunity to exercise his energies in adjusting the available supply of water 
so as to produce the best financial results. General rules cannot be given. 
In some cases, the problem is solved by cultivating a greater area during the 
cold weather than during the hot. In other cases (especially where the rivers 
rise in flood during the hot weather), the hot weather culture is taken as 
standard, and the canals are proportioned for the hot weather demand, the 
cold weather cultivation being fixed by the available supply in the river. In 
considering these problems the engineer must be chiefly guided by local 
experience, and the cases in which he is in a position to determine a priori 
the exact area of crops, and the method of culture, are infrequent. This is 
probably a blessing in disguise, for (except in newly settled countries) local 
experience has usually effected a very accurate adjustment of the methods of 
cultivation to local necessities. The work of an engineer is then usually best 
confined to the improvement of existing small scale practice in a scientific 
manner. Very careful investigations will usually show that while improvements 
in small details (such as the introduction of new manures, or varieties of plants) 
can be effected ; yet, broadly speaking, local customs are the result of long ages 


“DUTY” OF IRRIGATION WATER 


629 

of evolution, and possess all the adaptions and fitness necessary to secure their 
survival that characterise a well-established natural species of plant or animal. 
This statement must in no wise be considered as adverse to agricultural 
experimental stations. Such experimental stations form an integral portion 
of any large irrigation scheme, but the duty of the engineer is to modify his 
channels and works so as to suit the alterations in cultivation as they are 
adopted, rather than to hurry forward their adoption by means of premature 
modifications of the irrigation system. It is but small consolation to know that 
the system is admirably suited to a certain mode of cultivation, when the crops 
on the ground would be better served by channels designed on different 
principles. 

It must however be borne in mind that a cultivator who enjoys an unlimited 
supply of water, will almost invariably be found to be using at least twice the 
quantity he really requires to mature as good a crop as he obtains with excessive 
water. The question should always be investigated, and the methods given on 
pages 642 and 647 will usually provide ample proof and indicate the remedies. 
The introduction and enforcement of these remedies is another and much 
broader question which I do not presume to answer. Personally I believe that 
rapid improvement is only possible in cases of lift irrigation, where the fuel bill 
forms a powerful and effective argument. 

Quantity of Water applied during the growth of a Crop .— 
A certain amount of water is required for the development of any plant. This 
quantity varies considerably from an absolute minimum which will just keep 
the plant alive, up to an absolute maximum, which renders the ground so wet 
that the plant is ultimately killed. Putting aside such considerations, let us 
confine our attention to the quantity of water which is actually used in practice 
by skilled agriculturists. This quantity can be expressed in the same manner 
as rainfall, i.e. as a depth over the whole area covered by the crop. 

Thus, let an area of <2, square feet be occupied by a crop, and let the total 
quantity of irrigation water applied to mature this crop be v, cubic feet. 


• • • U 

Then, the depth of irrigation water used is plainly d= - feet. 


a 


The precise definition of the period during which the volume v , is applied, 
must of course depend upon local circumstances. As a rule, v, includes all the 
irrigation water used during the period between the first preparation for the 
crop, and its final removal from the ground. Water used in preparing the land 
preliminary to ploughing and harrowing, prior to sowing, should be included 
in the above irrigation water. 

Irrigation engineers define the “duty” of a given quantity of water, as the 
area of cropped ground of which the agricultural requirements are satisfied by 
that quantity of water. That is, when the duty of 1 cusec of water during a 
period of say October to April, is 180 acres, the agricultural requirements of 
180 acres during this period are satisfied by a continuous flow of 1 cusec. 

In its primary sense duty has no connection with the maturing of crops, or 
with the quantity of water required for this purpose. Thus, if we state that 
in the Punjab the duty for the month of November is 170 cusecs, we merely 
mean that 1 cusec flowing continuously during that month suffices to provide 
a satisfactory water supply for the agricultural requirements of 170 acres under 
crop ; and it must not be inferred that any individual acre of these 170 neces¬ 
sarily receives any, or still less, a proportionate, volume of water during the month. 


CONTROL OF WATER 


630 


If we wish to ascertain the depth of water supplied to the land (not neces¬ 
sarily applied to the cropped area, unless the cusec spoken of above is measured 
not far distant from the cropped area), we must also define the base, i.e. the 
period over which the duty is reckoned. Thus, the month of November having 
30 days, converting 1 cusec for 30 days into cubic feet, and acres into square 
feet, the depth of water applied is : 


since 


30x24x60x60 ^2x30 
170x9x4840 170 

24x60x60 1200 _ 

— 1 - 5 -= -7— = 1 '98 3 = 2 approx. 

9x4840 605 y J 11 


Since the agricultural operations in November usually consist of a single 
watering, as a preliminary to ploughing, it appears that this “ ploughing water¬ 
ing” (which is usually heavier than the waterings which are applied later on 
in the season), is about 4 inches in depth. But, as it will be shown later, this 
does not necessarily mean that the cropped area is covered with water to a 
depth of 4 inches in the sense that a 4-inch rainfall would “cover” the area. 

So also, if we are told that the duty of 1 cusec for the cold weather crops 
(wheat, etc.) is 202 acres, we cannot determine the actual depth of water used 
unless we know the number of days during which the canal supplied this 
1 cusec. For example, let the “base” be 170 days. The depth of the.water 

2 X 170 

consumed is - - - = 1*67 feet, say 20 inches. 

Taking another example, the basin canals of Egypt flow for 40 days, and 
the water covers the basin to a depth of approximately 5 feet. Consequently, 
the duty is : 

■——— = 16 acres per cusec. 

As another example. Willcocks (Egyptian Irrigation ) gives figures relating 
to the perennial irrigation of cotton, maize, etc., which permit the following 
table to be drawn up: 


Year. 

Areas under 
Crop in Acres. 

Discharge of 
Canals in 
Cusecs. 

Duty, Acres 
per Cusec. 

Depth of 
Water applied 
in Feet. 



For the month of May. 

1889 . 

1,200,000 

8,120 

148 

o '42 

1892 . 

1,500,000 

12,360 

121 

°'S 1 



* 

For the month of June. 

1889 . 

1,200,000 

7,060 

1 70 

°‘35 

1892 . 

1,500,000 

10,590 

142 

0’42 



For the month of July. 



(From the 1st to 15th only.) 

1889 . 

1,200,000 

10,590 

113 

0*27 

1892 . 

1,500,000 

j i 3 ,° 6 ° 

IT 5 

0*26 

































DEPTH OF WATER AND DUTY 


631 


The crops cultivated consisted principally of cotton and similar “dry” 
crops, with about 10 per cent, of rice and “wet crops.” In 1889 a great part 
of the rice perished, and the cotton crop was inferior. In 1892 the supply was 
inadequate. Thus, the figures 0*51 foot and 0*42 foot represent bare minimal 
depths ” for an area covered by the above combination of crops in a climate 
such as that of Egypt in May or June. So far as the circumstances are known 
to me, I believe the cropped area actually received about 75 per cent, of the 
above depths (see pp. 632 and 641). 

The usual duties in this locality (Egyptian Delta) are 113 acres per cusec 
for cotton and dry crops, and 63 acres per cusec for rice. At this rate, the duty 
requisite for the satisfactory irrigation of a combination of the above crops in 
the ratio given should be 102 acres per cusec ; or about o’bofoot depth of water 
per month of 30 days ; and a small pumping scheme should probably be 
designed to lift about 0*45 foot depth of water per month. 

The place where the “ duty ” is measured must also be stated ; for it is plain 
that if the 1 cusec is considered as measured at the head of the canal, the total 
corresponding volume of water will not reach the cropped area, as a portion 
will be lost by evaporation, and an even greater fraction by leakage from the 
canal during passage from its head to the irrigated land. The term duty can 
therefore only be held to be completely defined when the following are stated : 

(i) Its base, or the number of days over which it is measured. 

(ii) The place where the water is measured, and what allowances (if any) 
are made for losses during the passage of the water from the place of measure¬ 
ment to the irrigated area. 

If A represent the duty expressed in acres per cusec, and B, the number of 
days in the base period, we see that the depth of water “used” during the 
base period is given by : 

2B 

d = A feet 
A 


although it must clearly be understood that unless the duty is measured at the 
field, d , in no way represents the actual depth of water which the crop receives. 

As an example, it may be stated that on the Bari Doab Canal Kennedy 
found as follows : 

One cusec entering the canal is, on the average, reduced by absorption and 
evaporation to o‘8o cusec when it reaches the head of a distributary, and to 074 
cusec when it reaches the outlet from the distributary to the field watercourse, 
and to o'53 cusec when it reaches the field. Thus, on the assumption that 
A = 170 acres per cusec, when measured at the head of the canal, and B = 170 
days, which is fairly close to the average results for the cold weather crops, we 
find that: 

The depth of water which matures a crop if measured at the canal head 
is 2 feet; 

The depth of water which matures a crop if measured at the distributary 
head is r6o foot; 

The depth of water which matures a crop if measured at the outlet is 
1*48 foot; 


and the depth actually applied to the land is ro6 foot only. 

These figures are surprising, but are confirmed by Ivens’ results on the 


CONTROL OF WATER 


632 

Ganges canal, where one cusec becomes o'85 at the distributary head, 078 at 
the outlet, and 076 at the field. 

The results refer to very long canals, and if comparison is desired with 
American or Egyptian conditions, it would probably be fairest to consider the 
heads of these canals as corresponding to the heads of distributaries in Indian 
canals. Nevertheless, even under these circumstances, the depth “used,” if 
calculated on the duty of water passed into the canal, may exceed the actual 
depth which is received at the field by 33 to 40 per cent. 

It must, nevertheless, be remarked that the loss from village watercourses 
occurs in the cultivated area, and can hardly be regarded as without influence 
on the maturing of the crop. Hence, we may consider that the figure “ Duty 
at outlets,” or “At head of village watercourse,” although no doubt in excess of 
what is required, represents the water which matures the crop. 

The figure is peculiarly important to an engineer, as it represents the 
quantity of water which must be lifted when it is desired to irrigate an estate of 
an area of 2000 to 5000 acres by pumping water from a canal or river. 

The meaning of such terms as “ cold weather duty at head of canal,” and 
“ hot weather duty at head of village watercourses ” now become plain. 
When the number of days on which the canal is open during the “hot” or 
“ cold ” weather season is stated, the depth of water applied to the land can be 
calculated. It must be remembered that while the depth calculated from “ duty 
at head of village watercourses” is very nearly equal to the depth actually 
applied to the land (the only losses being leakage in the short village water 
channels), the depth calculated on the “ duty at head of canal ” is far greater 
than the actual. The losses in addition to those in the village watercourses 
arise from leakage from the canal and its branches, plus the loss caused by any 
water that is passed out of the canal by the escapes. In regard to this latter 
loss, since it is visible, and is easily measured, due allowance can be made if 
necessary. 

The above remarks show that the term duty needs to be clearly defined, but 
for that very reason its investigation forms the most practical method of deter¬ 
mining the size of each channel of a canal. Thus, given that a canal is required 
to irrigate A c , acres of crops, and that the duty during a certain period at the 
head of the canal is A H , the average discharge of the canal during this period 
must be : 

A c 

—- cusecs. 

A h 

So also, if the duty during the period in which the consumption of water 
is a maximum be Am ie.g. in the Punjab the period is approximately from 
October 15th to November 15th) the maximum supply for which the canal must 

A 

be proportioned is •—- cusecs ; the base being the interval between successive 

Am 

waterings. 

Next, taking a distributary, or branch canal, irrigating A d acres, the average 
A, 

supply is —, where 8 d is the average duty during the season considered, 

Od ’ 

measured at the head of the distributary, and the maximum supply is 
Ad 

. Similarly, the sizes of the smaller channels can be determined, when the 

Om 

duties measured at their heads during the various periods of the year are known. 



SPECIES OF CROP AND DUTY 633 

I he quantity of water required to mature a crop varies considerably. The 
most important factors affecting the question are : 

(i) The skill of the agriculturist, which is shown not only in the actual 
application of water, but also in the whole process of cultivation. 

(ii) The species of crop. 

(iii) The character of the soil, in which must be included not only its 

geological constituents, but also the depth down to subsoil water, 
and the amount of manuring and previous irrigation it has undergone. 

(iv) The rain-fall, temperature, and other characteristics of the weather 

during the period for which the crop is on the ground. 

In the long run, the first factor is more important than all the others. As 
a general principle, it may be stated that there is a certain minimum quantity 
of water which will mature a good crop. This quantity varies from year to 
year under the influences enumerated above, but any application of unnecessary 
water is injurious, and the ultimate result of excessive irrigation is a permanent 
diminution of the fertility of the soil. Unfortunately, an excess of water allows 
a good crop to be raised (in the early years of the practice) with far less labour 
than is necessary if the minimum quantity is used. Therefore, the personal 
interests of an irrigator (especially in newly developed countries) are adverse 
to the permanent fertility of the soil. Consequently, a skilled agriculturist who 
adapts himself to circumstances, will employ methods in a thickly settled 
country which differ widely from those which would be adopted in a newly 
developed area. 

For instance, in India, wheat is generally raised with about 2 feet depth of 
water; while in America, 4 feet is not considered abnormal. Both these 
quantities greatly exceed the possible minimum, and yet I consider that both 
are correct, and that both should be adopted in their respective countries if 
individual interests alone are considered. It will be evident that Indian 
practice is far better adapted for preserving the soil in a state of permanent 
fertility. Broadly speaking, any great excess over the minimum indicates an 
incorrect method of applying water, but the question will be discussed at length 
later. 

For the present, we can generally state that a skilled irrigator (especially 
in countries where he cannot readily obtain new land) will raise a good crop 
with far less water than an unskilled man, but the labour entailed is greater. 
So also, careful cultivation of the soil during the growth of a crop, by manuring, 
mulching, and hoeing, diminishes the amount of water required. 

The species of crop grown also largely influences the quantity of water 
required to mature it. Typical figures are given for Indian conditions, and it 
will be seen that the variations thus produced are very large (p. 640). 

Again, the character of the soil affects the quantity of water used. It will be 
evident that a loose, sandy soil absorbs more water than a heavy clay, and if in 
addition the subsoil water level is close to the surface of the clay, and is far 
below that of the sand, these differences will become even more marked. In 
one particular case, I found that a crop of wheat grown on sandy soil required 
three times the depth of water that sufficed to mature a similar crop grown by 
the same agriculturist on an adjacent patch of clay soil. 

In actual practice, however, the effect of the quality of the soil is 
somewhat obscured by the fact that crops requiring but little water are usually 


634 


CONTROL OF WATER 


grown on soils which absorb water readily, and vice versa. Consequently, the 
extra water absorbed by the soil is partly balanced by a saving in that necessary 
for crop growth. 

The effect of climate is important in the following cases : 

(i) If it is proposed to introduce a new crop into a district, a study of the 
water requirements of that crop in other localities, combined with the differences 
in rain-fall and mean temperature during the crop season in the two localities, 
gives valuable results. 

Thus, in considering the cultivation of cotton in Mesopotamia (see Willcocks, 
Irrigation of Mesopotamia ) in ordinary years it is found that a rain-fall of about 
2, to 2^- inches occurs during the early portion of the season of cotton cultiva¬ 
tion. Consequently, one less watering is required than is necessary during a 
similar period in Egypt where no rain occurs. Towards the end of the cotton¬ 
growing season, however, the mean temperatures are considerably higher than 
in the corresponding period in Egypt. It is therefore believed that during this 
period one, or even two waterings more than are given in Egypt will be 
necessary. The total depth of water required is therefore but little more than 
in Egypt, but its distribution during the period when the crop is on the ground 
differs greatly from that prevailing in Egypt. 

(ii) The effect of the variations in rain-fall and mean temperature, from 
year to year, on the quantity of water required to raise a crop, are by no means 
so marked as might at first sight be expected. This is due to the fact that 
unless the crop season is continuously rainy, evaporation from the wetted 
ground after each rain storm is (in climates where irrigation is usually practised) 
so intense that the soil rapidly becomes baked, and its surface caked hard. 
Consequently, a fresh wetting, either by irrigation, or by rain, is needed very 
soon afterwards. 

If the season is continuously wet, agriculturists are encouraged to plough 
and sow land which is not usually cultivated. This land is likely to absorb 
more water than land which is regularly irrigated, and crops needing more 
water than those usually grown will be raised on some portion of the area that 
is regularly irrigated. Hence, in a country which is well adapted for irrigation, 
the effect of a continuously wet year is not so much to increase the duty of the 
water, as to permit irrigation of a bigger area, and the raising of an unusually 
large proportion of crops requiring a great amount of water. 

There is, however, another and financially very important aspect of this 
question. There are many localities where the rain-fall is of such a magnitude 
that the staple crops can be grown without irrigation during about one-half 
of a long series of years, but require more or less irrigation during the 
remaining years of the period. In such cases, it is quite probable that un¬ 
irrigated crops will fail for five, six, or even ten consecutive years. A demand 
for irrigation is thus produced ; and it frequently happens in cases where 
careful preliminary investigations have not been undertaken, that irrigation 
works are completed just at the beginning of a spell of wet years. In such 
cases, any discussion of the duty of water is futile, and owing to the almost 
certain financial failure of the scheme, unnecessary. 

The above will, I hope, render it plain that the duty of water is a matter 
that cannot be readily predicted. In actual practice, it will be found that not 
only each canal, but also each estate supplied by a canal, has its own peculiar 
duty. These differences will ultimately (and under careful and progressive 


DETERMINATION OF DUTY 


635 

management, very rapidly) adjust themselves by slight and almost unperceived 
modifications in the sizes of the distribution channels. In the design of a 
canal, howe\ er, some average figure must be assumed, and it may at once be 
said that no matter deserves more careful preliminary study. 

The principles are fairly plain. We must, as far as possible, ascertain the 
duties actually obtained in similar localities with crops such as will be grown 
on the area which it is proposed to irrigate. A careful estimate should also be 
made of the areas likely to be irrigated, and local opinion canvassed as to the 
crops proposed. It will then be possible to discover whether differences exist 
in the area to be irrigated which are likely to cause any portions to demand 
more or less water in proportion to their extent. 

By such means, we can arrive at a figure for the average duty over the 
whole area, and can broadly determine whether any portions require special 
treatment. 

The matter is further complicated by the fact that in most irrigated 
countries the climate is such that two, or even three crops, can be raised in the 
year, and these crops will usually require very different quantities of water. 
The complete solution will therefore take into consideration not only the crops 
which are likely to be raised, but the w^ater which is available at different 
seasons of the year, and the relative values of the possible crops. 

It is necessary to remember that any large error in selection may lead to 
financial failure by forcing the agriculturists to grow unprofitable crops. 
Fortunately, the engineer is assisted by favourable circumstances ; he can 
afford to “ guess high, 3 ' in doubtful cases, and can justify his attitude by two 
undoubted facts,—Firstly, in the early years the agriculturists will be more or 
less inexperienced, and will use more water than in subsequent years. 
Secondly, during the early years of irrigation better crops are obtained from 
virgin soils by heavier watering than is later required. 

Hence, the logical attitude is to design the canal for a duty which is 
somewhat less than that usually obtained. Later on, as matters approach 
their normal state, measures may be taken to increase the duty, and the water 
thus saved can be utilised in extending the irrigation to fresh land. Indeed, 
the most marked feature of a really successful canal is its steady growth ; and 
the channels are, in the long run, more likely to prove too small, than too large. 

The above considerations are best exemplified by actual examples. I select 
the following : 

The first is Willcocks’ discussion of the possibilities of irrigation in 
Mesopotamia (.Irrigation of Mesopotamia, 1905), which may be considered as a 
reconnaissance in an almost unstudied country. 

From local observation it is found that the crops grown are very similar to 
those of Egypt, but that the summer temperatures are somew'hat higher, while 
the winter temperatures are slightly lower. The exact figures are tabulated by 
Willcocks (nt sufra, p. 31), w r ho assumes that the cold weather crops will be 
those of Egypt, and will not require more w^ater. For the hot weather, he finds 
that maize and similar crops are grown during the season May, June, and July ; 
while in Egypt similar crops and similar temperatures occur in August and 
September. Thus, the duty during May and June is taken as equal to that of 
the period August and September under perennial irrigation in Egypt. In the 
months of August and September, cotton alone remains on the land, and con¬ 
sequently only one-third of the area is occupied. 


636 CONTROL OF WATER 

The assumptions produce a state of affairs under which the water require¬ 
ments of the area agree very fairly well with the supply in the river, although 
the demand is but small during the months of March and April when the river 
supply is apparently at its maximum. 

The assumptions are probably justified. They really mean that from 
November to March the whole irrigated area is under such crops as wheat and 
pulses. From May to July the whole area is under maize and cotton, and in 
August and September one-third of the area is under cotton, the maize and 
other crops having been harvested. 

The duties are calculated as 86 acres in the hot weather, and as 244 in the 
cold, reckoned on the gross area. This latter figure is high, and it is 
assumed that a development of well irrigation equal to that now prevailing in 
Egypt will take place, otherwise a smaller duty would have to be assumed; 
probably approximately 160 acres if no well irrigation is adopted. The assump¬ 
tion can be relied upon, for should well irrigation not develop, it will be possible 
to give the extra supply required in order to provide for deficiencies in well 
irrigation, since the canal has three times the capacity required for the assumed 
cold weather duty. Therefore, trouble need not be anticipated until the 
irrigation of the whole country is so far developed that the cold weather supply 
of the river is insufficient for the requirements of the total irrigated area. So 
far as can be gathered, the river would suffice to irrigate about five times the 
area for which the project is drawn up. 

The crux of the whole question lies in the excessive reliance placed on the 
cotton crop ; for should this not become an important staple, the demand is not 
likely to fall from the calculated value of 7000 cusecs in July, to 2800 cusecs in 
August ; and if this does not occur, the supply in the river may ultimately be 
deficient in August and September. 

As a contrast to Willcocks’ reconnaissance, the method employed in the 
project for the triple Punjab canals, namely, the Upper Jhelum, Upper Chenab, 
and Lower Bari Doab, may be given. Here, the country is accurately surveyed, 
and the present state of cultivation is recorded almost too minutely. The gross 
area “ commanded 55 ( i.e . that which is irrigable if only the relative levels of the 
water and the land are considered) by the Upper Chenab canal is 1,608,618 acres. 
Of this, 5 per cent, is assumed to be occupied by roads and buildings, or 
otherwise unculturable. 75 per cent, of the remainder is assumed to be the 
combined quota of canal and well irrigation. The remaining 20 per cent, is 
either low-lying land, flooded by small streams, or which is otherwise capable 
of producing a crop without the assistance of irrigation, or forms a reserve 
against possible water-logging (see p. 747). 

The irrigable area is therefore . . . 1,146,141 acres. 

Existing well irrigation is . . . . 497,773 ,, 

So that the canal irrigation will be . . . 648,368 ,, 

In the actual project, the canal irrigation area is given by districts, and the 
percentages 5 per cent, and 20 per cent, are by no means assumptions, having 
been arrived at after careful enquiry and a study of the existing population and 
methods of cultivation. 

Half of the above area is assumed to be irrigated in the hot weather (May 
to September,—Kharif), and half in the cold weather (October to April,—Rabi). 


PUNJAB DUTIES 637 

I he Kharif duty is taken as 100 acres per cusec, this being a figure obtained 
from experience on well-maintained and skilfully cultivated canal systems some 
40 and 60 miles away. The gross discharge is therefore 3242 cusecs, plus an 
allowance for absorption (see p. 738) in the main canals. Experience has also 
shown that it is advisable to be able to give an extra supply of 25 per cent, in 
cases of emergency. We thus get the following table, where the capacity of 
each branch has been obtained by a similar calculation :— 


Channel. 

Cusecs Discharged. 

Ordinary Supply. 

Extraordinary 
Supply, 
f Ordinary. 

Absorption at 

8 Cusecs per 
million square feet of 
wetted surface when 
the Extraordinary 
Supply is running. 

Main line, upper . 

No irrigation 

No irrigation 

253 

Main line, lower 

1156 

1442 

679 

Raya branch . 

1050 

I 3 I 4 

130 

Nokhar branch 

435 

546 

65 

Khadir branch 

600 

75 ° 

34 

Total. 

3242 

4052 

1161 


So that the Upper Chenab canal has to carry 5213 cusecs for its own re¬ 
quirements. It also carries the whole supply of the Lower Bari Doab canal, 
which is syphoned under the river Ravi. This canal irrigates what is practi¬ 
cally a desert. It is assumed (from previous experience in similar canals) that 
85 per cent, of the gross area will be culturable. The commanded area is 
divided into two well-marked divisions, namely, the Bar, or high lands, where 
the subsoil water is 60 to 70 feet below the ground surface ; and the Bet, or 
low lands, where this depth is 33 feet in the Ravi Bet, and 45 feet in the 
Beas Bet. 

Thus, the percentages of irrigation permitted are assumed as :— 

Per Cent. Per Cent. Acres. 

In the Bar, 75 of culturable area = 6375 of gross area = 547,373 
In the Bet, 50 „ =42*5 „ = 335U55 

882,528 


The difference is due to the possibilities of water-logging. It must be 
remembered that these percentages will probably be exceeded in certain 
districts in the course of years, as the likelihood or otherwise of water-logging 
becomes better known. 

It is realised that in this district since the Monsoon rains ( i.e . Kharif season) 
are not sufficiently heavy to permit any cultivation on other than irrigated 
areas, it would be advisable for one-third of the above area to be cropped in 

























CONTROL OF WATER 


638 

the Kharif season, and two-thirds in the Rabi season. The supply in the 
river does not permit this ; and the assumption that half the area should be 
Kharif cropped, and the remainder Rabi cropped, although financially less 
desirable, has to be made. The canal is therefore proportioned at 1 cusec 
per 100 acres for 441,264 acres, with an allowance of 25 per cent, extra for 
emergency supplies, and an allowance for absorption in the main line and 
large branches calculated at 8 cusecs per million square feet of wetted area 
(see p. 738). 

We thus get: 


Channel. 

Cusecs Discharge. 

Ordinary, i.e. 
Kharif Area 

100 

Extraordinary : 
f Ordinary. 

Absorption. 

Main line . 
Montgomery branch . 
Gugera branch . 
Shergarh . 

No irrigation 

3549 

698 

166 

No irrigation 

443 6 

872 

208 

3 X 4 

544 

107 

This is a distrib¬ 
utary, so no 
absorption is 
allowed. 


1 The total capacity at the head is therefore . . 6481 cusecs 

Add the quantity used and absorbed in the Upper 

Chenab . . . . . . . . 5213?) 


f b L Total capacity of Upper Chenab canal at its head 11694 ,, 

The above is probably the most complete and carefully investigated project 
which has ever been made. It is, consequently, as well to state that in some 
respects it is not precisely a model one. If immediate financial returns were 
alone regarded, there is little doubt but that a greater percentage of area would 
be irrigated, and that this area would be afterwards reduced in those districts 
where water-logging became manifest. The policy followed is to allow such a 
percentage of irrigation that it will never be necessary to deprive any land 
which has once been irrigated of canal water, and therefore large extensions 
may be hoped for in most districts. If financial returns are alone considered, 
the ratio of Kharif and Rabi irrigation now adopted would be somewhat 
changed. 

The Rabi duty is 200 acres per cusec, so that were the irrigation divided 
into two-thirds of the total area Rabi, and one-third Kharif, the supply in 
each season would be the same, and the total capacity of the two canals (all 
allowances being decreased in the same ratio) would be about 7463 cusecs. 
Consequently, a notable economy in first cost could be secured. 

The question of the methods of regulation of the supply which are entailed 
by the fact that the maximum demand in the Rabi season is appreciably less 
than the maximum Kharif demand is discussed later (see p. 741). While no 

























VARIATION OF DUTY 


6 39 

difficulty in the actual irrigation is experienced, once the system is in good 
working order, it will be plain that if the seasonal demands were rendered 
approximately equal, many of the masonry works for regulating the water 
level and distributing the supply into the various channels in turn could be 
dispensed with. The extra cost entailed by the larger Kharif supply is there¬ 
fore not fully expressed by the extra capacity required in the earthen channels. 

A study of the river discharges indicates that a supply which would permit 
this ratio of Kharif and Rabi irrigation, could probably be obtained in nine 
years out of ten, and that the deficiency in the tenth year would be small. The 
improvident habits of the Punjabi, combined with the fact that the crops during 
the Kharif season form the staple food of the population, fully justify the course 
adopted. But if the population were better able to cope with a bad season, 
the Rabi irrigation could be largely increased, and the Rabi crops are at 
present the more profitable. My own experience on a canal which was similarly 
situated to the Lower Bari Doab leads me to believe that the Rabi area will 
probably increase in a greater ratio than the Kharif; and we may expect 
that the final result will be something more like 700,000 acres of Rabi, and 
500,000 acres of Kharif, in place of the 441,000 acres of Rabi, and 441,000 acres 
of Kharif, provided for. 

Regarding the matter in this light, the real meaning of the allowance of 
25 per cent, of extra supply becomes somewhat more plain. An engineer 
designing such a system for profit alone would consequently increase the Rabi 
area to the maximum permitted by the supply in the river, and would irrigate 
only such Kharif area as the capacity of the canal that will serve the Rabi 
area (with allowances for extra supplies) will permit. 

Variations in the Value of the Duty.—The considerations detailed above will 
render it plain that the “ duty ” of water in a given locality is almost as variable 
as the rain-fall. In Egypt the rain-fall is practically nil, and therefore the 
“ duty ” of water used in perennial irrigation might be considered as likely to 
be fairly constant. As a matter of fact, putting aside all years when the water 
supply is deficient, and fairly good crops (in fact in some years of moderately 
deficient water supply the term “good crops” is applicable) are raised on a 
limited supply of water, we find that the duty varies, although not so greatly 
as in India, from year to year, owing to such influences as extra manuring, 
the substitution of cotton for sugar cane, etc. The Indian figures are even 
more variable, principally owing to variations in the rain-fall. As the Indian 
conditions are more closely akin to those which generally prevail in irrigated 
countries, rather than to those of Egypt, I tabulate a selection of the figures 
given in the official reports on the subject. These figures are calculated on 
the average discharge at the heads of the canals, and if it is necessary to 
compare them with Egyptian or American values, they should be increased by 
about 25 per cent. If the figures are used to calculate the water which is 
actually applied to the fields, a base of 180 days can be taken, and the depths 
thus obtained should be multiplied by o'55 or o'6o. 

The Sirhind canal irrigates an area which is somewhat more sandy than 
the land commanded by the Bari Doab. The higher Rabi duties of the Sirhind, 
as compared with the Bari Doab, during the years 1894-1900 are due to the 
silt troubles in the Sirhind, which are known to have caused a considerable 
economy in water during this period. It is for this reason that I have selected 
these two canals as examples, since the figures form a proof of the principle 


CONTROL OF WATER 


640 

that strenuous efforts in economising water will enable an agriculturist to 
overcome such handicaps as sandy soil, etc. 


Year. 

Duties in Acres per Cusec. 

Bar 

Doab Canal. 

Sirhind Canal. 

Kharif Duty. 

Rabi Duty. 

Month of 
November. 

Kharif Duty. 

Rabi Duty. ; 

1893-1894 . 



Ill 

• • • 


1894-1895 . 

70 

I 12 

I 12 

20 

77 

1895-1896 

68 

J 35 

144 

44 

156 

1896-1897 

73 

139 

172 

78 

197 

1897-1898 

82 

170 

177 

93 

164 

1898-1899 . 

77 

162 

209 

66 

182 

1899-1900 

74 

164 

201 

87 

198 

1900-1901 

99 

149 

I48 

101 

110 

1901-1902 

86 

221 

I98 

55 

177 

1902-1903 


• . . 

202 


• • • 

Base 

180 days 

160 days 

30 

180 days 

160 days ; 


approx. 

approx. 


approx. 

approx. 

1 


While the absolute volume of water used is highly variable, a fairly close 
connection exists between the relative depths of water consumed by different 
crops in the same locality, and during the same year. 

Using the depth of water consumed by a crop of wheat as unit, we find 
in India as follows : 


Crop. 

Depth 

Ratio. 

Duration of Crop Season. 

Wheat ...... 

I 

5 months 

Barley ...... 

o*8 

5 )j 

Vegetables ..... 

r 5 

4 to 6 months 

Tobacco ...... 

2*5 

6 months 

Lucern and other permanent forage . 

3 '° 

6 „ 

Gardens ...... 

2*0 

6 „ 

Sugar cane ..... 

4*0 

10 to 11 months 


It so happens that the irrigation water applied to the wheat crops was, on 
the average, equivalent to a depth of 10 inches, and that 2 inches more was 
received as rain, but the figures for the absolute depth of water received by 
any crop are far more variable than the ratios tabulated above. It must also 
be remembered that the relative profits obtainable from an acre of crop have 
a great influence (eg. compare tobacco with vegetables) on the quantity of 























































AGRICULTURISTS EXPERIENCE 


641 

water an agriculturist will apply. Thus in localities where the prices differ 
from Indian rates this factor alone may produce marked variations. In Egypt 
the influence of the extra manuring given to valuable crops frequently causes 
the water consumption of a well-manured field to be relatively much less than 
the species or value of the crop would indicate. 

Estimation of the Duty of Water for any Crop , or Locality .—A study of 
the duties recorded on page 640 will show that they are so variable that any 
enumeration of the figures which are accessible on the subject would be as 
useless to an engineer who is preparing an estimate for an unstudied locality, 
as tables of observed rain-falls would be if they were used to estimate the 
rain-fall of a locality where observations were deficient. Consequently, the 
following discussion deals with the accumulation of facts by which local ideas 
on the water requirements of a crop can be checked, and its chief object is 
to enable the effect of the changes in the methods of applying water to the 
land on the water requirements of the crops to be estimated. 

It will be found that while an agriculturist has, as a rule, the vaguest (and 
often most erroneous) ideas of the quantity (or total depth) of water which is 
applied to a crop, he has always a very definite knowledge of the number of 
waterings which a crop receives, and of the intervals between the successive 
applications of water. His knowledge on these two points may be regarded as 
incapable of improvement; and it will also be found that he not only knows the 
number of waterings given in a normal year, but has a very fair idea of the 
effect of an excess above, or deficiency below the normal rain-fall, and is acutely 
conscious of the longest period that can elapse between waterings without 
damage to the crop. This knowledge should not be taken as final, for the two 
following reasons : 

(i) The small pioneer irrigation systems from which this knowledge is 
frequently derived are generally devoted to raising crops such as garden 
produce (i.e. melons and green vegetables, rarely potatoes, or vegetables which 
are able to stand transport), or fodder (such as green oats), and the more 
valuable crops such as opium, or condiments. These crops usually require 
more water than the less valuable staples which will be grown when a well- 
developed system of irrigation is introduced. The error thus produced is but 
small, as in the early years of irrigation the agriculturist will apply his 
experience of the above crops to the staple crops, and if the engineer does not 
give him sufficient water to permit this, the development of irrigation will 
probably be slow. 

(ii) If the development is sufficiently advanced to permit of staple crops 
being raised under irrigation, it will usually be found that these staples all 
require water at the same time ; and a Professor of Agriculture will be able 
to show that, in theory at any rate, far larger areas of mixed crops could be 
irrigated with the available water. This opinion must be neglected in practice. 
We are concerned not with “ things as they ought to be,” but with “ things as 
they are.” If, by a judicious adjustment of the water rates, and by scientific 
trials of new agricultural products, the agriculturist can eventually be persuaded 
to economise water, fresh tracts of land can be irrigated. 

The practical result therefore is to accept the local custom as fixing the 
number of waterings which we are prepared to apply, and to lay out the system 
so as to permit of its extension. This is most easily effected by stopping each 
small distributing canal somewhat short of its maximum possible length ; and 

4i 


CONTROL OF WATER 


642 

the ideas of scientifically trained agriculturists on the subject of new crops and 
possible economies in water may be accepted in this matter. On the other 
hand, when considering the supply which is to be given to the area, which it 
is proposed to irrigate at the start, local custom should be held as binding. 

The number of waterings being thus determined, the depth of each watering 
has to be considered. This is best obtained by an actual measurement of the 
water used (the best method is a triangular notch), and of the area covered. 
The expense is not heavy. A careful study of the depths of five waterings 
covering an area of seven acres (including a complete record of the weight 
of the crop) can be made (professional salaries and travelling expenses apart) 
for ^50 to ^)6o, and if the co-operation of an intelligent agriculturist can be 
secured, this expense can be decreased. I strongly recommend that at least 
three such studies should be made, on areas selected so as to permit the 
influence of the quality of the soil being determined. If, in addition, the rate 
at which the water is applied is varied, still more valuable results will be 
secured. Consequently, the fullest information would be secured if the depths 
of water applied under the nine following conditions were measured: 

I. Sandy Soil. 

{a) Water applied at the rate of f cusec. 
iP) „ „ i *5 » 

(0 55 5) 3 55 

II. Medium (loamy) Soil. 

(a) Water applied at the rate of ^ cusec. 

(^) 55 55 I 55 

(^) 55 55 ^ „ 

III. Heavy (clayey) Soil. 

(a) Water applied at the rate of cusec. 

(^) 55 55 3 55 

(^) 55 55 1 55 

The conditions specified above are selected in order to obtain information as 
to the rate at which water can best be delivered. The larger quantities are 
therefore suggested in sandy soil. The absolute quantities are selected from 
the experience of agriculturists using manual labour only, and in a flat country. 
Where machinery is employed, larger rates of flow might be advantageously 
applied. In a steep country, smaller rates of flow must usually be adopted. It 
will also be plain that if the cost of obtaining information were alone considered, 
it would be better to apply the larger rates of flow in the clayey soil, for a flovv 
exceeding two cusecs is somewhat difficult to handle in sandy soil. 

The depth of a watering as thus determined will usually be found to be 
fairly constant, except that the depth of the first watering (usually termed the 
“ploughing watering,” although it may either precede or succeed the actual 
operation of ploughing), is some 25 per cent, greater than those given when the 
crop is in the ground. The second watering is, as a -rule, a little deeper than 
the others ; but the difference is only detected by weir measurements. It will 
however, be found in certain crops that deeper waterings are desired at particular 
stages of the crop growth. In countries where irrigation has been practised for 
many years, any watering which is dignified by a special name must, as a rule, 


EXTRA DEEP WATERINGS 


643 

be suspected to be deeper than the average. The question is usually not an 
important one, but the matter must be recorded ; for, should one of these deeper 
waterings occur simultaneously with a low-water stage, in the river or other 
source of supply, its depth may prove to be the factor which fixes the total 
possible area of irrigation. 

Thus, in the Punjab, the depth of the ploughing watering combined with the 
possibility of a simultaneous low stage of the rivers during the period from the 
15th October to the 15th December, and more acutely from the 1st November 
to the 30th November, will ultimately fix the total irrigable area. 

In Bengal, a similar sudden demand for water from all rice cultivators, just 
before the rice harvest, taxes all channels to their utmost; and if the cultivators 
could be induced to grow varieties of rice which did not require this last drench¬ 
ing, the channels would probably irrigate an area greater by 50, or 60 per cent. 

In Egypt, on the other hand, the acute demand (in cotton cultivation at any 
rate) is not produced by any abnormal requirements of the crop, but occurs in 
May, June, and the early part of July, when the crop requirements are normal, 
but the supply in the Nile is low. In this country, when the present reservoir 
and reclamation schemes are fully carried out, it is probable that the require: 
ments of the maize crop during the ploughing watering will finally prove to be 
the factor limiting the extension of irrigation. 

Such studies (when properly carried out) will permit the duty of water as 
measured at the field to be determined. The losses which occur between the 
river and the field can be estimated by the figures given on page 738, or better still, 
systematic gaugings can be made on existing channels by the methods already 
discussed. The triple canal project quoted on page 637 shows the method of 
allowance for the losses in the major canals, and a similar calculation can be 
applied to the minor canals and watercourses. 

In many instances, however, the expense of such studies is grudged ; and in 
any case an engineer must be prepared to give preliminary figures which will 
justify an expenditure of even ^60 on “ mere theory.” 

The following notes on the normal depth of a “ watering ” are therefore 
useful. 

Putting aside such crops as rice, which grows in standing water, and valuable 
crops such as garden produce, fruit, and drug plants, which are supplied with 
water regardless of expense, it is found that the species of crop grown does not 
materially affect the depth of an individual watering, but merely influences the 
frequency of waterings. 

The depth of a watering is determined by the fact that the water is cut off 
when the soil farthest removed from the point where the water is turned on to 
the land is seen to be wetted, or covered with water. The extra depth given in 
a ploughing watering is probably largely caused by the fact that the agriculturist 
does not cut off the water until the clods have fallen in pieces through being 
soaked in water. Possibly a desire to saturate the ground to a certain depth, 
and thus to render it more easily ploughed, may also have some influence.' 

The depth of a watering is therefore fixed principally by the time which the 
water takes to cover the whole area of each plot into which the field is divided. 
During this period the portions of the plot nearest to the point where the water 
enters are covered with water which is absorbed by the soil. Thus, the least 
depth of a watering is secured when the field is divided into very small plots, 
each of which is rapidly covered with water. Finally, the smaller the individual 


644 


CONTROL OF WATER • 


plots, and the greater the rate of flow of the water, the smaller is the depth 
which is needed over and above the minimum requirements of the crop. 

In the case of irrigation from wells where the cost of lifting the water is the 
chief expense, and the rate of flow is but small, these individual plots are small, 
and resemble flower beds rather than fields, being, say, 16 feet x 4 feet as a 



Pldn 


_. 1 * 4 1 Sod Sodded bank 

Ridaes about W \TJWatercourse about 9-6" 

Vkiod V y- 1 

Sttfion 

Sketch No. 157.—Typical Field, irrigated from a Well. 


minimum, and 50 feetx 10 feet as a maximum. (See Sketch No. 157 and 
contrast with Nos. 220 and 221.) Such small areas are not advisable in canal 
irrigation, and in India areas of no feetx 55 feet are standard, the water beiim 
applied at a rate of o'3 to 1 cusec, or even more in some cases. In fact, practiced 
experience has taught all agriculturists experienced in irrigation to make a very 
equable balance ot the advantages between an economy in water secured by 
dividing the fields into small plots, and the extra labour entailed in constructing 










































































































































































































DEPTH OF NORMAL WATERINGS 645 

these plots. Thus, on the average (putting aside special methods employed for 
valuable crops), the normal size of a plot in any district bears a very close 
relation .to the normal rate at which water is applied in that district. The 
inigation engineer will probably consider that the plots are too large, but this 
conclusion will only be arrived at by underestimating the value of the labour 
expended in making the small banks surrounding the plots. I consider that the 
standard Indian area is a very fair balance between an engineers ideal and 
an agriculturist’s wish for rest. In countries where labour is more valuable, 
larger plots will be desirable ; but the question is very intimately connected 
with the value of the crop. The introduction of machine cultivation is at 
present a factor which tends to increase the size of the plots, but this is only a 
transient phase of the question. When harvesters are adapted to traverse the 
irregularities formed by the ridges surrounding the plots, and when machinery 
is employed for making these ridges, it will certainly be found advantageous to 
decrease the size of the plots. 

dhe fact that the greater the rate at which the water is applied the larger is 
the average area of the plots, causes the depth of a watering to vary but little, 
and actual measurements indicate the following: 

Well, or lift irrigation. 0*15 foot to 0^25 foot. 

Canal, or flow irrigation. 0*25 foot to 0*40 foot. 

As a general rule, we may assume ploughing or other heavy waterings to be 
o’33 foot. Succeeding less heavy waterings should be taken as o’25 foot. 
These figures assume the presence of skilled irrigators. Where the water is 
carefully economised, such figures as 0*25 foot for the heavy waterings, ando'2o 
foot for the lighter ones, are attained. In careless irrigation, such figures as 
0*50 foot for the heavy waterings, and 0*40 foot for the lighter ones, may be 
expected, and the waterings usually succeed each other at much closer intervals 
than a skilled irrigator finds requisite. 

The temperature and other climatic conditions seem to have very little 
influence on the depth of a watering, and the effect of all such conditions will 
be found to be amply allowed for by the variations in the intervals between 
successive waterings. 

In careless irrigation, however, the fields are not usually divided into plots, 
and the water is allowed to flow over a large area, with the result that the 
portions near entry of the water are deeply saturated, while the further 
boundaries of the field suffer from a partial drought. Such methods are 
advantageous to no one ; and, unless the custom is extremely firmly rooted, 
an engineer will hardly be well advised to design his channels with dimensions 
which tend to indefinitely prolong the practice. 

In areas where a marked slope, or irregularities in the surface of the soil, 
exist, an extra quantity of water must be applied in order to fill up irregularities 
in the natural surface. This extra amount can be estimated by levelling a few 
sample fields, allowance being made for the fact that the above depths of water 
are sufficient to submerge small irregularities such as clods, and furrows, and 
that the extra depth now considered is required merely to fill up those de¬ 
pressions and irregularities that exist independently of agricultural operations. 

The above principles permit the local duty of water for staple crops to be 
estimated with sufficient accuracy. Variations will occur from year to year, 
owing to abnormal rain-fall or temperatures, but these are incidental to all 


CONTROL OF WATER 


646 


agricultural operations. These irregularities are amply covered by the extra 
capacity of 25 per cent, which is given to the channels in the triple canal project 
(see p. 637). In selecting the exact figure which is to be assumed as the duty 
of the water, we must of course consider not so much the duty for the whole 
period for which the crop occupies the ground, as the greatest intensity of 
demand that occurs during the life of the crop. The dimensions of the channel 
are therefore finally calculated so as to supply the average demand when run¬ 
ning nearly full bore, and the most intense demand when carrying a little less 
than the extraordinary supply. 

For example, consider the month of November, in the Punjab. Nearly all 
the area irrigated during the cold weather receives a ploughing watering. One 

cusec therefore at the fields has a duty of —— J =180 acres. Allowing for 

0-33 

absorption in the smaller branches of the canal, one cusec at the head of the 

distributary has a duty of 150 acres, say. Thus, the extraordinary supply 

I 2 

will just permit 150 x 1*25 = 187*5 acres to be irrigated in the thirty days, from a 
channel the full supply capacity of which is one cusec. The period of intense 
demand having thus been tided over, the crops (unless assisted by showers of 
rain) will require an ordinary watering every thirty days. Thus, one cusec at 


the distributary heads will water 


2 x 30 


or 200 acres, and the real meaning 


o‘25 x 1*2 

of the statements “ Rabi duty is equal to 200 acres per cusec,” and “ It is 
desirable to be able to give an extraordinary supply of 1*25 x ordinary supply,” 
become obvious. 

Allowance for'abnormal rain-fall in the year of observation may be made by 
the following rule : 

On the average, every 2 inches of extra rain-fall occurring in casual showers 
replaces 1 inch depth of water, as applied to the fields. The figure is the 
result of an examination of fifteen years of statistics of the duty and rain-fall of 
eight small areas in the Punjab, by the method of correlation coefficients. The 
rule is only an average one, although the values of the eight correlation co¬ 
efficients cluster very closely (0*45 to o’57) round the value The rule 
evidently does not express the relative efficiency of rain and irrigation water 
in supporting the life of crops (I believe that rain is far more efficient 
than irrigation water) ; but expresses the fact that waterings are only given 
when required, while rain is equally likely to fall immediately after a watering, 
when not required, as at the moment at which a-watering would otherwise have 
been given. In countries where rain falls at fixed, or nearly fixed dates, or 
when the weather continues “rainy” for periods comparable to the normal 
interval between successive waterings, the principle laid down by Willcocks 
(see p. 634) may be considered as correct ; and in the Punjab I have frequently 
heard old farmers speak of the “ regular ” Christmas rains of their youth, which 
“were as good as an extra watering.” Nevertheless, the expression laudator 
temporis acti must not be forgotten in this connection. 

There remains one matter to discuss, namely,—How far, and to what degree 
should an engineer in preparing his project allow for methods of cultivation 
which he knows are wasteful of water ? 

The question is a very important one, for such methods not only waste water, 
but tend to ruin the land by the seepage water and alkaline salts which they 




EXCESSIVE WATERINGS 


647 


produce. Wasteful irrigation is consequently injurious not only to the land, but 
also to the corporation supplying the water, and to the whole community and 
its future interests. Local conditions must decide the question, but I have no 
hesitation in saying that the smaller the latitude which is permitted, the better ; 
and that an engineer who allows such conditions to become permanent will, 
sooner or later, find his employment gone, merely because irrigation will have 
ceased to be profitable, and extensions are no longer required. 

The worst cases (and also the most skilful irrigation in the world) occur in 
America. The publications of the Department of Agriculture (Bureau of Soils), 
and of the Geological Survey (Reclamation Service) will provide a surfeit of 
evidence. The matter, put in a nutshell, resolves itself into the statement that 
if wasteful methods are permitted, the irrigation channels must be doubled, and 
the drainage channels trebled in size. 

These remarks must not be taken as referring to the cultivation of such 
crops as rice, or the winter meadows of Lombardy. Rice needs from five to 
six times as much water as other crops grown in the same climate. It also 
requires drains in order to carry off this water, and its cultivation is therefore 
unlikely to produce alkalinity unless such drainage is neglected. Rice is not a 
crop to be encouraged, and in Lombardy it is not permissible to grow it within 
1100 feet of a town. The flight of the Anopheles (malaria-carrying mosquito) 
being about 200 to 300 yards, the object of this old regulation now becomes 
plain. Winter meadows, or marcite culture, are in reality methods of keeping 
grass warm during the winter, with a view to fostering growth which would 
otherwise be arrested. Such methods dispose of water which would otherwise 
run to waste, and since they require a well-drained gravel subsoil, they are not 
likely to cause water-logging ; but, nevertheless, the first signs of water-logging 
must be carefully looked for. Details will be found in Baird Smith’s Italian 
Irrigation and in Scott Moncrieff’s Irrigation in Southern Europe. 

Influence of the Rate at which Water is Applied to a Field 
on the Quantity of Water used in Irrigation. —When water is 
applied to irrigate an area of land, what actually happens is that the water 
covers the land to a certain depth (say y, feet), and then flows on to cover more 
land. Now, over the whole wetted area water is percolating into the soil. * We 
can therefore say that if water is applied at the rate of Q, cusecs ; then, at a time 
t, when an area of A, square feet is covered with water, we have the following: 


Q dt —ydA -\-pAdt 

where /, is the rate at which water percolates into the soil from the area which 
is already wetted by the water. Thus : 

‘A l0 * Q^A- 


Now, the irrigation of any plot of land is not considered to be complete until 
all the plot is wetted. Thus, the time taken to irrigate a plot of an area A 0 , is 


log ' q4a„- 

Now, in actual practice/, may be taken as 


15 


1,000,000 


, for water is absorbed 


by sandy fields at an average rate of 21 cusecs per million square feet, and by 
loamy fields at a rate of 8 cusecs per million square feet (see p. 739). 





CONTROL OF WATER 


648 


Let us assume that y = 2 inches = ^th foot. 

Thus 4 = 11,111 loge „ ^ -r-. 

Now, consider a plot of 6000 square feet in area, which is that which is 
usual in India. /A 0 = o‘O9 cusec. 

Now, if there were no absorption : 


Q4 — 


1000, or 4 = 


1000 

~Q” 


seconds, and the quantity 


used is 1000 cubic feet. 


Q, in Cusecs. 

4 , when Absorption 
is 15 Cusecs per 
million square feet. 

In Seconds. 

4, when there is 
no Absorption. 

In Seconds. 

Actual Quantity used 
when Absorption 
is taken into 
Account. 

2 

51 ° 

5 °° 

1020 cubic feet 

i *5 

688 

666 

1032 „ 

1 

1044 

1000 

1044 „ 

°'75 

1411 

J 333 

1058 „ 

°’ 5 ° 

2200 

2000 

1100 ,, 

0-25 

5° 6 5 

4000 

1266 ,, 


The great increase in the quantity of water used as Q, falls below 0*50 cusec 
must be noticed, and it is plain that if 2 inches are assumed to be an adequate 
depth, an irrigator who applies water at the rate of 0^25 cusec only must give 
his crop, on the average, a watering equal to 2*5 inches. Under such circum¬ 
stances, the crop near to the entrance of the water must receive far more than it 
needs. The case becomes still worse if the irrigator is lazy, and endeavours to 
save labour in constructing watercourses by doubling the area of his plots. We 

then have, 4 = 11,111 log e and with : 

Q —o‘i8 

Q = 1, 4 = 2200; or, the volume used is 2200 cubic feet in place of 2000 cubic feet. 
Q = °'5, 4 = 5066; or, the volume used is 2533 cubic feet in place of 2000 
cubic feet. 


The circumstances may at first sight appear to be abnormal, as it is plain 
that if y = 1 inch, the advantages of the greater rates of flow are less 
marked. The value y = 2 inches agrees fairly well with observation, and the 
quantities arrived at by these calculations are confirmed by accurate gaugings 
over triangular notches of the volumes actually applied to measured areas 
by skilled irrigators, who knew the object of the experiments. 

Certain tests of the quantity of water used by agriculturists in ordinary 
work appear to agree better with y = 2*5 to 3 inches. Under these circum¬ 
stances the advantages gained by a rapid application of the water are of course 
still more marked. The experiments were mainly conducted on virgin soil, 
where heavy waterings are known to be advantageous. It is therefore believed 
that the figures for y — 2 inches best represent the circumstances when 
measures are taken to secure an economical utilisation of water, and irrigation 
is well established. 





















WASTE OF WATER 


649 

Kennedy and Ivens working independently on the Bari Doab and Ganges 
canals came to the experimental conclusion that irrigators waste a large 
proportion of the water which they receive. The figures are startling. Out of 
1 cusec taken in at the head of the canal Kennedy found that the irrigator 
received 0^53 cusec, and “utilised” o'28 cusec. Ivens’ figures were o'56, and 
029 cusec per 1 cusec taken into the canal (see p. 631). The efficiency of 
Indian canals is probably higher at the present date, since owing to the 
systematic enforcement of rules concerning the sizes of individual plots (see 
P* 73 2 ) the irrigator “wastes” less water. It may, however, be doubted 
whether the difference is all “ waste.” The water saturates the soil, and is 
probably to a certain degree utilised by the crop, especially if this is a deep- 
rooted plant such as wheat or cotton. Nevertheless, it has been amply proved 
that an engineer working on methods deduced from a study of absorption can 
raise a better crop with a less depth of water than an ordinary irrigator under 
similar circumstances. 

The fact that when an irrigator chooses to adopt the engineer’s methods, 
and in addition utilises his agriculturist’s knowledge, he produces a far better 
crop with less water than the engineer, is a very fair proof that the methods 
are correct, however disappointing the result may be to the engineer (see 
Punjab Irrigation Branch Paper No. 12). 

Hence, we may finally deduce the following rules. 

The engineer should arrange to deliver the water to irrigators in as large a 
stream as they can handle. This rate will depend upon the available labour, the 
character of the soil, and on the general slope of the country. 

The irrigator can economise water by dividing his fields into plots of an 
appropriate area, and irrigating each separately from watercourses so arranged 
as to supply each plot individually as in Sketch No. 157, which also indicates 
the extreme care a skilled irrigator takes to avoid “ uphill ” irrigation of the 
individual plots (see also Sketch No. 220). 

The best rate at which water should be delivered, and also the appropriate 
size of the plot, can be investigated mathematically ; but the plan of experi¬ 
ments sketched on page 642 will not only settle these matters practically, but will 
also afford the engineer actual figures to justify his proposals. 

The irrigator can also economise water by carefully smoothing the ground 
previous to irrigation. This is effected in India by drawing a flat beam of 
wood across the newly sown ground, thus crushing down the clods and 
irregularities. 

The special methods adopted in the irrigation of tobacco, opium, gardens, 
or orchards, are hardly sufficiently important to affect the average consumption 
of water over a large area. Such special methods usually produce an economy 
in water, as only a fraction of the area is wetted, and hence the absorption 
during irrigation is reduced. 

Inundation Irrigation. —The figures connected with inundation irriga¬ 
tion are purely local in their application, and cannot be determined by the 
methods which have been previously discussed. 

The success or failure of inundation irrigation is settled by the two 
following conditions : 

(a) The amount of water absorbed by the soil. 

( b ) The mean temperature of the season succeeding the inundation. 

The conditions prevailing in Egypt may be considered as typical. The land 


CONTROL OF WATER 


650 

should be submerged for fifty days, but in bad years a submergence of six or 
seven days only may be obtained. A crop can then be raised, but not a good one. 

The flood water is drained off the land from about the 10th to the 30th 
October, and the crops are sown at once. 

The mean temperature at Cairo is as follows : 

October . 

November 
December 
January . 

February . 

March 

The crops grown during these months are those cultivated in Temperate 
climates. It is quite plain that if the mean temperature were materially less 
than the above figures, no crop could be grown on account of the cold. So 
also, if the temperature were such as to favour the cultivation of Tropical crops, 
it is open to doubt as to whether the saturation produced by one inundation 
would suffice to mature such crops unless the soil was unusually retentive, and 
the flood was of long duration. Thus, pure flood irrigation requires a some¬ 
what nicely adjusted relationship between the duration and depth of the flood, 
and the mean temperature of the season which succeeds the flood. If the 
question is ever considered in practice the publications of the U.S. Department 
of Agriculture give useful information concerning the mean monthly temperatures 
required for healthy growth of cultivated plants. 

The average depth of flooding in Egypt is 3*30 feet (1 metre). Depths 
exceeding 2 metres do not occur, apparently owing to the cost of the banks 
required to retain the water ; and a flooding of less than r6 feet (o'5 metre) is 
considered injurious. The figures are considerably affected by such questions 
as the quantity of silt in the water, and the permeability and retentiveness of 
the soil. 

In some Indian examples, where the banks of a reservoir are cultivated as 
the water is drawn off, good crops are raised if the land is only covered to a 
depth of 6 inches for ten days. In these cases, the subsoil water level is but 
slightly below the surface, and the crops usually receive one or even two 
waterings by lift from the reservoir, or from the subsoil water, towards the end 
of their growth. 

Design of Irrigation Works. —As will later appear, the logical method 
of designing an irrigation system is from the tail upwards. The preparation of 
a large project is, however, only likely to be undertaken by engineers who 
have some experience of irrigation work. 

The usual work of an engineer, or designer, is concerned with the design of 
structures of which the main dimensions are already determined. Thus, it 
seems best to describe and consider the rules for the design of irrigation works 
in the order in which the water flows down the channel. I shall therefore 
describe : 

(i) The diversion weir and headworks of a canal. 

(ii) The escapes. 

(iii) The aqueducts, syphons, and other works required to dispose of 
drainage water. 


73*5 degrees Fahr. 

^ 5’3 ” >> 

5 $ 1 
55' 1 

5^7 >> 

72*4 „ » 



6 5 * 


IRRIGATION STRUCTURES 

(iv) Bridges and other accessory works. 

(v) The head regulators of branch canals. 

(vi) Falls and rapids. 

(vii) The preliminary design of a branch canal. 

(viii) The final design of a distributary. 

1 he question of silt arises in nearly all these structures, and is treated 
incidentally ; but a special section is devoted to silt problems. 

Buckley’s Irrigation Works and Wilson’s Irrigation Engineering contain 
numerous detailed plans of individual works. Bligh’s Design of Irrigation 
Works (second edition) is almost indispensable. I have been forced to 
criticise some of Bligh’s ideas rather closely, but am in full agreement with at 
least 95 per cent, of the book. I would, however, state that I believe some of 
the hydraulic coefficients adopted are rather high if applied to the small works 
that a young engineer will usually design. For large works such as occur in 
India they are excellent. 

The sections of works that I give must be considered as illustrating 
principles rather than the best available examples. I have also endeavoured 
as far as possible to select only works I have personally examined. Engineers 
unacquainted with local conditions should bear in mind that Indian materials, 
especially bricks and mortar, are at the best only second class material when 
judged by British standards. Egyptian materials are better, but Egyptian 
irrigation is still directed by Indian-trained engineers, and I believe this 
influences the designs very materially. As an endeavour to sum up a very 
complex matter I would state that I believe the area of most of the designs 
shown is not excessive, but that given good material some of the thicknesses 
might be reduced. American designs if carefully tested for weak details are 
probably safe, and such material as I have seen is usually good. 

Relationship between the Design of Hydraulic Works, and 
their Maintenance. —This subject is of most importance in connection with 
earthen channels and natural rivers. The principles, however, are applicable 
in connection with all hydraulic constructions. The matter is discussed in 
regard to irrigation works, because the penalty of neglect then becomes most 
noticeable. The general principles-may be summed up in two sentences, as 
follows : 

The formation of vortices, or irregular currents, should be avoided. Pre¬ 
ventive methods are both cheaper and more effective than repairs. 

The first principle is very well illustrated by the facts given on page 719 when 
discussing the pitching of rapids. It is there shown that those rapids which 
cause the least trouble have smooth pitching, and that this smoothness has 
been attained by intelligent maintenance. So also, the Punjab type of fall (if 
carefully considered) is plainly designed with a view to preventing the forma¬ 
tion of vortices, or whirls. These illustrations arejthe more striking when the 
history of the development of the types now adopted is known. 

The present designs are then seen to be the outcome of long experience by 
engineers who were obliged to study the cost of maintenance very carefully, 
and whose improvements were severely criticised in the light of theories based 
on the idea that “the energy of the falling water should be dissipated in boils 
and whirls.” It is almost amusing to read the struggles made by various chief 
and superintending engineers in order to obtain a “boil” somewhere, and the 


CONTROL OF WATER 


652 

equally strenuous endeavours on the part of the men who have inspected the 
damage to get these “ boil ’’-producing angles filled in with concrete or cheap 
rubbish. It may be said that the theory is still alive, and that the present 
designs are accepted only because they do their work so well that the theorists 
are not often given an opportunity to criticise. 

The present American designs for overflow dams betray the same errors. 
The usual idea is that the “ rough masonry of the ogee, or other curve, breaks 
the falling water into foam.” The statement is correct, and the breaking up 
process does no one any harm, because the face stones of a well-made dam are 
very large, and are very firmly fixed in comparison with the thin sheets of 
water that they break up. The falling sheet of water, however, usually arrives 
at the bottom of the dam not as foam (unless it is a thin sheet), but as a mass 
of whirling water, which can and does scour out pebbles and sand. The water 
cushions which are sooner or later constructed below every “overflow” dam 



that normally acts as an overflow, show the correct method of dissipating the 
energy of the fall (i.e. not by friction of water on stone or earth, but by friction 
of water on water). It is quite probable that better results could be obtained 
by carefully dressing the masonry to a smooth surface, were it not that this 
class of work is expensive. 

Thus, we may consider that the ordinary rough-surfaced overflow dam is 
successful only because the dam is strong enough to resist the shocks caused 
by the falling water without material damage. It is also doubtful whether the 
usual overflow dam, even when constructed of first class material, would prove 
satisfactory if it were continually acting as an overflow. A proof of this 
statement is difficult, but my list of dam failures includes what is apparently an 
excessive proportion of overflow dams which retained volumes of water which 
were small in comparison with the annual discharge of the stream supplying 
the reservoir. The list does not pretend to be a complete one, and therefore 
the suggestion is put forward with diffidence. The Austin dam failure (see 













































SMOOTH-FACED BELLS DYKES 653 

pp. 346 and 394) may be taken as an example. In this case the foundations 
appear to have been naturally weak, and although the failure can be explained 
without any assumption of damage by the action of the overflowing water, it is 
known that some damage had occurred. 

Similarly, the Habra dam (see p. 372) was also greatly subject to overflow, 
and though its working stresses were no doubt high, they were not so 

abnormally high as to necessarily produce failure, independently of overflow 
action. 

1 he old ogee falls (see Sketch No. 158)5 which were constructed of second- 
late brickwork, had to be made smooth to prevent their destruction. In 
consequence, the energy was dissipated downstream of the masonry, and the 
scoui holes thus produced sooner or later undermined the masonry work of the 



fall. The raised sills and steps indicated in the sketch show various methods 
that were tried in the hope of producing a better design. These are evidently 
first steps towards the modern water cushion, but the angles are evidently 
inadvisable as tending to produce boils. 

Bell’s training dykes (see p. 667) show a very logical development of the 
correct principles. The large scale plans of such training works {eg. Sketch 
No. 159) show the manner in which the principle is applied. Nevertheless, it 
is found that the principle can be carried still further with advantage. The 
banks are faced with two or three feet of rubble stone, and, according to the 
usual theories, this should be laid so as to present a rough surface to the river. 
In practice, however, experience shows that a smooth face is advantageous, 
and Bell recommends that not only should the rubble be hand-packed to a 
smooth face, but that where possible the stone should be selected so as to 






































CONTROL OF WATER 


654 

assist in obtaining a markedly smooth face. When it is realised that some of 
these training works consume rubble stone in quantities of 10, to 20 million 
cubic feet and more, it will be plain that the advantages secured must be very 
considerable in practice. 

Kanthak applied the principle at Madhupur. The conditions prevailing at 
Madhupur are discussed on page 662. When submerged during floods the 
training dykes are exposed to an intense erosion from water carrying boulders 
with velocities exceeding 20 feet per second. 

The old design for the narrow crests and rough slopes of such dykes is 
shown in Fig. 1, Sketch No. 160. Fig. 2 shows the broad crest with smooth 
slopes introduced by Kanthak. The improvement has produced a material 
saving in maintenance costs. 

The above applications are concerned with water which moves at high 
velocities, but equal advantages result when earth channels which carry water 



at velocities of 2, or 3 feet per second are considered. Thus, in Sketch No. 
161, ABCDEF represents the banks of a canal as constructed,.and GHKL, the 
section of the channel as calculated from the designed bed slope, and the 
discharge of the channel. 

At first sight it would appear legitimate to leave matters to Nature, and to 
expect that the extra area will silt up more or less rapidly. As a matter of fact, 
a reach of this character is usually a source of trouble, as scour very often sets 
up in the normal sized reaches, either above, or more generally below the 
enlarged reach, or tank. In some cases (usually in canals which have curved 
reaches near this “ tank ”) no silt is deposited in the tank. The troubles are 
easily cured by a series of brushwood profiles, outlining the section GHKL (at 
say every 1000 feet length of the tank, for a tank 50 feet wide, and in proportion 
for narrower tanks). The expenditure is well repaid by the deposit of silt which 
occurs, and strengthens the banks. Once silting has begun, any signs of the 
channel meandering between the banks AB, and EF, should be carefully 
watched for; and should be stopped by the removal of excrescences, and by 























REGIME 655 

placing small, partial profiles of brushwood across any marked bends that may 
tend to form (see Sketch No. 219). The matter is of practical importance, as 
in many cases the natural soil is so tender that breaches continually occur until 
a good berm of silt has been deposited. 

1 he two lower figures of No. 161 show the application of similar principles 
to stone training banks (or channel profiles) below falls and rapids (see p. 721). 

On well-maintained canals (say ten or fifteen years old), all the channels 
will be found to be built up of silt, the water flowing on beds and between 
berms of silt. The future existence of such conditions should be kept in mind 
when designing a canal. In fact, the existence of silt in a water may be 
regarded as a favourable circumstance, provided that the laws of the disposi¬ 
tion of silt and the proper proportions of the channels are carefully studied, and 
that the results are utilised in schemes for maintenance. A good engineer 
should be able to modify the grades and levels of the distributary system at a 
very small cost by such means as temporary dams which slowly raise the water 
level in reaches where the banks are weak. Thus, in one particular case I found 



c o 


Profiles in Sitting Reacti 



Stone. Training Ranks belou Falls or PapnJs 


Sketch No. 161.—Silting Profiles and Training Banks. 

that it was possible to silt up and raise the bed and water level of a channel 
which proved to be too low, at the rate of 2 feet a year. So also, the careful 
working of a fall, or of a regulator, will permit a permanent local drop in the 
water surface to be obtained by scouring. This is often advisable where 
drainage questions have become acute, but careful arrangements should be 
made for disposing of the silt which is thus set in motion. 

Regime. —The term regime of a river or canal is used as a convenient 
expression for the adjustment which exists between the size and cross-section 
of the channel and its mean discharge. Thus, a reach of a river, or of a canal, 
is said to be in good or permanent regime when the river does not decisively 
attack its banks, or does not scour out or deposit silt in its bed, even although 
it is known that the individual particles which form the bed and banks of the 
river are in rapid motion downstream. The regime is considered to be bad 
if the banks are continually attacked, or if large quantities of silt are deposited 
in, or are scoured out of the channel. 

The terms good and bad are obviously relative. A canal, say, 50 feet in 
width, can hardly be considered to be in first class regime unless its actual cross- 
section agrees with the designed cross-section to within a foot or so ; and 































CONTROL OF WATER 


656 

reaches which are designed to be straight should not diverge more than two or 
three feet from a straight line. In a large torrential river, however, the regime 
is considered to be permanent unless the services of a special pilot are required 
when navigating the river. 

The regulation of an irrigation system, or of a river, is a convenient 
expression for the control which the engineer in charge has over the water level, 
and for the methods by which this control is obtained. Thus, in the Punjab 
the water level in the remotest branches of a large system can be predicted 
(accidents apart) to a tenth of a foot, and alterations of three or four feet can be 
effected in a period not greatly exceeding the time required for the water to 
travel from the head of the canal to the desired point. In a well-regulated 
river (flood time excepted), the water levels can generally be adjusted nearly as 
accurately. Whereas, in natural unregulated streams, the water level entirely 
depends upon the quantity of water which may be flowing down the stream 
channel. 

Headworks. —The term headworks forms a convenient expression for the 
structures required to divert water from a river into a canal. 

The ratio in which the total volume of water passing down a river is divided 
between the natural river channel and a canal taking out from the river, is 
obviously dependent upon the slopes and relative levels of the water surface 
in the river and the beds of the river and of the canal. In some cases, the 
canal can be so graded that this natural division of the volume discharged by 
the river suffices to supply the canal with all the water that is required. 

We thus get the simplest class of headworks, where neither the canal nor 
the river are in any way controlled, and where the canal takes the water that 
it can get. Such works suffice in many cases, especially when the irrigation 
is effected by inundation, and the river rises in high flood at more or less fixed 
periods of the year. The risks of a partial failure are obvious ; and, as a 
general principle, this method of securing a supply of water is only successful 
when the river floods are very regular in occurrence, and are in most cases 
produced by melting snow. Typical examples are found in the basin irrigation 
of the Nile, and in the inundation canals of Northern India. 

The natural method of securing a more certain supply of water is to grade 
the canal at so low a level that the desired supply can be secured at all seasons 
of the year. It is then usually found that the natural division of the river 
discharge will generally give the canal more water than is required. Thus, a 
head regulator, or line of movable gates, is constructed across the canal ; and 
by partially closing these gates the excess of water can be diverted down the 
river. This method is frequently found to be entirely satisfactory and will 
then probably prove to be the cheapest. If, however, the river flows in alluvial 
soil, or if the bed is liable to shift to any extent, trouble may occur in the 
course of time, arising from the “ retrogression of levels.” This term expresses 
a slow alteration in the level of the river bed, which may lead to the formation 
either of a “ deep ” in front of the canal head, and a consequent difficulty in 
securing the required supply ; or less frequently to a “ shallow ” or bank which 
may choke the canal with deposits of sand or gravel. These difficulties can 
usually be surmounted by forming a bar across the river. Typical sections 
of such bars are shown in Sketches No. 162 and Fig. 1 No. 180. The river 
works are comparatively simple, and the method should be adopted in all cases 
where the excavation of the low-level canal does not prove too costly (see p. 684). 


HEAD WORKS 


657 

In the majority of cases, however, especially when the full supply discharge 
of the canal is of about the same magnitude as the low water discharge of the 
river, such a design would necessitate a very costly canal, and an enormous 
canal head regulator, in order to keep the river out of the canal during floods. 
The canal is therefore graded at a relatively higher level, and it becomes 
necessary to raise the water level of the river by a weir or dam, in order to 
force the desired supply into the canal during low water seasons. This is the 
typical form assumed by headworks, and will be discussed at length. 

1 he following general principles are obvious. The height of the dam may 
vary from a small quantity, such as 1, or 2 feet, up to 150, or 200 feet ; and the 
higher dams are plainly not only diversion works, but permit a certain volume 
of water to be stored up. We are thus led to regard a tank or reservoir 
irrigation system merely as a development of the more usual river diversion 
system of irrigation. 

The obstruction produced by the dam or weir encourages the deposit of 
silt at or near to the canal head. Therefore, unless the river carries very clear 
water, the weir must be provided with scouring or undersluices for the removal 
of silt. This question will be treated in detail later on. 



The level of the canal bed or sill of the head regulator must be sufficiently 
below the highest level to which the river surface can be raised to permit the 
full supply of the canal to be forced into it when the discharge of the river is at 
its minimum. On the other hand, any marked elevation of the river level 
during floods is unnecessary, and necessitates a larger head regulator, and 
may cause damage to the weir. Thus, a certain portion of the rise in the 
river level should be produced by movable dams, or shutters. The calcula¬ 
tions are simple, but the requisite information is usually deficient. 

Let us first consider the flood discharge Q/. 

The term “afflux” is used to denote the difference between the high flood 
levels upstream and downstream of the weir. 

The fixed portion of the weir must be at such a level and of such a length 
that when the weir and undersluices are passing a discharge Q/, the afflux is 
not so great as to cause serious flooding, or to overtop the canal regulator, or 
the training banks upstream of the weir. The appropriate coefficients of 
discharge of the weir and the undersluices are discussed on pages 132 and 168. 
As a rule, the various upstream works are designed so as to be 4, or 5 feet 
above the calculated afflux level when the downstream high flood level is 
assumed to be the maximum observed before the weir was constructed. 

42 
































658 CONTROL OF WATER 

Consider the low water season, and let Qi, represent the maximum capacity 
of the canal. 

Then, the relative levels of the sill of the head regulator and of the top of 
the movable portion of the dam must be such as to permit Qi, to be forced 
into the canal. In this calculation an allowance for possible obstruction of the 
canal by silt deposits must be made. The sill level and the discharge capacity 
of the undersluices are determined by their object in scouring out silt deposits. 
The question therefore entirely depends on the average silt content in the 
water. General rules cannot be given, but the principles are discussed in 
detail on pages 695 and 700. 

The accurate determination of the proportions and relative levels of the 
weir, the undersluices, and the canal head regulator, can therefore only be 
arrived at by a series of trial estimates of the cost of the whole headworks, and 
of the first reach of the canal (so far as the cost of this work is affected by its 
bed level). It is doubtful whether the preliminary studies of the discharge of 
the river are ever sufficiently extensive to permit a really accurate solution 
to be arrived at. The designer should, however, in all cases know the relative 
costs entailed by such operations as “raising the weir level one foot,” “ex¬ 
cavating the canal bed one foot deeper,” and the “ unit costs of an extra length 
of undersluices, or head regulator,” etc. 

The river training works which usually accompany headworks are so 
entirely dependent on local circumstances that no general treatment of the 
question can be attempted. 

Working of a River for Irrigation Purposes.—The subject which it is 
proposed to discuss in this section is one which has received but little attention, 
and that almost entirely of an unsystematic nature. 

Its nature and principles are best defined by a series of examples, and I 
must at once state that the theories set forth should not be considered as any¬ 
thing more than suggestions. My only justification for publishing them is the 
feeling that some one must take the first step ; and the more searching the 
criticism aroused, the more satisfied I shall feel. 

The leading principle is as follows : 

When a river is utilised for irrigation, large volumes of water are drawn 
off, and the whole regime is altered, usually for the worse. It is only very 
rarely, however, that the demands for irrigation or power are so intense that 
the entire flow of the river is diverted. Thus, if the canal is provided with a 
regulator, or head sluices, and if the river is blocked by a weir with a movable 
crest or sluices (preferably both), it is possible to exercise a certain amount 
of judgment in selecting the water which is taken into the canal, and in 
disposing of the surplus water passed down the river. 

The primary object of this selection is to keep silt out of the canal as far as 
consistent with the correct performance of the duty for which the canal is 
constructed. This is of course best effected by the rejection of all water which 
is heavily silted, and by taking an excess of clear water into the canal for 
scouring purposes whenever possible. This side of the question has been 
frequently discussed, and is fairly well understood. The advantages obtained 
by a correct system for disposal of the surplus water in the river after the 
requirements of the canal have been satisfied are less well known, and it is 
proposed to discuss the principles of “working” a river, and its canal, with 
this object. 


RIVERS CARRYING SANE 


659 

The methods at present employed are best illustrated by examples. It is 
believed that a study of these methods will prove useful not only in the 
working of existing canals, but also in the design of the weirs and the head 
regulators of new canals. 

Working of a River carrying Sand only.—I select the Sirhind canal as an 
example. This canal takes out from the Sutlej, at Rupar (Punjab). The 
river at this point has a slope of ggVo) the maximum discharge is 130,000 cusecs 
approximately, and the minimum recorded is 2818 cusecs. 

The canal can carry 6000 cusecs and has a slope of 5 anc ^ as a general 
rule, it may be said that the river is completely diverted into the canal for 
about two months (usually January and February) each year. Sketch No. 163 
shows the general arrangement of the weir, undersluices, and regulator. 

From 1893 to 1898 large quantities (amounting to as much as i9‘6 million 
cubic feet in five months in the year 1899, while deposits of 4 million cubic feet 



Sketch No. 163.—Plan of Sirhind Headworks. 


* 

in 10 days were not unusual) of sandy silt were deposited in the head reaches of 
the canal, especially in the first twelve miles (the above figures referring to 
deposits in this length only). Matters became so bad that in 1893 a total 
failure of irrigation was apprehended, and it was only by taking in quantities 
of water greatly in excess of what was really required for irrigation, and wasting 
these at an escape of twelve miles below the head, that the canal was kept in 
a more or less workable condition (see Sketch No. 198). 

A study of the available records leads me to believe that during the early 
portion of this period it was thought that the path of salvation lay in taking in 
all the water available up to the full capacity of the canal, and rejecting the 
surplus which was not required for irrigation, by means of the escape. 

After long and systematic studies of the size of the silt (see p. 758) it was 
realised that the trouble was caused by the coarser sand, and the sill of the 
regulator was consequently raised (see Sketch No. 164). 















66 o 


CONTROL OF WATER 


Thus, in 1894, the following remedies were adopted (see Kennedy, Punjab 
Irrigation Papers , No. 9) ; 

I. The capacity of the escape was increased from 2000 to about 
4000 cusecs. 

11 . The canal was closed down during heavy floods. 

III. The divide wall AB (see Sketch No. 163) was constructed so as to 

form a pond or silt trap, which was occasionally scoured out 
through the undersluices. 

IV. The regulator sill was permanently raised to the extent of 7 feet 

above the floor of this pond, and was provided with a movable 
sill which could be raised still higher when the level of the water 
in the river permitted. 

The first two ideas are excellent, and should be adopted where possible. 
In this particular case clear water is a rarity, and could only occasionally be 
passed out through the escapes, as the demand for irrigation in the clear water 



season is acute. The use of the silt grader not being thoroughly understood, 
the canal was often unnecessarily shut off simply because the water looked 
muddy (see p. 763). 

The third idea is also good, but its full advantages were not obtained 
because the surplus water in the river was passed off through the undersluices, 
i.e. close to the canal head or regulator. The silt trapped in front of the 
regulator was thus stirred up, and fresh silt was brought into and deposited in 
the silt trap. Consequently, the raised sill had but little effect, for the silt 
grading experiments clearly show that the disturbance produced by the water 
entering the regulator was sufficient to lift silt of all grades up to over the 
raised sill, if such silt lay on the river bed outside and near to the sill. This 
being about the coarsest grade of silt which the river carries, the raised sill 
(although excluding a certain fraction of the coarser silt) was not capable of 
keeping detrimental bed silt outside the canal unless all silt which was 
sufficiently coarse to deposit in the canal was dropped in the river bed before it 
reached the pond or “ silt trap ” in front of the regulator. 

The above-mentioned methods somewhat ameliorated conditions, but it was 







































SILT TRAP IN RIVER 


661 


not until 1901 that the final and most important remedy was introduced. This 
was simple, but it forms the keynote of the working of all rivers which carry 
sand only. 

The surplus water was systematically diverted as far as possible from the 
regulator, and was passed off by dropping the shutters at the far end C, of the 
weir (see Sketch No. 163). 

The principle is to prevent any sand (mud, since the canal velocity will carry 
it forward, does not matter) from reaching the vicinity of the regulator. At 
first sight it will appear that this method must finally cause the area ABY to 
silt up solid. This is avoided by systematically sounding this area ; and, when 
necessary (usually about once a month in the low water season), closing the 
canal completely for 24 hours, and passing the whole flow of the river through 
the undersluices. The regulator and the undersluices are never opened 
simultaneously. The effect is excellent. In the eight years from 1893 to 190°* 
the mean yearly quantity of silt deposited in the canal during the silting 
periods and removed during the clear water periods was 137 million cubic feet. 
In the first four years (1901 to 1904), after the adoption of this principle, the 
average deposit was 3^9 million cubic feet. The amount of silt that per¬ 
manently remains in the canal is now about 1 '6 million cubic feet, correspond¬ 
ing to a mean depth of o'12 foot, which is immaterial in a canal which can run 
137 feet deep, and is designed for 8 feet depth. 

The problem therefore has been completely solved. 

The necessary conditions are as follows : 

(i) The river in its low stages must be entirely under control, so that the 
surplus water can be easily and certainly diverted to the bank opposite to the 
canal head. 

(ii) The undersluices must be of such a capacity that, when fully opened, 
the flow through them is sufficient to scour out the silt trap and also to form 
a channel connecting the silt trap with the deep water channel which is 
created on the farther side of the river. 

These conditions are easily secured in rivers carrying nothing larger than 
coarse sand. 

In some of the later canals the weir crest is laid not at a level, but with a 
fall of two or three feet towards the end corresponding to C, in Sketch No. 163. 
Personally, I doubt whether this is advisable, as it appears likely to cause the 
flood channel to work over towards the farther bank at C. This seems un¬ 
necessary, and if the action became too acute, the undersluices might not be 
able to scour out the connecting channel when required. The Rupar (Sirhind 
Canal) weir is level, and under the present conditions it serves its purposes 
admirably. 

The floods scour out the deposits splendidly ; and, as will be noticed, the 
two deep water channels XY, and XZ (see Sketch No. 163) which the method 
requires, have become permanent features of the river bed. 

Working of Rivers carrying Boulders or Gravel.—These rivers are less 
easily controlled than sand bearing streams. Their floods are more intense, 
and the low water supply will hardly suffice to scour out and maintain the 
channel corresponding to that denoted by XY, in Sketch No. 163. The 
examples which are best known to me are the river Ravi, at Madhupur (sup¬ 
plying the Bari Doab canal), and the Jumna at Tajewala (supplying the 
Eastern and Western Jumna canals). 


66 2 


CONTROL OF WATER 


In the above cases, any attempt to divert the surplus water to a distance 
from the canal headworks would probably produce so great a deposit of shingle 
in front of the canal head that the undersluices could not scour it away. 

The rivers being torrential, it is impossible to guarantee the maintenance 
of a weir with falling shutters across the river. At Tajewala the weir is 
usually in fair working order, while at Madhupur the weir is generally buried 



Sketch No. 165.—Tajewala Bar, or Undersluices, previous to 1876. 


in shingle, and receives but scant consideration when the problem of regulation 
is dealt with. At both places the engineer in charge has to “ get the river 
under control ” at the beginning of each low water season. This is effected by 
blocking such channels as divert water from the canal head by means of more 




Sketch No. 166.—Tajewala Undersluices, from 1876 to 1896. 


or less (usually less) permanent dams of boulders and brushwood, or occasionally 
of rubble masonry in lime mortar. These headworks are now generally held 
to be wrongly located, and it is thought that sites farther down the river, where 
sand alone would have to be considered, would be preferable. This statement 


PlCR 



Sketch No. 167.—Tajewala Undersluices, as partly reconstructed in 1896. 


may be correct as regards Madhupur, but I am not convinced that it applies to 
Tajewala. In any case, the problem must be faced in other countries ; and the 
fact that the above rivers have not as yet been permanently controlled does not 
materially affect the method of working them, as the shingle deposit would 
certainly be increased if the river were permanently weired, or barred in any 
way. 

The exigencies of the situation are best explained by Sketches No. 165, No. 

166, and No. 167, which show three sections of the combined weir and under- 




























































































RAISED SILLS 


663 

sluice used at Tajewala. It is sufficient to state that the first two were destroyed 
in the years noted in the sketches, and that it may be anticipated that the 
present design will sooner or later be destroyed. No masonry on earth can be 
expected to stand the impact of boulders ranging up to 5 feet in diameter, under 
river velocities of 20 to 25 feet per second. 

The regulation of these rivers in their low water stage is entirely effected by 
the undersluices, and the low water channel is kept close to the canal head. 
(This produces the rather confusing terminology shown in Sketch No. 170 



Sketch No. 168.—Madhupur Raised Sill and Regulator. 


where what is usually termed undersluices is noted as a regulator, and the term 
head is used for the canal regulator.) Thus shingle and boulders would enter 
the canal were it not that the canal head is provided with a raised sill. Sketch 
No. 168 shows the design adopted at Madhupur, and the raised sill added in 
1906. The Rupar design (see Sketch No. 164) is also suited to these conditions. 
Sketch No. 169 shows the Tajewala canal head. This, at first sight, has no 
raised sill ; but, as a matter of fact, the whole regulator is raised, as a per¬ 



manent deep water channel has formed in front of the work, soundings of 11 feet 
being regularly obtained within 2 feet of the face wall. This is a favourable 
condition for keeping silt out of the canal, but it cannot be considered as good 
practice. The error made is obvious. The opening of the sluices (“ Regulator ” 
in sketch) nearest to the regulator (“Head” in sketch, see Sketch No. 170) 
is always the one which is first opened. If the problem were better understood, 
there is no doubt that if this opening and the next one were kept closed, the 
deep water channel could be slightly diverted by passing off surplus watei 
through the third and fourth openings. We might then hope to make the cioss- 
section of the river in front of the canal head, of the form SS, shown in Sketch 










































CONTROL OF WATER 


664 

No. 169. Erosion in front of the regulator would then be minimised, but more 
gravel would enter the canal. 

At Madhupur matters are in a better state, as it has been found possible to 
maintain a level floor in front of the canal head or regulator. These statements 
reflect no discredit upon the officer in charge of Tajewala, since silt troubles 
are far less acute on the Western Jumna canal than on the Bari Doab. 
Madhupur is worked with too great a consideration for erosion, and too little 
regard to silt. At Tajewala the reverse is the case, and as the demand for 
water is more acute at Tajewala, the engineer at the latter place appears to 
have been on the whole the more successful of the two. In neither case does 
it appear that the best method has been grasped. The deep water channel 
should not be kept immediately in front of the canal head, but at a short dis¬ 
tance away from it ; the exact distance being fixed by the condition that the 
deposits of shingle immediately in front of the regulator (shown by the line SS, 



»jj . .3 &V) . 

Soil 1 ' of tier 

Sketch No. 170.—Plan of Tajewala Headworks. 

in Sketch No. 169) can be scoured away when necessary by opening the under¬ 
sluices. The canal head gates at Tajewala are of a somewhat peculiar type and, 
except when the river is very low, form a raised sill so that the water enters the 
canal at a level at least 3 feet above the masonry sill shown in Sketch No. 169. 

It will be plain that sand (at any rate) will be drawn into the canal. At 
Tajewala sand alone enters the canal, but at Madhupur pebbles and occasional 
boulders are carried in. These two canals irrigate flat land in their lower 
reaches, and it is impossible to obtain sufficient velocity in the tail channels to 
carry this sand forward. Thus, scouring escapes form an integral portion of 
the canal, and must be provided. 

The headworks of the irrigation canals of Lombardy are situated on rivers 
which are only slightly less torrential than the Ravi, or the Jumna. The canals, 
however, do not irrigate flat land, and therefore sandy silt causes but little trouble. 
The canals date from mediaeval times, and their headworks are usually 
unprovided with regulators. Thus, pebbles and also boulders enter the canal. 
These are scoured out by escapes and sand traps. 














SIZE OF REGULATORS 


665 

We may therefore assume that the escapes found necessary on the Western 
Jumna are only required because the tail portions of the canal irrigate flat land. 
\\ ere the slopes of the whole irrigated area of the same character as those of 
Northern Italy, it is probable that the precautions taken at Tajewala would 
suffice to exclude all detrimental silt. 

d he circumstances at Madhupur are somewhat less favourable ; and the 
escapes and the double head reach now adopted would probably be required, 
however steep the tail channels might be, since at present silt deposits mainly 
occur in the head reaches of the canal. The Madhupur conditions, however, 
are not likely to occur in carefully designed systems. The headworks date 
back to 1864, and the modern troubles are mainly attributable to the fact that 
the canal carries about 50 per cent, more water than it was designed for. 

In considering the design of headworks of canals under the above 
conditions the following rules appear to be advisable : 

(a) The regulator or canal head should be relatively larger than is usual in 
the present designs. We wish to get the water into the canal with as little 
disturbance as possible. The Tajewala regulator could with advantage be 
made 25 to 30 per cent, larger than it is now, while an enlargement of the 
Madhupur regulator is known to be urgently required. The double head reach 
channel employed is described on page 766, and it is quite probable that if this 
system of working were abandoned, and if the entire length of the regulator 
was used to admit water, the sand deposits occurring in the lower reaches would 
be decreased. 

(b) The undersluices should also be increased, not necessarily in length, 
but they should be placed deeper in relation to the regulator, so as to give 
greater scouring power. The question, however, needs very careful considera¬ 
tion, and should be experimentally tested. The Tajewala undersluices are 
probably too deep when worked as at present, although not necessarily so if 
they were worked in the manner that has been suggested. The Madhupur 
undersluices are certainly not sufficiently powerful. 

The principle to be borne in mind is that the ordinary low water flow is 
insufficient to produce any material effect upon the shingle deposits near the 
regulator. The undersluices should therefore be capable of passing away the 
minor,freshets that occur in the low water season. The canal should then 
be shut down, and these freshets should be utilised for scouring in front of the 
regulator. 

It will be obvious that the root of all the troubles is the fact that the river 
is not under control during the periods when the major part of the motion 
of the shingle and boulders occurs. The engineer is expected to scour out 
deposits that are produced when the mean velocity of the river is about 15 
to 20 feet per second, by manipulating low water flows which rarely, if ever, 
give a mean velocity in excess of 5, or 6 feet per second. The marked 
extension of the subsidiary weirs and training banks upstream of the canal 
head (p. 666) is in essence an endeavour to secure a fall sufficient to permit 
the low water flow to be used as a jet to scour away boulders. The difficulties 
are great, the maximum flood of the Ravi being about 170,000 to 190,000 
cusecs, and its minimum low water flow only 1200 cusecs, while very few years 
pass without flows of 1500 to 2000 cusecs being recorded. The figures for the 
Jumna are slightly less variable. In view of the size of the rivers, it is doubtful 
whether any other solution can be found. In a smaller river of equally variable 


666 


CONTROL OF WATER 


flow, however, it would appear advisable to erect a relatively high dam (say 
20 or 30 feet) with undersluices at as low a level as possible, and thus provide 
a means of working the river as is done at Rupar. 

The first cost is no doubt heavy, but the dam will provide storage capacity, 
and the present cost of maintenance and repairs at Madhupur and Tajewala 
forms a very heavy drain on the profits of what are even under present 
circumstances abnormally prosperous irrigation systems. 

General Remarks. —The above discussion is confined solely to the 
working of existing canals. Where a choice is possible, a site similar to that 
at Rupar should be selected. The maintenance of headworks resembling 
those at Tajewala or Madhupur is an abominable business. At Tajewala, the 
system of spur dykes, training walls, etc., extends at least 15 miles upstream 
of the canal head, and at Madhupur 8 miles is probably the usual limit. The 
financial returns of an irrigation canal are so excellent that these enormous 
works are justifiable. Nevertheless, there is little doubt that if the headworks 
were situated on a less torrential portion of the river, an equally good use 
could be made of the flow of the river. 

As a general principle, rivers in the torrential portion of their course should 
be utilised only for power, and the irrigation development should be effected in 
the lower reaches of the river where silt of a sandy nature alone occurs. 
This division will be seen to be logical. In torrential reaches of a river, the 
head requisite for a power development can generally be secured by relatively 
short head and tail channels. The general slope of the country being steep, 
the head channel can be graded so as to produce velocities which will carry 
forward all sand, and possibly even small gravel. These particles must be 
removed from the water before it reaches the turbines, by means of sand traps, 
or silting basins ; but since the general slope of the ground is steep, sites for 
such traps or basins can be easily found. 

When the site for headworks is selected in the sand-carrying reaches of a 
river the following principles should be borne in mind. 

It appears that (contrary to accepted practice, which is based on the 
supposition that hard clay foundations exist on the bank towards which the 
river travels) the regulator of a canal should, if silt problems alone are 
considered, be situated on that bank which the stream as a whole tends to 
quit. Local variations due to the existence of marked and permanent bends 
may render it possible to discover a favourable site on either bank ; but, as 
a rule, it will be found (in the Northern Hemisphere at any rate) that rivers 
flowing towards the north attack the eastern bank, and that rivers flowing 
towards the south attack the western. As an example, it may be noted that 
the Nile flows north, in the Northern Hemisphere ; and, as a matter of 
historical record, the western bank was the one to be first reclaimed. Similarly, 
the Punjab rivers flow south, attack their western banks ; and, with one 
exception (the Western Jumna canal), all canal heads are situated on the 
eastern banks. 

The regulation of the river should be worked so as to produce still water 
on the canal side, keeping the main stream during low water on the other 
bank. The scouring out of the local deposits in the silt pocket should be 
effected during short closures of the canal, while floods are depended on to 
scour away the general accumulation of silt which occurs above the weir. 

In cases where a site on the bank which the river tends to attack must be 


BELLS DYKES 


667 

selected, the problem is more complicated. In actual examples, the solution 
is usually one of brute force, combined with expensive maintenance. The 
canal is systematically cleared of the silt deposits produced by the scour of the 
river banks, and large quantities of stone are thrown in front of the regulator 
and undersluices during each low water season, so as to preserve them from 
erosion in the succeeding floods. The work is costly, and in large rivers may 
entirely swallow up the whole profits of the undertaking. In small, and placid 
rivers, the disadvantages are less acute ; but, even in such cases, a site which 
the river tends to quit is preferable. If the worst comes to the worst, dredging 
a channel from the deep water stream to the canal head is cheaper than 
protecting several miles of bank. It therefore appears preferable in all such 
cases to train the river for some distance above the headworks, so as to 
produce a slight tendency to quit the canal head. The following suggestions 
for the design of such training works are put forward with the remark that the 
principles are fully proved, and have been applied for many years past in 
connection with bridges over rivers flowing in beds which are easily eroded. 

Broadly speaking, the problem is to direct the main stream of the river 
away from the canal head, and to provide a place in the river bed where silt 
can be deposited during low water periods, and swept forward during floods. 
This has been completely solved by Bell’s system of “ bunds,” or dykes (see 
Spring : Indian Rivers . . . Guide Bank System ). 

Consider a river which is normally 5000 feet broad. It will be found that 
such a river, when flowing in a sandy bed, is capable of eroding this bed to a 
certain depth (let us say 60 feet). This depth will depend upon the velocity of 
the river, the size of the sand grains, and their angle of repose when wet; and 
is obviously governed by the rate at which the water can pick up the sand, the 
maximum depth of a scour hole being that at which the sand falls in from the 
surrounding portions of the river bed as fast as the water can pick it up. 

The training of such a river is effected as follows :—A certain breadth, 
somewhat less than the normal width (usually about three-fifths) of the river is 
selected, and the river is trained to this width for a length of about one to one 
and a half mile, by means of dykes or banks parallel to the main stream of the 
river, and faced with stone of a size such that the river current cannot carry it 
away. The stone may be, and is, undermined ; but the stone facing of the 
banks is made of such a thickness that when the river has eroded to its 
maximum depth, the facing still forms a continuous layer over the face of the 
bank when its slopes are continued to a depth equal to that of the deepest hole 
which the river can possibly erode (see Sketch No. 159). The length of the 
bank is fixed by the condition that the most acute bend which naturally occurs 
in the river cannot reach up to and erode the canal, or railway embankment, 
as shown in Sketch No. 171. 

The river is thus forced to flow through a constricted bed, and can (within 
limits) be directed as required. Sketch No. 159 shows typical designs; and 
the plan of the dykes should be such as to give as little opportunity as possible 
for whirlpools to be set up, and the stone facing should be packed by hand to 
as smooth an external face as possible (see p. 653). 

The most severe attack will obviously be made on the heads of the dykes, 
and these are provided with an extra protection, as noted in Sketch No. 159. 

Let us now consider what happens in the constricted channel between the 
dykes during a flood. The channel will evidently scour out to a depth such 


668 


CONTROL OF WATER 


that the cross-section of the constricted channel is very approximately equal to 
the average cross-section of the natural river, the slight difference being 
caused by the increase in the mean velocity as determined by Kennedy s 
law (see p. 754). 

Thus, during each flood we have a heavy scour in the constricted channel, 
and the area thus scoured out is filled up with fresh silt during the low water 
season, pro tanto reducing the amount of silt reaching the weir or canal head. 



These general principles of river training and control being clear, their 
application to a canal headworks is, I think, obvious. 

A constricted channel should be established some distance above the canal 
head, and should be arranged so as to direct the flow of the river to about the 
middle of the weir ; i.e. where the normal breadth is 5000 feet, the prolongation 
of the nearer training bank should cut the weir about 2000 feet away from the 
canal head. This being done, the river is properly directed ; and, what is 


















INUNDATION CANALS 669 

probably still more important, the deep scoured channel between the training 
banks forms a very effective silt trap during the low water season. 

A complete design would of course specify the distance between the weir 
and the tail of the banks, and between the canal head and the line of the 
nearer bank measured perpendicular to the direction of the river. These are 
obviously very important ; since, if the second is too great, the river may quit 
the canal head, and costly dredging may become necessary ; while if too little, 
the river may attack the headworks. 

Similarly, if the first is too big, heavy deposits may form in front of the 
weir, and canal head, during the floods ; and if too small, the weir may be 
attacked. In actual practice, however, such works are not started until a weir 
and headworks have been in existence for some years, so that the necessary 
information should be on record. At Khanki (Sketch No. 172) the railway 
training works are obviously much too far above the canal head to be useful. 



A logical treatment of this subject would include the design of the whole 
plan of the headworks of a canal. Unfortunately, the practical aspect of the 
matter renders this treatment useless. In every case the headworks of a canal 
must be designed with incomplete information, since, even if really systematic 
preliminary studies were made for a generation, they could only acquaint us 
with the regime of the river before thfe diversion of its waters for the canal ; 
and no amount of previous knowledge would allow us to predict the regime as 
altered by the almost total diversion of the low water flow. Thus, the practical 
view of the matter is that we have a headworks, and (possibly after minor 
modifications) we should accept this as a natural feature, and work the river to 
the best advantage of the canal. 

Working of Inundation Canals. —In many countries it is usual to 
irrigate by canals which take out from the river at a level which enables them 
to draw water during flood time only. 











CONTROL OF WATER 


670 

The design of such works is usually somewhat empirical. A canal head is 
cut, and is expected to supply water during one season. If, at the end of that 
season it is not absolutely silted up, it is held to be a successful head, and is 
used until it becomes less expensive to cut a new head than to dispose of the 
deposits accumulated on the banks of the old. 

The old principles followed by Arab engineers in Egypt are stated on 
page 752, and allowance being made for local conditions, they are found to be 
those used in all places where flood irrigation is effected. I believe that it is 
possible to obtain somewhat better results by a careful consideration of the 
effects on the canal itself. The most heavily silted waters are those which 
come down with the rise of the flood, and a shallow canal head will draw a 
greater proportion of such waters, and will therefore be more likely to fail 
through silting. The matter needs careful consideration, for although the 
waters of the highest floods carry most silt, the surface water of a river, stage 
for stage, carries least silt. An ideal design therefore, would be one which 
would permit the canal to be closed off during the rise of a flood, and would 
yet allow only the top layers of the river water to enter the canal when it was 
open. The ordinary flood or inundation canal has no regulator or head gates, 
and the two conditions are consequently conflicting. 

The logical solution would appear to be as follows :—If a favourable site 
for a canal head is found, as indicated by the principles discussed on page 666, 
and is confirmed by the fact that the canal does not markedly silt during its 
first season, it would appear advisable to lay stone pitching across the head, 
and to put in temporary wooden gates, which can be shut down when the 
river water contains an abnormally large proportion of silt. Such a process is 
not recommended in the case of canal heads situated at places where the river 
is likely to attack its banks, as the mere fact that stone pitching is put in would 
probably produce a severe attack on the canal head. The risk is justifiable in 
cases where the banks are known to be fairly stable, and such reaches are 
probably the only places where satisfactory sites for a canal head are likely to 
occur. The advantages of locating the head on a permanent ana-branch of 
the river, if such can be found, are too plain to need discussion. 

The matter is also of interest as it explains the rapid cessation of irrigation 
which follows once the maintenance of the canals is neglected. 

The process is as follows : Maintenance being neglected, the canals begin 
to silt. This small initial silting causes the next year’s supply to be drawn 
from waters carrying a greater proportion of silt, as the canal bed is now so 
high that it only draws water when the river is in high flood; and the silt is so 
rapidly deposited that the clearer water of the falling flood is not taken in, or is 
taken in in a far smaller quantity than is requisite for scouring out the silt 
deposit. In the third year this action is still more marked, and in the fourth 
the canal probably ceases to flow. 

Weirs. —The term weir is frequently employed to denote a low dam across 
a river. The distinction between a weir and a dam of the overfall type lies in 
the fact that water is usually passing over a weir, and it is only rarely that some 
portion of the weir is not submerged. In an overflow dam, on the other hand, 
the dam is not usually submerged for more than three or four weeks during the 
year. Thus, the primary object of a weir is to raise the level of the water in a 
stream, permitting a portion of 4 the normal discharge to escape ; while the 
primary object of a dam of the overflow type is to store up the normal flow of 


TYPES OP WEIR 671 

the river, flood water alone being lost. This difference in object is accompanied 
by a decided contrast in the construction and design of the two species of dams. 
The term weir is therefore restricted to dams which are so frequently submerged 
that protection against erosion by water passing over them forms an integral 
portion of their design. 

Weirs may be divided into three types: 

{A) A weir consisting of a dam with a vertical drop wall to raise the 
water level, and a horizontal floor at or about tail water level, to 
prevent erosion, as per Sketch No. 173. 

(B) In this type the vertical wall also exists, but it is backed on its 
downstream side by a long slope of packed rubble over which the 
water flows. The rubble is retained in position by core walls of 
masonry, which form square or oblong cells into which the 
rubble is packed. (Sketch No. 174.) 



Fig.. 1 shows the original construction ; fig. 2 the alterations after the failure ; fig. 3 the 
pressures under the weir apron shortly before the failure ; and fig. 4 typical sections 
showing the damage that had occurred upstream of the drop wall before the apron 
cracked and failed. 

( C ) The cross-section of the weir is similar to that of type ( B ), but the 
slope consists of smooth masonry of a definite thickness. Core, 
or drop walls, reaching to a deeper level than the masonry 
platform, exist, but do not form a necessary portion of the weir, 
their function being mainly to prevent local erosion. (Sketches 
Nos. 179, 181, 182.) 

Type ( A ).—This type is best suited for localities where a firm and not 
markedly permeable foundation can be secured, e.g. clay, hard-pan, or firm 
gravel. The design of the dam itself follows the usual rules for dams, allow¬ 
ance being made for the depth of water passing over the dam, and for the 
diminution of weight caused by submergence, when selecting the least favour¬ 
able case. Sketch No. 173 shows the section which is generally adopted in 
India, and Sketch No. 176, Fig. 1, the type usual in America, the section given 
























































CONTROL OF WATER 


672 

being that of the Granite Reef weir. The two forms of the overflow face of 
the dam differ widely. In making a selection it should be realised that the 
Indian type is more likely to sustain damage in the floor; while, in the 
American type, the dam itself forms the weaker portion of the work. Thus, 
the quality of the available material and the character of the foundations must 
decide the question. 


jaw 


.. 


vJ 1-5 

L 64' h K 

r.N.L. rrOivU SS6 


ft itknj M/IHriS 




Rubble Stone 



Hind Fjcscri Hubble 


--- to , " 

Hubble Stone ----- 



sits 

-S'- 

i/65 


Sont Uctr 


Minimum SO' 



h- 40’ —H 

i* 


—04’ - 

S(Ming SDullea 

< 

• - 36' -* 

_ Slope 

f 

- - Hmsgc 90 - 5 - 3 - 

Mdsimum Ob' 

/ in in 

_ 

L 


Hubble 


Hubble 


Hubble ‘ ------ 


OKia Heir 


Sketch No. 174.—Sone and Okla Weirs. 

Note .—The difference in breadth of these two weirs roughly indicates the possible advan 
tage gained by the deeper foundations. 




Mahanadi Neir 


Sketch No. 175.— Colleroon and Mahanadi Weirs. 

Note .—The Colleroon Weir is probably about as narrow as is consistent with safety in 
coarse sand. The Mahanadi Weir shows the transition from type B to type C. 
The reversed filter seems to me excellently located. 


The American type may be recommended when first-class materials and a 
good foundation can be secured (say masonry in Portland cement, founded on 
weak rock, shale, or firm gravel). 

A dam of the Indian type can be erected on clay, or even on sand founda¬ 
tions (although this is not the type which is best adapted to such conditions), 
and can be constructed of brickwork, but will require constant maintenance 
and repairs, especially in the apron. 










































































































AMERICAN TYPE 


673 

On the other hand, in the American type of dam failures are serious when 
they do occur ; while the Indian type (if well looked after) has never failed so 
rapidly as to cause a disaster. 

The section of type (A), possesses certain theoretical advantages over the 
section afforded by types (B), and (C). 

I am inclined to believe that these advantages are somewhat over-estimated ; 
but it will be plain that if the quantity of water passing over the weir crest is 
the same in both cases, the velocity at the section just below the vertical drop, 
in type (A), will be far less than the velocity at the same distance downstream 
of the weir crest in types (B), and (C) ; and erosion and wave action on the 
downstream apron is therefore not so much to be feared. Records of actual 
maintenance costs confirm this view. 

On the other hand, the pressures on the foundations are far more localised 
in type (A), and unless the limits of pressure usually adopted (see p. 682) are 
greatly exceeded, it will usually be found impossible to obtain an adequate 



© 



- -3/-- 

K.U 9 . 

s 

% 

- si's" -- 

Raring f to ? thick 

s' 

•- Sid' -► 

- J'Mc / in 1 ? 

f 

■- 4 f -- 


r.f.f 

^eough Rubble 

& 

•S 

% 

I 


Rubble filing 


1 

r.i.r 

Large Rubble 

l <4 < 


Pieces Orcpn 


R.l. -/ 


LdQuna Heir 

Sketch No. 176.—Granite Reef and Laguna Weirs. 


base for the dam except in rock, shale, or extremely hard clay. Messrs. 
Pearson and Atcherley’s theory regarding the vertical sections of dams (see 
p. 374) must be carefully considered, for neither clay nor shale foundations 
can be considered as capable of assisting the dam to any great degree against 
horizontal tensions. 

A study of existing weirs of this type leads me to believe that the results of 
the above theory may be advantageously applied, and will prove valuable in 
indicating when type ( A) can be used. 

Type {B). —Often called the Anicut type. This is probably the oldest type 
of dam in existence, some of the Madras anicuts being more than 1500 years 
old. Both type (Z>), and type (C), can be maintained on foundations of the 
finest and most permeable sand. The choice between the two types is really 
determined by the available material and labour. 

Type (i>), contains but little cut stone, or mortar, and can consequently be 
erected where supplies of material and skilled labour are hard to obtain. It 
is, however, costly, requiring continual and unremitting maintenance. When 
fine sand forms the foundation, it is found economical to grout the rubble stone 

43 















































CONTROL OF WATER 


674 

heap, or to face it with cut stone, or concrete blocks, so producing a bulky 
form of type (C) (eg. the Mahanadi weir, Sketch No. 175)* Where clay 
foundations exist, a weir of type (A), is usually adopted, and proves ad¬ 
vantageous as being more cheaply maintained. Thus, type (B) (as is 
indicated by a study of the existing examples) should be restricted to coarse 
sand foundations, and even in these cases it is doubtful whether it would not 
be advisable to employ type (C). 

Since type (Z>), requires but little skilled labour, while well sinkers and 
masons must be employed in type (C), the choice between the two types is 
usually determined in India by the character of the available labour. I 
consider that type (B), should only be employed in other countries when large 
and cheap supplies of rough stone are accessible. 

Cases may occur in which rough rubble can be cheaply deposited in large 
quantities over the whole of the weir site by means of modern transporting 
machinery. The following notes concerning two rubble stone weirs existing 
in Madras are a digest of the information given by Welch (Engineering Works 
of the Kistna and Godaveri Deltas ), and may then prove useful. 

The most interesting example is the weir over the Kistna river. The 
maximum flood recorded was 770,000 cusecs, and the weir has a length of 



Sketch No. 177.—Kistna Weir. 


approximately 3400 feet. The section adopted, with the actual levels existing 
at three points after thirty years of careful maintenance, is shown in Sketch 
No. 177. 

This section may be considered as the minimum possible, for in 1894 
(thirty-nine years after completion), an attempt was made to raise it three 
feet, as shown by the dotted lines. The weir at once began to give trouble 
through the formation of deep scour holes (750 feet x 20 feetx 12 feet average 
depth, and 250 feetx 20 feetx 12 feet average depth), in the 74 feet wide apron ; 
and the masonry wall of the weir cracked. 

The usual inter-departmental discussion then followed as to the possible 
effect of a newly constructed railway bridge some 3000 feet below the weir, 
and its training works. The discussion is naturally only of local interest. The 
useful deduction is that the energy generated by the 3-foot drop on to the apron 
was sufficient to remove the stone work. This was recognised, and the lower 
wall (shown in dotted lines in Sketch No. 177) was built so as to obtain a water 
cushion. 

In 1896, after the second largest flood on record, the apron was again 
damaged, and the talus was badly scoured. 

The 3-foot wall was therefore removed, and was replaced by falling shutters 
of the usual design. The real lesson is that the weir was very accurately 
































TALUS OF AN TOUTS 


675 

proportioned for the original drop of 14 feet, and was not capable of resisting 
the extra action thrown on it by increasing this drop to 17 feet. It will be 
fairly plain that a far narrower weir could be made to retain the 14 or 17 feet 
drop if water cushions were used. This, however, requires a large quantity of 
cut stone, and Cotton (the designer of the weir), having considered such a 
design, finally abandoned it because the present design, although calling for a 
far greater bulk of rough stone, was really cheaper in view of the extra cost 
of cut stone. 

Under modern conditions, however, water cushions appear to be advisable ; 
and if put in during construction, before the deposition of the rubble renders 
excavation difficult, they will not entail any great extra cost. 

As a contrast, I give the sections of the Godaveri weir (see Sketch No. 178). 
This has to pass 1,500,000 cusecs, and is 11,945 feet in length. A priori , it 
would therefore appear that of the two weirs this one should be far more easily 



Sketch No. 178. —Godaveri Weirs. 


maintained, especially since the difference of levels is, on the average, somewhat 
less than the 14 feet existing on the Kistna river. 

As a matter of fact, the weir has only been maintained by a yearly expenditure 
of large volumes of rough stone (the records, which are known to be incomplete, 
indicate that at least 290,000 cube yards were expended in the first 20 years 
of the weir’s existence). In the light of present experience, the reason for this 
comparative failure is fairly obviousThe concave curve, is a very efficient 
means of directing the overflowing water against the talus, and the damage is 
probably caused not so much by actual transport of stone down the river, as by 
burying it in the deep holes which are excavated by the water, and afterwards 
filled with sand. 

The lesson may be useful, as many overflow dams are still designed with 
tail aprons composed of loose rubble. These are unadvisable unless they rest 
on clay or shale ; and in sand they should be replaced by a pavement made 
of closely fitted blocks of concrete. This aspect of the question has been 
realised by the designer of the Granite K.eef flooi (see Sketch No. 176)? anc 
his practice should be followed if the ogee type of dam is adopted. 
































































676 


CONTROL OF WATER 


The difference in design between the Dowlaisheram weir (which is typical 
of the major portion of the weir) and the short length known as the Ralli weir, 
should be noted. The masonry of the latter is laid on a pile of rough stone, 
and most engineers would consider that it was the more favourably situated of 
the two ; but, as a matter of fact, it causes the most trouble. This is easily 
explained in the light of experience of Punjab weirs. The river carries coarse 
sand only, and what would be called fine silt in Egypt, or the Punjab, is almost 
entirely absent. Thus, it is doubtful whether the interstices in the rubble 
are even now stanched, and in the early years of the weir’s existence the masonry 
during the flood season was exposed to an uplifting pressure, probably very 
nearly equal to the afflux over the weir. The masonry being thus strained and 
simultaneously exposed to shock from the overflowing water, it may be expected 
to crack, and each crack forms a point of attack. So, quite apart from any 
possible settlement produced by the removal of sand from under the rough 


50'of very Stone 


: MS'Masonry in Lime 

rS'hightollingShuirers A MS', do- in / Lime : /Sana 
d /( 0-5 Concrete 



Original Section in Shallot/ Portion of River 


increased to i‘ and grouted 



-W- 


R.UK3-IS _ 

Concrete 

ruddle Clay $ ^ 

'ft U. 7 US 


Additions in Shallot! Portions 


J_ R.L. 122-5 

V Dry Stone 


T 


>0 - pjdffl,: Oifv 'C ) • _ -f uddle ’ 

T nrigynal_Ped of£hanpeL.LJls^\ __ 


__OriQjjiaJ Pirching of _ Try 


Hole. The R.L. of top of Heir varies slightly; aft other 
mrk is laid at corresponding, relative level. 


K.1.609-3 


Additions in Deep Channel 


Section as above 




Section as above 


Sketch No. 179.—Lower Chenab Weir. 

Note .—The upper figure shows the original design, which partially failed three years after 
construction, by uplifting pressures on the apron masonry (see p. 685). The two 
lower figures show the additions upstream of the crest wall, which have secured 
satisfactory working for over thirteen years. 


stone (which is more likely to occur in seasons of low water than during floods), 
the damage to the Ralli weir could have been predicted. Experience of such 
weirs leads me to conclude that sand forms a better foundation than clay for 
flat portions of masonry, and that clay is superior to loose stone. This is fairly 
evident if we consider that in rivers which do not carry fine silt a certain amount 
of percolation under the masonry must be expected. If a definite channel is 
formed, it must be expected that the masonry will crack either from the uplift¬ 
ing pressure thus brought to bear, or, owing to lack of support; and although 
such channels are less easily formed in clay than in sand, once formed they are 
far more likely to remain open and to increase in size. In rivers carrying much 
fine silt, it is probable that rough rubble under small differences of pressure will 
soon become almost as impermeable as masonry. 

It would therefore appear that all the weirs which are considered in this 
section could be greatly strengthened by a puddle coating upstream, in the 











































































PUNJAB WEIRS 677 

position shown in Sketch No. 179 of the Lower Chenab weir. I believe that 
this device has been adopted in the new Madras weirs. 

Type (C). —This is the type now usual in the Punjab and Northern India 
generally, and may be considered as the form which is best adapted for all 
cases where the foundations are not sufficiently good to permit the adoption 
of type (A), and where local conditions do not cause type (B) to be cheaper 
(see Sketches Nos. 179, 181 and 182). 

I shall therefore discuss at length the rules which are at present adopted 
in the design of weirs which belong to this type, and shall merely refer incident- 
• ally to the rules for types (A) and (B). 

The rules are mainly empirical, and I doubt whether any general agreement 
on the matter yet exists amongst engineers. It must also be noted that while 
the results of the theory now put forward agree very fairly with the general 
practice in weirs, considerable differences will be found when the cognate 
question of undersluices and regulators is discussed. 

Although these difficulties are partially, if not wholly, explained by differences 
in the intensity of tail erosion, the very fact that our rules endeavour to take 
into account such an accidental and incalculable factor as erosion is ample justi¬ 
fication for extreme caution in their application. Therefore, although Bligh’s 
treatment (see Design of Irrigcitio?i Works, 2nd edition) is closely followed as 
regards weirs and undersluices (but not in the case of regulators), I have 
endeavoured to indicate its weak points, since many of Bligh’s designs seem 
to me to be somewhat hazardous, being (in my opinion) the fruit of experience 
which has been gained under conditions which are more favourable than those 
which occur either in the Punjab or in Egypt. Nevertheless, the theory may 
be followed with a certain degree of confidence, for should the design which is 
initially adopted prove insufficiently strong, the necessary remedial measures 
may easily be discovered by an application of the principles laid down. In 
costly works, such as weirs, an engineer may be excused for “guessing low,” 
provided that he has previously indicated the correct remedies, and has 
“ guessed sufficiently high ” to avoid a really troublesome failure or disaster. 

Taking matters at their worst, none of the designs shown (which include all 
known cases of bad failures) have ever resulted in so sudden a collapse that 
temporary remedies could not be applied, and the principle of the upstream 
apron introduced by Gordon and Clibborn provides a very excellent means of 
strengthening a weak weir. 

Design of Weirs.—The design of all types of weir is intimately connected 
with the possibilities of percolation under the weir structure. The rules now 
given were arrived at after a study of existing works. It must, however, be 
stated that close personal acquaintance with seven such weirs leads me to 
believe that published drawings never properly represent the exact circum¬ 
stances. The drawings show the initial construction of the weir ; and, in some 
cases, where large modifications have been made after construction, these are 
more or less accurately recorded. Large sums, however, are annually spent in 
repairs and improvements on nearly every weir. These are generally patch- 
work additions to the aprons and talus, and vary from point to point along 
the weir. So also, large quantities of stone or concrete blocks are thrown in 
yearly, in order to stop local erosion. In particular the drawings usually show 
the talus as a horizontal layer of loose stone or blocks. Any inspection which 
is conducted under favourable circumstances will generally reveal that a pell- 


678 


CONTROL OF WATER 


mell arrangement of loose stone exists at the tail of a weir ; and, in some 
cases, this is really a loose stone facing sloping down at an angle of 45 degrees, 
and more or less buried in sand. Some statistics of such repairs are given 
on page 675, and it will be plain that in an old weir (especially one belonging to 
type B ), twice the volume of loose stone shown on the drawings is distributed 
somewhere in the neighbourhood of the weir site. Thus, the rules given below 
may be considered to represent a structure which can be maintained without 
undue risk. The final and permanent structure is quite another matter, and is 
probably arrived at after 20, or even 30 years’ of careful maintenance. 

A comparison of the designs of weirs and undersluices, as contrasted with 
the designs which are found sufficient for head regulators, has led me to believe 
that the value of the constant c (see p. 679), is considerably influenced by 
erosion on the downstream side of a work. Where erosion is absent (as in 
regulators), c, has a value which is approximately only one half, or even one 
third, of that which is found requisite in cases where deep holes or channels 


upper jnelum bar 



X) 


0-lb' Boulders onedge in lime 
■* 01b' Boulder Masonry 


■ S '-S V ‘Mason/y Blocfis 


TheCreitol me Bar Mores me genera! lerel of me /fiver Bed varying bentcen f.i.SH nearUnderSluices n> K.l Mi near oppasifcbank. 


— Upstream Apron 


lo 


neremmi merm or mm 
Core 
Noll 


Top of Sputters 


-T ■ 


—— Ocunstream Impermeable apron 

—- L 


THUS me nine 

- Talus --— 


TiIdling to protect Cloy Ppm ao>' 


it 1 1 11 11 n-rrrn-riTTTT 


Clay Impermeability - 



masonry Impermeability - 


Hon me Lon Hater uret is 
usually a/ or above the 
OP 0/ /tie Oounstrram fibrin 


Sketch No. 180.— Bar across Jhelum (Type C.), and Diagrammatic Sketch of Type C. 


may form at the tail of the apron. Record plans rarely, if ever, give any 
information regarding the size or depth of these holes even in the low water 
season. 

Subject to these remarks, we may consider that all weirs may be divided 
into the following portions (see Sketch No. 180, lower Fig.) : 

(i) The upstieam apron, which may, or may not, include one or more drop 
walls, or cut-offs. 

(ii) The curtain, or core, wall, or dam wall proper. 

(iii) Ihe downstream apron, with its drop walls and cut-offs. 

(iv) The downstream talus, or pitching. 

Percolation is checked by the impermeable portion of the weir. This, in 
any typical case, is composed of the two aprons, and the core wall. 

The theory of percolation under an impermeable dam or coating has 
already been given (see p. 292). The practical aspect of the question is obscure, 
and although the necessary data exist in a few cases, the results obtained are 
conflicting. Putting aside a few newly constructed weirs, it is plain that the 
cut-off walls are rarely, if ever, carried down to a depth which is sufficient to 
have much effect in stopping percolation. 


































































IMPERMEABLE BREADTH 


6 79 


Thus, for the type of weir that is now generally employed, we have merely 
to consider 2 b, (see Sketch No. 180) the total breadth of the impermeable 
portions of the weir (clay or masonry, or grouted rubble). 2 b, should obviously 
be some multiple, of the maximum total head of water which is retained by the 
weir. 1 he maximum total head usually occurs when there is no water flowing 
over the weir, and is therefore the difference between the top of the shutters on 
the weir, and the low water level downstream of the weir, say H c . 

Bligh finds that the relation is expressed by 


I. 2b = 5 to 9H c . 
II. 2 b= i2H r . 

III. 2 b= 15H,.. 

IV. 2b = i8H c . 


2 b —cllc, 

In clay, shale, or shingle. 

In coarse sand. (This is the usual type.) 
In fine sand, e.g. Punjab sand. 

In mud and silt, such as in the Nile. 


and : 


I consider that any attempt to define the terms coarse sand, fine sand and 
silt is at present futile. We require considerably more knowledge of the 
relation between the size of the grains and the conditions producing the 
failures I have endeavoured to describe by the terms fountaining and piping 
(see p. 299). The sands used in the experiments there described were selected 
as being typical of Classes II. and III., i.e. “Madras” and “Punjab” sands. 
Spring (ut supra , p. 667), when discussing the scouring of rivers, gives a large 



Sketch No. 181.— Rupar Weir. 


number of sand-sifting analyses, and it would appear from these that, broadly 
speaking 80 per cent, of the grains of a Madras sand are retained on a 40 
mesh sieve, while 80 per cent, of Punjab sand grains pass through a 75 mesh 
sieve but are nearly all retained on a 100 mesh sieve. Similarly, about 60 per 
cent, of Egyptian grains pass through a 100 mesh sieve. These figures are 
given as rough guides to engineers who have no knowledge of the localities 
referred to. In practice I consider that systematic experiments are necessary, 
even when a successful weir already exists on the river it is proposed to deal with. 

Bligh also considers that where the curtain wall or cut-offs are deep, twice 
the sum of their depth below the aprons should be added to the breadth ; and 
the total quantity thus obtained should be put equal to 2 b. 

The Laguna weir (Sketch No. 176) shows an existing design, where sheet 
piling is used in order to form a cut-off. A definite statement cannot be made 
on this point. No doubt the very deep (20 to 30 feet) cut-off walls of steel 
piling recommended by Bligh check percolation ; although, according to 
theory (p. 296) they are not as efficient as the same length of horizontal apron ; 
but the rules are obtained from a study of existing weirs, where no such 
deep cut-offs exist. Thus, Bligh’s extension of his rules must be regarded with 
caution. The matter is extremely important, for if deep cut-off walls are even 
only half as efficient in stopping percolation as Bligh considers them to be, 
their adoption will certainly enable considerable economies in design to be 


























68 o 


CONTROL OF WATER 


effected. For the present, and until further evidence is available, I think that 
it is wise to regard the shallow cut-off walls in most of the existing weirs as con¬ 
structed merely as stops against localised percolation. Their main function, 
however, is to prevent any undermining of the weir masonry by pot-holes, which 
may form at the up and downstream edges of the masonry apron. 

Thus, in my opinion, shallow cut-off walls act as an aid to the loose block 
talus, and cannot be regarded as in any way equivalent to an extra length of 
impermeable stratum of masonry or clay. The question of the precise function 
of deep cut-off walls of sheet piling must be left open until practical experience 
has accumulated. 

The total breadth of downstream apron and talus is fixed by Bligh as 
follows : 

L= iocsJ^— \J for sanc ^ foundations, 

where c , is the constant in the equation 2£ = cH f , IT,, is the height of the 
fall over the weir, i.e. the difference of level between the masonry crest of the 
weir, and the low-water level downstream of the weir, or the normal bed level 
below the weir, whichever happens to be the greater, and q , is the number of 
cusecs that pass over each foot length of the weir during the maximum flood. 

In clay, or in weak rock, it is sufficient to put L = 6H?,. 

The results of this formula agree very well with the figures obtained from 
drawings of a large number of Indian weirs. The formula may therefore be 
accepted, but is purely empirical. 

The breadth of the downstream apron ( i.e . the impermeable portion of the 
breadth L, as obtained above), in the case of dams belonging to type A , is 
given by the equation : 

w — 4 C\ / 

v 13 

where H.,, is the fall from the top of the shutter to the top of this apron. In 
dams belonging to type (2>), aprons do not occur, and in those belonging to 
type (C), Bligh puts : 

w = 4 c\/^ 

v 13 

The formulae are empirical, and do not agree closely with practice, except 
in the case of type (C). 

In the design of weirs belonging to type (C), as existing in the Punjab, w, 
is usually fixed by the condition that the masonry apron must extend at least 
as far down the weir as the place where the standing wave is likely to occur. 
In actual practice, the whole breadth of the downstream slope is sooner or 
later either grouted up, or surface pointed with mortar, with the object of 
reducing the cost of repairs. The latest designs (see Sketches No. 180 and 
No. 182) therefore show the whole slope as constructed of masonry, and in 
view of the fact that grouting up the loose rubble tends to increase the uplifting 
pressure on the masonry, this provision appears to be correct. 

In clay, or weak rock, o/ = 3H s , is found to be sufficient. 

The thickness of the downstream apron is obtained by estimating the static 
pressure which exists on its lower surface, and which tends to blow it up. 


APRON THICKNESS 68 1 

Let Aj, be the length of the line of creep to any point in the downstream 
apron, i.c. : 

A : = the breadth of the impermeable portion upstream of this point, plus 
(according to Bligh) twice the depth of all the intervening drop walls. 

Then /, the thickness required, is given by the equation : 

t _4 H -h 
3 P -i 

where the apron is submerged at low water, and 

/ _4 H-h 
3 P 

where the apron is not submerged, where p represents the specific gravity of 

the masonry or clay, whichever is employed, and k = —, and H, is the difference 

of level between the top of the shutters and the bottom of the apron at the 
point considered. This obviously secures an excess of 33 per cent, of dead 



weight against the probable upward hydrostatic pressure. The theory already 
given might be employed in order to calculate h , in the following form : 

H x 

h --— cos -1 - (for notation see p. 292) 

TV C 

but the designs of existing works are such that no great difference occurs 
whatever formula is used ; and, as already stated, sufficient information does 
not exist to justify any very wide departure from the lines of existing design. 

The dam wall itself is usually proportioned as a dam to resist a head equal 
to H r . Thus, if rectangular, its thickness would be represented by : 

y_ He 

Vp — i 

the factor p— 1, being used, since the wall may be considered as submerged. 

The top width, however, is usually 1 foot, and, better still, 2 feet, greater 
than the height of the shutters ; and where these are high, this often determines 
the width of the wall. 

The formula has a theoretical justification in weirs belonging to type (A). 
In types (B), and (C), the formula appears to give unnecessarily great width, 
but the advantage of having a heavy, stable wall so as to resist the stresses 
produced by the water pressure on the shutters is obvious, and any decrease 
appears inadvisable, although in a few weirs belonging to type (A), slightly 
thinner walls have been found satisfactory (Sketch No. 174). 

































682 


CONTROL OF WATER 


The pressure of the dam wall on its foundations should be calculated. The 
maximum values found in practice are usually those produced by the piers of 
the undersluices, and may be taken as : 

One ton per square foot, for fine silt, as in the Nile. 

Two tons per square foot, for coarse sand. 

Four tons per square foot, for clay. 

The value given for clay agrees very well with ordinary practice, but the 
values for sand and silt are lower than those which occur in similar soils in 
the case of such structures as bridge piers. It is therefore possible that 
pressures as high as 2 tons per square foot for silt, and 4 tons per square foot 
for coarse sand, might be employed ; especially if the sand is prevented from 
moving under erosion by a coffer dam of sheet piling. The question is not of 
great importance, as the dimensions of the curtain walls are generally fixed 
by other considerations. 

A study of Sketches No. 181 and No. 182 will show that these formula? 


Masonry on d-ttt' 

Loose Stcnc facec^ nits Hand Pacted-Monoh/tnc Concrete 6,Ms wells sunk to X.l 091 

ID's K /AJ' .. , . _j 

—‘ g' ■*— 


tirCrSco]^ 


—-!• ‘oo 

Wll \ K.L.7 V/-0 

I 






vir 



for Section of Herr see skctc'i N°- t&t 


Loose S/One faced witti ,-unJ Med Stone 

.i 

* 

I ” it-L.nf -m /j'L. . 

"4 ^ -! eiter ReJ 

—-I— etc'. -4 


Longitudinal Elevation 






e.L.iol-i 
K.L. OH-/ 


I i e.L.ioi-p 

- 4 - ; t- 

I- 12-5 ^-1 V-f-? Coi 

Section CD. 


e.iJM-e 
Concrete Stocks 


Section d. &. 


Sketch No. 183.—Groynes of Lower Jhelum Weir. 


lead to results which agree fairly well with present practice. The sudden 
diminution in thickness at the second drop wall in the case of the Jhelum 
weir (see Sketch No. 182) is justified if the drop wall is relied upon to largely 
stop percolation. Qua damage by erosion, the lengths AB, and CD, are 
units ; and if the theory is too closely followed the thinner portions of these 
floors might fail, and thus start the destruction of the thicker parts. Whereas, 
by keeping the thickness uniform, each length has a uniform strength to resist 
erosion, and is likely to fail independently. A complete breach of the weir 
is thus rendered less probable. 

In all types of weir the masonry apron should be split up into cells by cross 
masonry walls parallel to the stream flow, carried down as deep as the cut¬ 
off walls and spaced say every 200 feet along the length of the weir. The 
object is plainly to localise and prevent the extension of any hole that may 
form in the apron. 

The layer of spalls and fine stone shown in Sketch No. 182 and in 
No. 175, Fig. 2, may also be noted. This is a new idea, and is termed a re¬ 
versed filter. The object is to provide stone which it is hoped will fall into 
and fill up any pipes tending to form in the sand, and so stop the further 




















































REVERSED FILTER 


683 

removal of the sand in the same way as the gravel bed retains the sand of a 
slow sand filter. The idea is the fruit of a discussion of certain experiments 
made by Clibborn ( Experiments on the Percolation of Water through Sand). 
The principle appears to be sound, and it is obvious that if it works well 
nothing further will be heard of the matter. The position appears to be well 
selected, for should piping occur, the thin masonry over the stones will probably 
crack, and will permit the water to escape in an upward direction, which is 
exactly that which is most favourable for the action of a reversed filter. 

Spalls and run of the breaker stone are cheap, and the principle might be 
extended with advantage by depositing similar masses of stone on the down¬ 
stream side of each drop wall. The proposal was discussed during the design 
of the jhelum weir, and was abandoned on the ground that the stone might 
provide an easy path along the cut-off walls for the water. In my opinion 
this is unlikely, and in any case the mere fact that a cut-off wall has been 
sunk secures that the sand near its face has been disturbed, and, consequently, 
in all probability already provides the easy path. 

Curtain Walls , or Cut-offs. —The idea at present held in the Punjab 
is that curtain walls merely prevent erosion. This is very well illustrated by 
Floyd’s statement (see Upper Chenab Canal Project Estimate ), as follows : 

“For the crest wall {i.e. the dam itself) it is proposed to sink a line of 
wells 12 feet x 8 feet (in plan) to a depth of 18 feet below the mean bed level 
of the river, which will take them to 5 feet above the bed of boulders found in 
the borings made on the site.” 

This really means that the lime plugging of the wells will reach the boulder 
bed, and the inference that the boulders indicate a stratum which the river 
has never yet eroded is confirmed by their appearance. This selection con¬ 
trasts strongly with Bligh’s idea that curtain walls stop percolation, as the 
design plainly forces the percolation towards a stratum which is favourable to 
percolation. 

Personally, I am inclined to believe that a line of wells has but little 
influence, and, as will be seen from the Okla weir (Sketch No. 174), weirs of 
type (P), stand very well without curtain walls, or cut-offs of any description. 
A really well grouted (see p. 980), and perfectly impermeable cut-off formed 
of sheet piling has never yet been thoroughly tried. Such walls exist in 
Egyptian barrages [e.g. at Esneh), but they are shallow, and their function is 
probably only to retain the sand under the heavy pressure of the barrage piers. 

The Lower Jhelum weir (see Sketch No. 182) is amply provided with deep 
cut-off walls. Nevertheless, it partially failed under the action of a strong- 
cross stream current running parallel to the length of the weir. As a contrast, 
the Lower Chenab weir (see Sketch No. 179) has no deep walls, and although 
it did fail, its failure is amply explained by the insufficient length of impermeable 
aprons. The actual failure, moreover, occurred on the site of an old, deep 
channel. Consequently, although it is possible that had a curtain wall been 
carried down through the newly deposited silt into the firmer old bed of the 
river, matters would have been improved, it is not certain that deep walls were 
necessary. 

Hence, I must confess that I am incapable of deciding the question, although 
I consider that Bligh’s theories are very attractive, and deserve testing. 

The Upstream Apron. —A certain, and perfectly safe economy can be 
secured by taking advantage of the principle of the upstream apron. Sketch 


684 


CONTROL OF WATER 


No. 179 shows this apron as adopted in the repairs which were effected on 
the Lower Chenab weir. The wells are generally unnecessary, as the correct 
level for such an apron is at, or near to, the bed level, where it is not exposed 
to erosion. The design adopted in such cases consists of 3 feet of puddle 
clay, covered by 2 feet of concrete blocks. The clay should be well joined 
to the masonry of the dam wall by the methods already discussed (see p. 323). 
The advantages are obvious. We wish to secure a certain length of im¬ 
permeable coating. Downstream of the weir all structures are exposed to 
wave action, and erosion; and an impermeable downstream apron must 
therefore be formed of costly masonry. Upstream of the weir any structure 
situated 3, or 4 feet below the level of the fixed crest of the weir is but slightly 
exposed to erosion, and the upstream apron can therefore be made of the 
cheaper and equally effective (qua impermeability) clay. The 2 feet thickntss 
of rubble, or concrete blocks, (blocks are better as affording less shelter for 
watersnakes and crayfish, or other animals, which might bore through the clay), 
secures the clay against erosion. 

Groynes. —Erosion by cross currents has to be provided against in all 
weirs that cross wide rivers. This is effected by means of groynes of the type 
shown in Sketch No. 183. The angle between the groyne head and the weir 
should be pitched with concrete blocks, so as to prevent erosion of the sand 
by the vortex formed a little downstream (with regard to the cross current) of 
the head of the groyne. 

Bars.—So far we have assumed that the weir raises the water level of 
the river to a certain extent. Thus, take a river with a bed slope of 7 r 0 Vo > 
feeding a canal with a bed slope of -gjyQQ. The weir is supposed to raise the 
water level 13 feet. The saving in canal length is consequently : 

I 0 

—,— feet = 34,700 feet. 

aw T>—5(ho 

This alone may pay for the whole weir. 

In a torrential river, however, the saving in canal length may be in¬ 
appreciable ; and in such cases, a bar or weir the crest of which is at, or very 
close to the normal bed level of the river, may suffice to secure a complete 
control of the river. Wherever possible, a bar of this description should be 
adopted in preference to a weir, for the river being torrential, the velocities 
over the weir in flood are likely to be very high if the weir obstructs the 
natural waterway to any extent. As will be seen when discussing the Bara 
failure, velocities exceeding 30 feet per second will probably destroy any 
raised weir. 

Sketch No. 180, Fig. 1, shows a bar erected on the Jhelum river, in an 
extremely torrential reach (probably as bad a case as is ever likely to be 
dealt with). The section is very large, but it is quite impossible to unwater to 
a depth greater than that which is shown by the foundations, and piling is 
unprocurable. 

In cases where sufficient pumping power is available, a far slighter 
design in sheet piling and masonry about 3 feet below bed level would 
suffice. 

Sketch No. 184 shows a timber section which has performed very good 
work in America. The Sidhnai weir (see Sketch No. 162) crosses a 
markedly non-torrential river, and shows a good type where percolation (rather 





NARORA AND KHANKI FAILURES 685 

than erosion) has to be prevented. The Bengal gates (Sketch No. 190) may 
also be used in sand bearing rivers. 

Failure of Weirs.—Three cases are selected.—Firstly, the Narora weir. 
The original design is shown in Sketch No. 173, and the large additions 
(which are probably unduly extensive) are also shown. The floor was blown 
up for a length of 350 feet, and it is probable that the failure was due to the 
floor not being sufficiently thick to resist the upward water pressure. The two 
pipes show the pressures which were actually observed by Beresford shortly 
before the failure. The values of the pressures, (H -/«), thus obtained seem 
to indicate that the upstream clay apron was that portion of the impermeable 
stratum which proved most efficient in diminishing the pressure arising from 
percolation. So far as the observations go, Bligh’s theory regarding the 
efficiency of drop walls is confirmed. To my mind, the lesson is mainly that 
weirs belonging to type ( A ), are unsuited for sand foundations. 



Sketch No. 184. — Timber Bar. 


The second example is the Chenab weir at Khanki. Sketch No. 179 

id 

shows the original design. The ratio _y, is approximately equal to 8*3, in 

-t"lc 

place of 12 or 15. So also, the upward pressure downstream of the core wall is 
about 9 feet of water, which is slightly in excess of the weight of the 4 feet of 
stone masonry in lime mortar. The apron, however, did not blow up, as was 
the case with the Narora weir ; and the circumstances attending the failure 
rather suggest that localised percolation occurred, of an intensity which was 
sufficient to undermine and finally crack the apron. The circumstances are 
obscure ; the failure occurred at a point where the sand is known to be 
less well consolidated than is usually the case. The weir also appears to have 
sustained rather rough handling by the sudden dropping of long lengths of 
crest shutters, followed by an equally rapid raising. Nevertheless, the section 
is obviously weaker than usual, and the manoeuvres above referred to are 
required in the systematic regulation of any river which is subject to sudden 
freshets. 





















686 


CONTROL OF WATER 


The failure of the Bara weir (Peshawar district), which I take as the third 
example, was of an unusual character. Sketch No. 185 shows the cross- 
section. The weir was a small work, only 124 feet in length over all, and 
crossed an extremely torrential river with vertical banks 30 feet high. 1 he 
circumstances are peculiar, the river section suddenly narrows to a width of 
82 feet at the tail of the weir. Thus, the afflux is probably small, but the 
velocity over the weir is very great. The weir withstood several floods, of 
which one at least passed over at a mean velocity of 24 feet per second. It 
finally failed, and was completely destroyed by a flood which, if the weir stood 
until the maximum level was attained, must have had a mean velocity of at 
least 32 feet per second. 

The conditions are plainly unsuited to a weir. The bed slope of the river 
is about and the water level could be maintained at the elevation 5637 
by means of a bar situated 500 feet upstream of the present site. This 
solution was adopted when the work was repaired ; and, judging by the 
relative costs of the original and the new design, it should have been selected 
when the canal was first constructed. 

Summary. —An examination of successful weirs of the types discussed above 
leads to the following general principles of design. The weir should be con¬ 
sidered not as a dam, but as a carpet laid over the sand so as to prevent erosion. 


I FI Stone 


Srcnff Asml** 


l& Soouocrs t* LimG 


\r. L. 5595 


^.■-. 343-7 


k> 3 r<- 


^ Rubble Stone In White Lime , 

r.l.55*. 

-- 50'- * 3 * 4 - 



ShinolC 


Sketch No. 185.—Bara Weir, or Bar. 


Percolation under this carpet is dangerous, and can best be checked by a 
coating of puddle covered with stone upstream of the crest of the weir. If 
marked percolation occurs, the danger lies not so much in the actual percola¬ 
tion, as in the removal of sand from under the weir, thus forming a definite 
channel. Consequently, reversed filter beds at the tail of a weir are a very 
valuable means not so much of checking percolation (for they probably increase 
it), as of preventing the dangerous effects of percolation. From this point of 
view, rigid masonry in a weir is a mistake, as it prevents the stone carpet from 
falling in and filling up any defined channels that may form. On the other 
hand, if there is no covering of large blocks or rigid masonry, the upper stones 
of the carpet are likely to be displaced and carried away by floods. Thus, the 
masonry portion of the weir should be supported by shallow drop walls at 
frequent intervals, and should be as thin as is consistent with resisting the wave 
action of the overflowing water, and the upward pressure caused by percolation. 

Even the masonry of the Lower Chenab weir is thicker than is requisite if 
an upstream apron is put in ; although, until this upstream puddle coating was 
laid, the uplifting pressures were sufficient to severely tax the masonry, and a 
smaller thickness would probably have failed. 

A masonry core wall at the tail of the downstream apron is of course 
necessary in order to prevent erosion, should the talus blocks be removed. 
Such walls are not intended to sustain water pressure in the sense that the dam 
or curtain wall does. The smaller drop walls serve two purposes, they assist in 
































DESIGN OF A WEIR 


687 

localising any damage done to the apron, and also act as chases to prevent 
the formation of percolation channels immediately beneath the stonework. It 
would therefore appear that they should be numerous and shallow, rather than 
few and deep. The upper surface of the downstream apron should be of cut 
stone in hydraulic mortar, pointed with cement, and should be carefully 
inspected during each period of low water. 

If these ideas are followed to their logical conclusion, the proportioning of a 
weir would probably be as follows : 

(i) The dam wall would be made rectangular, and of a thickness such that: 


where p is the specific gravity of the masonry. The foundation level of the 
dam wall would then be fixed by a consideration of the pressure produced on 
the sand ; or, in practice, would probably be laid as deep as the subsoil water 
level permitted. 

•(ii) The downstream slope would be of good masonry, of sufficient thickness 
to resist the action of the water passing over it (say 2 feet in ordinary cases, and 
3 feet where severe action was anticipated). These remarks only apply to a 
weir belonging to type (C). 

(iii) The length of the upstream apron of puddle clay and concrete blocks 
would then be calculated by the condition that the percolation pressure H — h, 
acting on the downstream apron was not sufficient to blow it up, or say : 

H — h = 2 feet when the downstream apron was 2 feet thick. 

The downstream apron would provide the remainder of the length 2 b — cH c , 
which is required to prevent localised percolation. A drop wall, or line of 
sheet piles, would then be placed at the tail of the downstream apron in order 
to check local erosion. The downstream talus of square concrete blocks would 
then be continued so as to provide the required total length L, given by Bligh’s 
rules. 

The general agreement with the Chenab weir as originally constructed is 
obvious, provided that the fatal defect caused by the absence of the upstream 
apron is neglected. 

The above proposals lead to a design which contains the minimum possible 
quantity of cut stone masonry. Although probably more bulky than the present 
designs, it will prove cheaper, as the extra bulk consists of clay and concrete 
blocks ii.e. hydraulic lime concrete), and these are cheap. Also the larger 
portion of the impermeable coating is found in the upstream apron, where it is 
subject to but slight erosion. 

When this design is sketched out, it will probably be found that the differ* 
ence of level between the top of the weir and the normal bed level is such that 
the downstream apron is obviously somewhat short (it certainly will be so if 
tested by Bligh’s empirical rules), and the tail cut-off wall is therefore somewhat 
higher than usual. A modified design with a somewhat longer apron, and con¬ 
sequently a somewhat lower tail cut-off wall, will therefore prove cheaper. The 
final design can best be arrived at by trial estimates of cost, and will greatly 
depend upon the unit prices of masonry, concrete blocks, and the material of 
which the cut-off wall is composed (which, in India, is usually masonry wells; 
and in other countries is probably steel sheet piling). Finally, the location of 



688 


CONTROL OF WATER 


the standing wave must be considered, and estimates of the relative costs of an 
extension of the masonry apron, or the provision of an extra thickness of con¬ 
crete blocks where the wave occurs, must be made. 

So far the question of the relative cost of work done in the dry {e.g. the 
masonry tail apron), and of work done in the wet {eg. the foundations of the 
dam wall, and possibly the puddle clay upstream apron) has not been considered, 
but this will also have some influence upon the final design. 

Maintenance of Weirs. —The maintenance of a weir requires the careful 
attention of a skilled engineer during each low water season. It is so much 
a question of local knowledge that, contrary to the usual practice in Public 
Services, the officer in charge is rarely transferred to any other post. 

The work usually consists of the following repairs : 

(i) On the masonry work. Re-pointing all eroded joints, the renewal of all 
displaced stone, and the careful smoothing off of all irregularities and filling up 
of all hollows. 

(ii) Concrete blocks. These are examined and replaced. The advantage 
of being able to inspect as much of the work in the dry as is possible is obvious, 
and forms the principal objection to the upstream apron. For this reason, a 
design in which the upstream apron is not at bed level, but is say from 4 to 5 
feet below the weir crest, is preferable ; for ring banks of sand can then be 
cheaply constructed so as to permit an examination of the weak spots which are 
disclosed by soundings. 

The maintenance of the talus is less difficult, as a bare patch is not neces¬ 
sarily dangerous. In some rivers it is possible to expose the major portion of 
the talus during low water seasons. Where this, is not possible, as at Khanki 
(Chenab), the places which require repairs are found by soundings, or by wading 
over the talus. A small island of loose sand is then made at the spot discovered. 
Concrete blocks, previously prepared and seasoned in the block yard which is 
attached to each headworks, are laid on this island ; and the weir shutters 
above the island are manipulated so as to direct a current of water against the 
sand. The sand scours away ; and, when the process is skilfully managed, the 
block can be dropped into place to a nicety. It must, however, be remembered 
that the regular horizontal talus where blocks are carefully arranged in order, 
rarely exists in practice. 

Talus repairs are occasionally effected in Egypt by filling the interstices with 
ballast, and then grouting up. The talus is more regular than is usual in the 
Punjab, and this process may assist in obtaining the result. The Nile floods, 
however, are believed to be far less severe in their action than those of Indian 
rivers, and in any case it is a matter of doubt whether the orderly arrangement 
shown in the drawings is best for the weir. 

Special Precautions to be adopted i?i the Construction of Weirs. —In all 
hydraulic constructions founded on permeable soil or sand, springs or “boils” 
may be expected to occur in the area exposed when laying their foundation. 
In fact, the absence of such springs may generally be regarded as a sign that 
the foundations are too shallow, and should be deepened. 

If properly treated, these springs give but little trouble. On the other hand, 
if they are either disregarded, or if their flow is checked before proper prepara¬ 
tions have been made, they will inevitably burst out in some other locality, 
usually just where their presence is least desired. 

In the first place, it should be realised that the ring banks which enclose the 


CLOSURE OF SPRINGS 


689 

working area must be set well back from the work, and it will be found that a 
far larger area than that of the work itself can advantageously be unwatered. 
In my own practice, I have usually located these banks by the rule that a line 
drawn from the bottom of the foundation excavation to the water level in front 
of these banks shall in no case have a greater slope than 1 in 10. 

This may be regarded as a minimum in small works where the extra area 
thus taken in forms a large portion of the whole area surrounded by the bank. 

Even flatter slopes may be considered advisable in large works, as the extra 
width secured is useful for such purposes as temporary railway lines, and the 
storage of material. 

Each spring, or boil, that occurs must be separately dealt with. The ruling 
principle is that the spring must not be covered with masonry, or in any way 
sealed up until it is surrounded by a ring of firmly set masonry of so large an 
area that the spring when sealed up will find it more easy to burst up outside 
the area covered by the masonry, than in any portion of this area. Thus, if a 
spring is / feet distant from the nearest boundary of the masonry, it should not 



be sealed until the ring of well set masonry round it has a radius of at least 
/ feet. 

Sketches Nos. 186 and 187 show two methods described by Hanbury 
Brown (.Irrigation as a Bra?ich of Engineering). Here, in each case, masonry, 
or concrete, is deposited all round, and as close to the spring as is possible 
consistent with the water of the spring being unable to wash away mortar or 
cement while setting. A ring of brickwork in clay is then built up round the 
spring, and the water is allowed to rise up inside this ring until it can be 
conducted away over the set masonry by means of pipes or launders. The 
masonry is then carried across from the scar end of the set masonry to this 
temporary ring of bricks in clay, and the sand through which the spring bubbles 
is carefully dug out (say 12 inches below foundation level), and the space is 
filled in with ballast so as to form a reversed filter. This masonry having set, 
a tube perforated with holes is placed so as to carry away the water. The 
brickwork in clay is then removed, and the whole vacant space is built in with 
cement masonry, or concrete, the tube being left open so as to permit the 
water to pass away freely. When this last material is thoroughly set, the tube 

44 



















CONTROL OF WATER 


690 

is closed off by a screw cap. The second arrangement where the draining 
tube is horizontal and discharges into the small well A (see Sketch No. 187), 
which is kept free from water by means of a hand pump, is preferable. In my 
own practice, where a vertical tube had to be used, I have been accustomed to 
screw on a second length of tube (say 10 feet high), and to pour in cement 
grout. Then, unless the spring water issues under a pressure exceeding 20 feet 
head, the grout is injected into the ballast and fills all the void spaces which 
may have been produced under the set masonry while excavating round the 
spring. 

This method must be used in springs under a pressure such that the water 
rises well over the top of the completed masonry. It obviously entails a good 
deal of costly work in cement, masonry, or concrete. In India the springs do 
not usually issue at a very high pressure, and it is generally possible to build 
a small wall of brick in clay, or sand bags, round the spring, to such a height 
that the spring ceases to flow, the pressure of the water ponded up inside this 
wall being adequate to stop the flow. In such cases it is sufficient to build a 
wall, and to deposit rich hydraulic lime concrete over the whole area occupied 
by the spring, and to remove the wall when this has set. The wall should be 



absolutely water-tight, for if any water is allowed to escape the lime may be 
removed from the concrete, and setting will consequently be prevented. 

In certain cases, none of the above methods are sufficient, and the spring is 
then probably not of local origin. For example, there are at least two springs 
in the Delta barrage (Egypt) which, judging from their temperature, are 
probably not directly derived from the Nile. The best that can be done in 
such cases is to guide the spring away from the work by building masonry over 
it, and injecting grout over its original site, after the spring has made its 
appearance outside the work. A thick reversed filter covered with loose blocks 
of concrete or stone should then be laid over the final exit. 

Well, o?' Pile Junctions .—A line of wells or metal sheet piling is frequently 
used as a cut-off wall. Examples exist in the Esneh barrage (cast-iron piling), 
and in the Jhelum, and other Indian weirs. 

The section of the Esneh piles is shown in Sketch No. 82 (p. 320). After the 
piles have been driven, the junctions are made watertight by cleaning out the 
space between the piles, with a water jet, and then injecting cement grout. 

In most of the Indian weirs the line of wells is assumed to be & sufficiently 
watertight, the wells being square in section, and sunk very close to each 
other. The Indian well sinkers are very skilful, and probably watertightness 



















CLOSURE OF WELL SPACES 


691 

is eventually secured through the stanching by silt that occurs as the weir grows 
older. In one case, where such a line of walls was momentarily exposed, the 
interstices appeared to be filled with a material resembling good puddle. In 
Egypt, the sand being finer, and the well sinkers less skilful than in India, more 
systematic measures have been adopted. Hanbury Brown (ut supra) describes 
the work at Shubra as follows : 

The wells were sunk 6 inches apart, and piles of half-inch steel plate, 
stiffened with T irons, were driven upstream of, and close to, the wells. 



A pipe was then water-jetted down to the level of the bottom of the wells 
in each angle between the piles and the wells, and was filled with sand in 
order to exclude the grout from the floor. The floor being completed (in 
this particular case the floor was of loose rubble grouted with cement), the 
pipes were cleared of sand and were run in with grout. The above is an exact 
description ; but, in my opinion, the pipes should have been grouted prior to 
the floor being grouted, as there is no assurance that the cleaning of the pipes 
did not produce a void under the rigid grouted floor. 

















CONTROL OF WATER 


692 


Undersluices, or Scouring Sluices.— The principles governing the 
design of the masonry portion of undersluices are the same as those employed 
in weir design. Although the water does not fall over the undersluices, it 
rushes through them when opened for scouring purposes, with a velocity which 
often exceeds the flood velocity over the weir. Thus, the masonry aprons must 
be quite as thick as in the weir, and tail erosion is probably more intense. The 
upstream apron of an undersluice is more liable to erosion than in a weir, and 
must therefore be made thicker, and cannot be relied upon to the same extent 
as in a weir. This is not of very great importance, as the total length of the 
downstream apron and talus pitching required below the undersluices is far 
greater than is necessary in a weir. The difference is probably intimately 
connected with the fact that inspection and maintenance are obviously less easy, 
and marked erosion is consequently more likely to occur. 

Bligh has reduced the matter to the following rules : 

Total length of downstream apron and talus pitching is equal to 


^ IO V 75’ 

where the symbols have the same meaning as in the similar equation relating 
to weirs. 

The length of the downstream apron is equal to 7Gy/ 

The rules are empirical, and agree less closely with practice than the 
similar rules for weirs. This fact is not surprising. The stability of the 
foundations of undersluices almost entirely depends upon the amount of tail 
erosion, and this is still more influenced by local conditions than is the case in 
weirs. For example, if a river is worked on the new Rupar method (see p. 659) 
erosion at the undersluice tail only occurs during floods when the difference of 
level producing percolation under the floor is but small. Whatever erosion has 
then occurred is rapidly filled up soon after the flood ceases by the coarse 
silt scoured out from the silt trap. In a river which is worked in the old method 
of regulation by undersluices only, erosion may, and does, occur during the 
entire season of low water. The water causing the erosion is probably (relatively 
to the normal river water) somewhat devoid of bed silt, as it has passed in front 
of the canal head, which is known to produce disturbances which tend to raise 
the bed silt. 

Bligh’s rules appear to agree best with the construction of undersluices on 
rivers which are, I believe, still (or were at the date of the drawings) worked 
on the older methods. 

The method of working also influences the necessary width of the imperme¬ 
able masonry apron. In undersluices worked on the new principles, the width 
of impermeable masonry shown in the drawings is only about one-half to two- 
thirds that given by Bligh’s rules. The explanation is obvious. The masonry 
bed of the upstream silt trap forms a fairly efficient impermeable apron, as the 
interstices are stanched by fine silt. The design is also affected by the fact 
that the talus is considerably wider than is the case in weirs ; so that under 
the new principles of river regulation downstream erosion is less likely to occur 
below the undersluices than below the weir. 

The foundations of the piers of undersluices need careful consideration. 
The pressure on their base is great. In Indian practice, the piers are usually 


UNDERSLUICE PIERS 


693 


founded on lines of wells sunk to a depth which is at least equal to the total 
height of the masonry pier above the foundation level. 

Under the conditions prevailing in India, this is probably the cheapest 
solution. 

In Egypt, and in countries where well sinkers are less expert, and piling is 
more easily obtained than in India, the pier foundations are carried down as 
far as the subsoil water level permits, and the whole area covered by each 
individual pier foundation is surrounded by steel or cast iron piling, well 
grouted at all interstices (see p. 690). The normal depth of the bottom of this 
piling appears to be about 15 or 20 feet below the subsoil water level ; and as 
this apparently suffices, the Indian type of well foundation is probably (con¬ 
sidering the coarser grade of Indian sand) somewhat deeper than is necessary. 
As a matter of experience, I have never been able to find any record of pre¬ 
judicial cracks or weaknesses in the piers of any Indian undersluices. 

A study of the thickness of floors of undersluices in the light of the theory 
already developed for weirs leads to somewhat puzzling results. 

If Bligh’s rule: 

/ = 4 H -h 
3 p-i ’ 


is accepted as correct, nearly all undersluice floors (as at present constructed) 
are found to be too thin. Thus, at Khanki, t =- 4 feet, where the theory would 
give 7*5 feet; and at Narora, t = 5 feet, and theory requires 10 feet. Neither 
of these works has ever shown signs of failure. Equilibrium is possibly 
secured by the load produced by the weight of the piers, and if this is the case, 
the floor between the piers acts as an arch, which it is certainly capable of 
doing when its thickness and span are considered. A more probable sup¬ 
position, however, is that the paved silt trap upstream of the undersluices 
rapidly becomes so stanched with silt as to act as an upstream apron. The 
question deserves careful consideration in view of the fact that the modern 
tendency is to use Stoney gates of large span, and to put in as few piers as 
possible. 

Bligh suggests that the action of the out-rushing water should be con¬ 
sidered as the factor determining the thickness of these apron floors, and finds 
empirically that 


where H, is the maximum head which the undersluices sustain. A similar 
divergence between theory and practice is found in regulators, and the fact 
that neither of these works is continuously exposed to the maximum head H, 
may explain the matter. Nevertheless, the question cannot be considered as 
settled, and deserves further investigation. 

The proportions of piers must be determined as in the case of a dam. The 
thrust produced by the water pressure acting on the pier, and the two halves 
of the sluice gates on either side of it, can be calculated. This can be com¬ 
pared with the weight of the pier and arches and roadway (deductions being 
made for all portions of the masonry upstream of the gates which are sub¬ 
merged in water). The resultant must fall within the middle third. 

The discharge of undersluices is usually fixed by a consideration of the 
area of the obstruction of the natural river channel produced by the weir. The 


CONTROL OF WATER 


694 


afflux, or rise in the water level upstream of the weir compared with that down¬ 
stream of the weir (which may be regarded as the natural level of the highest 
floods in the river) is calculated. The formulae employed for the weir discharge 
are given on page 133, and for the undersluices on page 164. The calculation 
4s important in determining the height to which the undersluice gates should 
be raised, or when damage to land or to the canal works is considered. 



There was originally 124 feet of boulder pitching downstream of A. This is no longer 
visible, and a deep hole exists from 50 to 100 feet downstream of A. As, however, a 
very few concrete blocks every year keep the retaining wall foundations secure it is 
probable that the pitching exists beneath the sand surface. 



Faijptjad Escape 



The method of determining the capacity of the undersluices appears to be 
illogical. Undersluices are not provided for flood disposal purposes, although 
they are used for passing flood water. Their essential function is to regulate 
the river, and above all to scour out silt deposits in front of the canal head. 
Thus, the discharge capacity of undersluices should be a function of the low- 
water discharge. I suggest that the undersluices should be capable of passing 












































































































UNDERSLUICE CAPACITY 695 


the average discharge of the three low-water months when the water is 
headed up to the top of the masonry of the weir, and the discharge of the 
maximum ordinary low-water freshet when the water is headed up to the top 
of the shutters. It is believed that the capacities thus calculated agree fairly 
well with those provided in existing works. Since undersluices are scouring 
machines, it hardly appears necessary to state that the openings should be as 
wide as possible (say 20 to 25 or even 30 feet in span), and that they should 
be provided with Stoney gates. The old Bengal type of gate (see Sketch 
No. 190) is cheap, and relatively obstructs floods less than the arched type, 
and may also be employed in clear water streams where silt is not feared, and 
where the river is regulated by means of undersluices. It is useless in cases 
where the regulation is effected by means of the weir shutters. 

The above treatment of undersluices is obviously deficient. The facts, I 
believe, are as follows, the theory is incomplete, and owing to the rapid intro¬ 
duction of the new methods of river regulation (p. 661) a study of existing 
designs is not likely to be very useful. A large number of sections have been 
collected by Buckley (Irrigation Works of Lidia). I believe these to be 
strong enough for the old methods of regulation, and if so they are over strong 
when the newer methods are employed. With one marked exception, the 
undersluice is usually that portion of the headworks that gives least trouble in 



Sketch No. 191.—Lower Jhelum Undersluices. 


maintenance, which is usually a mere matter of routine, so many hundred cube 
feet of blocks deposited in the downstream pitching per year. 

Canal Regulators. —The control of the quantity of water admitted into 
a canal or any one of its branches is usually effected by means of a series of 
sluice gates erected in a wooden or masonry structure across the canal. The 
term regulator is a convenient description of the whole structure. The typical 
regulator consists of a series of piers which carry the sluice gates ; and, for 
convenience, the openings thus afforded are usually arched over so as to 
provide a platform for the machinery which is used to raise or lower the gates, 
and this platform generally forms a passage for traffic. I do not propose to 
consider the design of the platform, as this depends upon local conditions. 

Head Regulators. —The regulator at the head of the main canal which 
controls the quantity of water admitted to the whole system is one of the most 
important works connected with a canal, and its design largely influences the 
whole state of the canal, and above all its silt regime. 

Canals for flood irrigation, or inundation canals, are not usually provided 
with head regulators. This defect (for it must be considered as such from a 
scientific point of view) must be accepted in many cases, for the floods of rivers 
which rise to a sufficient height to inundate the surrounding country are usually 
so violent as to cause large and widespread erosion of their banks, which 





























CONTROL OF WATER 


696 

would sooner or later destroy any regulator. The water brought down by the 
floods usually contains sufficient silt to render the choking of the head reach 
of the canal in one year quite possible under unfavourable circumstances. 
Thus, the annual silt clearances of such canals may be partly regarded as the 
price which is paid for dispensing with a regulator. Nevertheless, once a 
river has been got under control, it will frequently be found advisable to provide 
one large regulator, and to admit through it the water which is required for 
several inundation canals. The Jamrao canal in Sind ( PJ.C.E ., vol. 157, 
p. 278), and the Ibrahimiya canal in Egypt are cases where this improvement 
has been carried out, and these examples illustrate the substitution of perennial 
for flood irrigation which usually takes place when these regulation works are 
carried out. 



Sketch No. 192.—Lower Chenab Regulator (1) and Undersluices (2). 


The design of a head regulator largely depends upon the following 
conditions : 

(a) The difference between the bed level of the canal (or the lowest water 
level in the canal in cases where the canal is never closed down), and the 
highest flood level (corrected for the afflux produced by the weir if one exists) 
in the river. 

( 3 ) The quality of the silt carried by the river, and its liability to deposit 
in the canal. 

The difference of level specified above is the maximum head of water which 
the regulator is required to sustain. The circumstances differ widely from 
those which exist in weirs and undersluices ; for, although the work is usually 
founded upon soil which is as permeable as that which supports the weir and 
undersluices, tail erosion does not occur. Thus, the theory already given on 
page 292 indicates that the depth of the core or cut-off walls is of more import¬ 
ance than the breadth of the impermeable apron. At first sight this statement 









































































REGULATOR FOUNDATIONS 697 

does not seem to be confirmed by a study of the designs of existing works. 
Except at Khanki (Sketch No. 192), Okla, and possibly some of the Madras 
weirs, the core walls of the regulators are carried but little, if at all, deeper 
than those of the weir and undersluices (compare Sketch No. 193 with Nos. 
191 and 168). In the case of some Egyptian works the core walls of the 
regulators are considerably more shallow than those of the weirs and 
undersluices. 

It must be remembered that in India, at any rate, the core walls are almost 
invariably carried down to as great a depth as local conditions permit. There 
is no doubt that in many places the constructional engineers, taking advantage 
of exceptionally favourable local conditions at the regulator site, have carried 
the regulator core walls to a greater depth than that shown in the designs. 
In some of the new projects this procedure has been sanctioned for adoption 
wherever possible. As a general rule, using the notation given on page 293, 
we find that a= H, or that the depth of the core wall is equal to the head of 
water retained. The rule is not closely followed owing to the circumstances 



explained above. The breadth of the impermeable apron is usually given by 
the following rules of Bligh : 

Class I. The width is usually determined by the length of the 
piers required to sustain the water pressure. 

Class II. For coarse sands, as in Madras, or for 

the usual type of sand . . . 2b = 2, to 3H 

Class III. For fine (Punjab), or Bengal sand . . 2b = 4, or 5H 

Class IV. For fine silty sand, as in Egypt . . 2b = 8 , or 9H 

It will be noticed that these figures do not bear a constant ratio to the 
similar figures given for weirs or undersluices on page 679. 

The explanation is probably to be found in the fact that the finer the sand 
the more easily it is eroded ; for it is unlikely that the relation between the 
head necessary to produce fountain failure and that required to induce piping 
failure through an equal length of sand, is materially affected by the size of 
the sand grains. It is also probable that the deeper foundations of the piers 
of both regulators and undersluices produce the same effect as a deep core 
wall across the whole breadth of the work. 

The dimensions of the piers and their foundations are proportioned by 
the rules given for undersluices. The thickness of the masonry floor is usually 
fairly close to VH ; but, as will be seen when the Trebeni design is discussed, 
local conditions may cause this to be insufficient. 
























































CONTROL OF WATER 


698 

The clear water way through the regulator should be relatively large, in 
order to minimise any disturbance in the entering water, and thus reduce silt 
troubles. A velocity of 3 feet per second should not be exceeded in waters 
which carry sandy silt. In rivers which carry boulders and gravel, the usual 
rule is 5 feet per second ; and 7 feet per second is certainly too high. In my 
opinion, 3*5 to 4 feet per second should be adopted in these cases wherever 
possible. The advantages of large sluice gates are obvious, and spans of 
30 feet are usual. It must, however, be realised that until quite recently the 
20 to 30 feet spans of regulators were usually divided up into three small spans 
by jack piers (see Sketches Nos. 192 and 193 and p. 7°0 an d that our 
experience of 30 feet spans is limited. Nevertheless, I see no reason why 
spans of 60 or even 80 feet should not be adopted with advantage ; for, 
unless the retrograde step of using spans of 10 or 15 feet is considered 
advisable, Stoney or other “ frictionless ” gates must be used. The total 
cost of a fixed length of such gates largely depends upon their number, as 



ST 4 - Z 

1 



~N 



r-T- 


— 1- 



* 

s- — 4 — 77 

Lj 


—I 

"V 


l rrr 


J-“ 




Sketch No. 194.—Trebeni Regulator. 


the frictionless gear is far more expensive than the steel I beams, and plating 
which form the gates. 

In silt-bearing rivers, it is desirable to design the regulator so that water 
can be drawn off from the surface of the river at whatever level this may be. 
The arrangements adopted entirely depend upon the variation in river level, 
which may be taken as the difference between the highest flood level and the 
top of the weir, or its shutters. Sketch No. 194 shows the Trebeni (Bengal) 
canal head, which is admirably adapted for cases where this variation is great. 
The projecting double arches can be blocked by baulks of timber, so that 
surface water alone is taken into the canal. The design is an excellent one, 
as the energy of the water which falls over the arches is dissipated in the 
water cushion that can be maintained by the manipulation of the draw gate ; 
and if damage does occur from this cause, it will be found on the upstream 
side of the sluice gates, where it can do least harm. 

The front arches are only 7*5 feet in span, measured parallel to the length 
of the regulator ; and, in view of the desirability of splitting up the falling stream 















































































.REGULATOR GATES 699 

into small bodies (as discussed under h alls, see p. 724), this may be considered 
to be the proper size. In the existing work, the sluice, or draw gate channel, 
is only 6 feet in span ; but this might with advantage be increased to 20, or 
even 25 feet, if Stoney, or other modern gates were used. 

The sketch of the Qushesha, Egypt, escape (No. 195) shows a very interesting 
example of another (and in my opinion far more costly) method of dealing with 
the problem. This work is not a regulator, but is an escape for draining a large 
series of flood irrigation basins. My criticism only refers to the adoption of 
a similar design for a regulator, as I am not sufficiently conversant with the 
local requirements to state whether the upper falling gates are required in the 
actual work. 

The cross-sections of the Khanki and Rasul head regulators (i.e., Sketches 
No. 192 and No. 193) show the application of the principle of the “raised sill” 
(see p. 660), for the exclusion of silt in rivers where the variation in level is 
less than at Trebeni. Sketches of the elevation of these works are not given, 
as the designs were made prior to the introduction of the Stoney sluice, and 



the gate spans are less than would now be advisable. The Jamrao canal head 
(see Sketch No. 196) is better designed in this respect, although in most cases 
sluice gates would have to be substituted for the regulating beams shown in 
the sketch. 

The design of head regulators in coarse sand follows the same principles. 

The cross-sections of the Tajewala regulator and of the Madhupur regulator 
show the forms of raised sill adopted in rivers which carry boulders (see 
Sketches Nos. 168 and 169). 

As already stated, neither of these works can be considered as correct 
solutions of the problem of excluding gravel and sand from the canal. The 
rivers are not properly under control. If they are ever got under proper control 
there is no doubt that a raised sill of the Rupar type will soon be built across 
the regulator, so as to skim the surface water from the comparatively still pool 
that will then exist in front of the regulator. At present, as stated on page 662, 
the engineers construct dams across the river as it falls, after the flood season ; 
and were the sill level any higher than it now is, it would probably be found 
impossible to secure a continuous supply of water in the canal during the 

































































700 


CONTROL OF WATER. 


interval between the last flood and the completion of the temporary regulating 
works. The adjustable gates used at Tajewala permit a temporaiy laised 
sill to be produced during the low water season. While the gates themselves 
and the 6 feet wide arches are almost prehistoric, the principle is a good 
one. 

The length of the waterway of the head regulator is probably one of the 
most important factors in the whole design of a headworks ; and there is no 
doubt that the penalties of insufficient waterway are very forcibly brought 
under the notice of all concerned with the working of the canal. The rules 
already given enable the nett area of the waterway to be calculated, and if 
any divergence from these rules is contemplated, it should certainly be in the 
direction of increasing rather than reducing the area of the waterway. 


R12$°°** Hcn]finhl teem j ~ 


TapE Shulte/s RLjo _ 

Crest of fair R.L.7 _ 




0-8. Bnck on End 
08. Concrete• , 

05 Sr/ck Ballast 


2 — 


?! 


165 


R.L.XS 

ft. L 205 
ff.L/5 

M Supply R is 


Top ofSylllU.5 

I * 

M 9 


-— 

- 32 - 


Li 

! 1' 1 

i ! < 

Jl.JL- j [ 

LU 


40 


Fmnsrmm. 75 'of E'Mdswrj, 
loo'oht' nrc/iino, 


fit.LS 

ff.L-12 


falls T'squdre 


Cross Section 



The principles of the calculations concerning the length of free waterway 
and the level of the sill of a canal head regulator are illustrated by the figures 
given in the “ Project Report of the Upper Chenab Canal.” 

The nett waterway of the canal head regulator is 253*5 feet long. The 
raised sill will be 3*5 feet above the floor of the silt pocket, and 2*98 feet above 
the canal bed level. The full supply depth in the canal being 11*56 feet, the 
depth over the sill, considered as an orifice, is 8*58 feet, or the nett area is 
2177 square feet. The maximum discharge of the canal is 11,694 cusecs. 
Thus, the head required to produce this discharge, assuming a coefficient of 
o*8o (see p. 168), is given by the equation : 

- 11694 

o*8o is/2gh - — 5‘40 ; 


or, h = 0*93 foot. 









































































REGULATOR WATERWAY 


701 


The actual difference of level between full supply in the canal and the top of 
the shutters is ro8 foot, so that a margin of o - i5 foot head remains available in 
case the canal becomes somewhat silted. 

This method of calculation evidently affords a somewhat greater margin 
than stated, for the discharge is calculated as though it occurred through a 
submerged orifice, in place of over a drowned weir, and the piers of the regulator 
being nicely tapered off, the coefficient o’8o is probably somewhat low. 

If the accurate drowned weir formula is used, it will be found that the 
available margin of head is 0*20 foot. It is, however, plain that it is inadvisable 
to force the engineer in charge of the weir to head up the river to the level of 
the top of the shutters, except on rare occasions, lest he be caught by a sudden 
freshet. The whole design is intended to keep the velocity at entry low, and 
it will be found that the ordinary maximum supply, 9320 cusecs ( = fx 11694 
cusecs), can be passed in under a head of about 078 foot, and that the velocity 
will not exceed 4*33 feet per second. This value is probably somewhat high, 
and a waterway proportioned for a velocity of 3, to 3*5 feet per second would 
be preferable, were it not for the extra cost entailed in constructing an additional 
length of about 50 feet of regulator. 

The design considered above is composed of 13 bays, each 24*5 feet wide, 
and each separated into three openings 6*5 feet wide, by jack piers 2*5 feet 
thick. In the work as constructed, however, these jack piers were abolished, 
and Stoney gates 25 feet wide, span the whole opening of each bay. Thus, the 
clear waterway is 317*5 feet long, and the nett area as finally adopted is 
2700 square feet, so that the extraordinary supply passes in at a velocity of 
4*34 feet per second, and the “full supply” at a velocity of 3^47 feet per second. 
The advantages gained by the use of Stoney gates of large span are excellently 
illustrated by these figures. It may be remarked that the original designers 
were well aware of the advantages of Stoney gates, but were hampered by 
somewhat peculiar local conditions. Therefore, being competent engineers, 
they designed the work so that little difficulty was experienced in inserting 
Stoney gates when these local conditions ceased to exist. 

Failures of Regulators.—The most instructive example is the failure of the 
Menufiah regulator (a portion of the Delta barrage works in Egypt), which 
occurred on the 26th December 1909. The failure was very rapid, the 
regulator being reduced to a mass of masonry fragments within an hour of the 
first signs of failure. 

Sketch No. 197 shows Mougel Bey’s original design, which does not appear 
to have been added to or repaired in any way. The regulator was the only 
portion of the Delta barrage which was held not to require the grouting 
operations described on page 981. The failure is stated to have been caused by 
piping, and probably only one defined channel existed when the failure 
commenced. Personal inspection of the sheet piling permits me to say that 
the downstream line of piling was imperfect, since gaps an inch or more in 
width existed in many places between adjacent piles. Otherwise, the con¬ 
struction was first rate in quality, and it is believed that the whole of the 
foundations were laid in the dry. In my opinion, the work is amply safe 
against piping in the restricted sense in which I consider that the term is best 
employed. The failure probably occurred in the following manner : 

Fountain failure was set up opposite to some unusually defective portion of 
the sheet piling, and this gradually removed the sand under the foundations 


702 


CONTROL OF WATER 


from between the lines of sheet piling. A void space was finally formed under 
the work. Then piping began. Once sand removal started, the masses of 
stone which were thrown in downstream of the work in order to fill up the 
scour holes produced by each flood were of but little assistance, as the sand 
was swept through the interstices between the stones, so that the work was 
practically in the same condition as if tail erosion had occurred. If my theory 
is correct, the second line of sheet piling upstream was positively detrimental. 
The fact that the regulator failed when it retained only 3 metres (say 10 feet) of 
water, and had previously on frequent occasions retained 4 metres (say 13 feet) 
without showing any signs of failure, is of course not surprising ; for once a 
passage extended partly across the breadth of the foundations, a smaller 
pressure would suffice to complete the failure. 

The circumstances cannot be considered as typical of regulators in general, 
as tail erosion is known to have occurred to such a degree that systematic 
soundings were taken after each flood with a view to ascertaining its extent. 

The work would probably have been saved had it been possible either to 



Note .—The upstream and downstream levels vary, but it is believed that the difference 
never exceeded I3’i2 feet (4 m.), and was usually less than 10 feet. 

prevent this erosion, or to construct a satisfactory and sand-tight cut-off wall to 
supplement the defective sheet piling. The clearest lesson to be drawn from 
the failure is that engineers should distrust wooden sheet piling. So far as I 
was able to observe, the piles were originally driven very closely together, but 
were not jointed in any way ; aud it will be obvious that while a line of wells 
10 feet in thickness may be said to be practically sand-tight, even when the 
spaces between the wells are 6 inches or 1 foot in width, the effect of a 1 inch 
gap in a line of sheet piling which is 6 inches thick at the most, is far more 
detrimental. It will also be plain that if my theories concerning tail erosion 
are accepted the drop from the regulator floor to the canal bed is a mistake. 

Scouring action of Escapes.—The broad principles of the action of an 
escape are best illustrated by an example. Let us consider a channel which 
in steady flow carries 6 feet depth of water. Let us suppose that the head 
regulator is opened so as to produce a depth of 8 feet; but that the escape 
being opened the depth at the escape still remains 6 feet, part of the water 
being passed out by the escape, and part going on down the canal. The 
















































ESCAPES 


7°3 

flow is obviously variable, and the depths and velocities at any point between 
the head and the escapes can be calculated by the rules given on page 485. For 
the general treatment of the subject it will suffice to note that the velocity at 

the head is at least 1*15 ( ^ mes during normal flow, and just above 

the escape the velocity is 1*54 times the normal value. Kennedy’s rules show 
that the quantity of silt carried forward per foot width of the channel is very 
approximately proportional to v 2 ' 5C ‘. Now, ri5 2 - 56 = 1-44 approximately, and 
r 54 2 ' 0 '' = 3*oo approximately. Thus, if the normal velocity is that which is 
just sufficient to carry forward the silt which exists in the water as it enters the 
canal, the water near the head is capable of carrying forward 1*44 times this 
quantity of silt or allowing for the extra quantity of water entering about 
°75 x 1 '44= 1'08 times the percentage of silt existing in the water. The water 
near the escape, if fully charged, will carry three times as much silt. The extra 
quantity of silt thus picked up being relatively coarse in size, is carried forward 
as bed silt, and is probably nearly all carried through the escape if this be 
designed with its sill a foot or so below the canal bed. Thus, during the 
scouring period, about three times as much silt is scoured out and removed as 
enters the canal in an equal period of normal flow ; and this is probably at 
least twenty times as much as is deposited in the head reach during this period 
of normal flow. 

In an actual example, the change in surface slope produced by the difference 
between the 8 foot depth at the canal head, and the 6 foot depth at the escape 
would naturally be taken into account when calculating the velocity ; and the 
scouring action would therefore be more marked than is indicated by the above 
figures. So also, the alteration in depth produced by silt deposits should be 
allowed for ; since it is probable that a gauge reading of 8 feet at the head of a 
silted canal will only correspond to 6 or 7 feet depth of water, the difference 
being the thickness of the silt deposit. As already indicated, more accurate 
solutions could be obtained if the fact that the flow is variable were allowed for. 
The calculations would then be best made by assuming the quantity of water 
which enters the canal, and the depth at the escape, and calculating the depth 
at the intermediate points. Theoretically, at any rate, it is then possible to 
predict the quantity of silt which is removed from each 1000 feet length of the 
canal between the head and the escape. Such refinements appear unnecessary, 
unless the silt content of the entering water has been previously determined 
with greater accuracy than is at present customary. A skilled engineer when 
considering a canal which has been under observation for some years can 
probably select values which will agree fairly well with the results of observation, 
but such data are not likely to be available when it is desired to design an 
escape for a new canal. Thus, the more accurate solution appears to be un¬ 
necessarily complex. It may be observed that the value of C, in the equation 
v = CV^ is somewhat influenced by silt deposits. As a general rule, C, has a 
higher value in a reach in which fine silt is uniformly and regularly deposited 
than is the case for a similar reach in which silting has not occurred. I have 
personally observed values of C, which are 20 per cent, greater than those which 
were observed on apparently similar channels in which silt had not deposited ; 
and reliable observers have found an excess of 30 or even 35 per cent. The 
silt deposited in the head reach of a canal, however, is coarser than that in the 
reaches above referred to. Accurate experiments are difficult, because of the 


704 


CONTROL OF WATER 


irregular manner in which the silt is dropped. It is generally believed that 
after heavy silting C, decreases to about 90 per cent, of its normal value. The 
capacity of an escape is best fixed by calculations which proceed upon the above 
lines. Thus, let us assume that the normal discharge of the canal is 2000 cusecs, 
and that about one-seventh of the silt taken into the canal is deposited in the 
head reach. The above calculation shows that an escape with a capacity of 
1100 cusecs should suffice to keep the canal clear, if an extra 1100 cusecs of 
moderately clear water can be run to waste during 24 hours at intervals of about 
20 days. The assumption is favourable ; and, as a general rule, escapes are 
not so powerful relatively to the canal discharge. The usual rule is that an 
escape can pass off a quantity of water which is not greatly in excess of one-third 
of the normal flow of the canal. This is probably a small capacity, as trial 





l_1_1--—1- j _l_1 

O I 2. 3 A. 3 6 M'i '~ r * 

Sketch No. 198.— Plan of Sirhind Canal. 

r • . >'* , J. . ' 1 j .: - • , ) ■ y 4 . ».• 

calculations show that scouring is better effected by taking in large quantities 
of water for a short time, rather than an equal total quantity distributed over a 
longer period. 

Also the capacity of the escape and of the escape channel needs to be con¬ 
sidered, as the head reach of the canal is usually in deep digging. 

The design of an escape proceeds on the same lines as that of a regulator, 
with the following exceptions : 

(a) The gates should open at the bottom. Raised sills are of course useless. 

(b) The velocity through the escape should be as high as possible, 15 to 20 
feet per second being probably the maximum. 

For this reason, pitching of the bed and sides of the canal at and near to 
the escape is necessary. The size and length of this pitching is best determined 











ESCAPES 


7°5 

by experience, although the velocity calculations made when the capacity is 
determined form a valuable guide. 

In all calculations concerning the capacity of scouring escapes it must be 
carefully borne in mind that the permanent discharge capacity is usually fixed 
not by the size of the masonry work (i.e. the escape itself), but by the size and 
silt-carrying capacity of the escape channel. This is admirably illustrated by 
the Chamkourand Daher escapes on the Sirhind canal (see p. 704). The calcul¬ 
ated discharge capacity of the original escape was about 2000 to 3000 cusecs. 
This was found to be insufficient (in reality due to an erroneous system of 
working), and was increased to a calculated capacity of about 5000 to 6000 
cusecs. It will be evident that as the capacity depends on the level of the water 
in the canal, accurate calculations are impossible when a badly silted canal is 
considered ; but it is known that the sluices could discharge all the water that 
the canal could carry when badly silted. As soon, however, as the scouring 
action of the enlarged escape became really efficient, the escape channel was 
obstructed by deposits, and about two years after the enlargement it was found 
that if more than 2000 cusecs was passed through the escapes valuable low- 



Sketch No. 199.—Escape. 


lying land was flooded. The escape channel has since been carefully attended 
to, and owing to the improved working of the canal is now able to perform its 
duties efficiently, and can probably carry 4000 cusecs if required. 

Similar figures could be given for other escapes, and as a general principle 
it may be stated that nearly all scouring escapes which work efficiently are 
sooner or later found to be capable of flooding the banks of their tail channels 
if opened so as to pass their maximum discharge. Thus, the best location for 
an escape is that which has the shortest possible escape channel. 

Auxiliary Escapes. —In countries where rain falls during the irrigation 
season, skilled irrigators frequently refuse to take water when rain threatens ; 
and the occurrence of a rainstorm produces a sudden and general cessation of 

demand for water. 

In large canals water frequently takes 2 or 3 days to travel from the head 
to the tail of the canal. Thus, even with the best system of regulation, auxiliary 
escapes must be provided in order to carry off the excess of water which is thus 
permitted to enter the canal. 

No rules can be given for such escapes, as they entirely depend upon the 
existence of depressions, or rivers, into which the water can be turned. Undue 
haste in constructing such escapes during the early years of the canal’s exist- 

45 











































CONTROL OF WATER 


706 

ence may be deprecated. The behaviour of the agriculturists is unlikely to 
render the use of such escapes indispensable until their skill in irrigation has 
increased. Also, the existence of unnecessary escapes is conducive to careless 
methods of regulation. Thus, auxiliary escapes should be provided for under 
the head of “possible and additional works to be constructed, if and when found 
necessary.” 

Escape Reservoirs .—It is sometimes advisable to construct small reservoirs 
at favourable sites, into which surplus water may be diverted. The water is 
then not lost, as is the case when it is turned into an escape channel. In silt¬ 
bearing canals, these reservoirs rapidly silt up ; and sometimes the value of 
the land which is thus reclaimed renders this method of disposing of surplus 
water financially profitable. 

Canal Drainage Works. —I do not propose to enter into the rules which 



are adopted for proportioning the thickness of the masonry of the walls, piers, 
or arches of canal drainage works. The rules generally followed are those 
employed in other branches of engineering ; but, as a matter of fact, an exact 
theoretical investigation usually leads to far slighter dimensions than those 
which are employed in practice. 

Experience is the real basis of the proportions generally adopted ; and in 
all probability the factor which determines the thicknesses adopted is not 
strength, but rather the prevention of leakage. 

My object is to illustrate the correct outlines of the large scale plan of the 
works now considered, as this determines the general hydraulic efficiency. 

(a) Aqueducts.—Aqueducts are required either for carrying a canal over a 
river, or for carrying a river over a canal. As a rule, there is rarely any 
alternative, as the relative levels of the two bodies of water determine the 































































AQUEDUCTS 


707 


design. Where choice exists, it is usually best to carry the smaller body of 
water under the larger one, the maximum flood discharge of the river, of 
course fixing its size. When the canal is carried by an aqueduct, a certain 
economy can generally be effected by increasing the velocity of the water. 
The matter needs careful calculation. Where silt exists, it is not advisable to 
make the depth of water in the aqueduct much greater than in the canal, unless 
the aqueduct is arranged as a silt trap, and is provided with orifices for dis¬ 
charging silt. In any case, the whole length of the earth channels leading up 
to and away from the constricted section should be carefully pitched with 
brickwork, or other resistant facing. The alteration in cross-section should 
proceed gradually. In silt-bearing canals length of tapered section = 25 x 
difference in bed width, and in clear water = 5 x difference usually produce good 



results (see Sketch No. 206). It will usually be found advantageous to pitch 
the upstream portion of the receding channel with roughened pitching of the 
form shown in Sketch No. 214 ; but the tail portion of the pitching should be 
smooth, so that the water reaches the unlined earth section devoid of all 
turbulent, scour producing eddies. 

The foundations of an aqueduct may either be deep, and formed of wells, or 
of piling under each separate pier, as is indicated in Sketch No. 200 of the 
Kali Nadi (Ganges Canal) pier foundation ; or the whole stream bed may be 
pitched, and the piers supported on relatively shallow foundations (Sketch No. 
201, compare also No. 206). The deep type is usually adopted in fine sand, 
and the shallow type in coarse sand or clay. There seems to be no real reason 
for this selection, and considerations of cost may be relied upon to settle 
the question. 


















































7 o8 CONTROL OF WATER 

As a rule, the mean velocity of canal water in an aqueduct does not exceed 
14 feet per second, and 8 or 10 feet per second is more usual. The leal 
difficulties are caused not by damage to, or waves in the aqueduct, but by 
reducing the velocity of the water after it leaves the aqueduct to the 3 or 4 foot 
per second, which is permissible in earthen channels. The value of the velocity 
finally adopted will consequently to a certain degree depend upon the length of 
the masonry channel. The longer this is, the greater will be the saving pro¬ 
duced by an increase in the mean velocity, and therefore, the greater the 
expenditure on roughened pitching and water cushions downstream of the 
aqueduct that is economically justified. There appears to be no valid reason 
why 20 feet per second should not be adopted in a long aqueduct if the required 
fall is available. 

The calculations concerning the drop required to increase the velocity from 
the 3, or 4 feet per second which occurs in the upstream earth channel, to the 
value of 8, 14, or 20 feet per second adopted in the aqueduct, are referred to 
on page 16. 

( b ) Syphons.—The question of silt has a large influence upon the design of 
syphons. Sketch No. 202 shows the type which is usually adopted where a 



canal is syphoned under a river, or a clear water stream under a canal. The 
downstream vertical well produces a quasi-fountain exit of the water, which 
dissipates the energy of the increased velocity in the syphon, and but little tail 
pitching is required. The deposition of silt is unlikely, as the canal flows 
steadily for say 300 days in the year. 

The mean velocity in the syphon should be fairly large, in order to prevent 
any silt deposits. The usual rule is about 8 feet per second for maximum 
supply, or 10 feet per second in extraordinary supplies. No difficulties from 
tail erosion or scour have occurred in cases where the velocity was 16 feet per 
second, even though the earthen channels eroded badly at 6 feet per second. 
It is therefore believed that when the vertical well is adopted, and the fall is 
available, a velocity in the syphon of 12 feet per second for maximum supplies 
may be adopted in tender soil. This velocity may be increased to 16 or 20 feet 
per second in firm soil. Provision should be made for downstream pitching 
“ if required.” 

Where the canal is a flood canal, carrying large quantities of silt, and only 
flows intermittently, the type shown in Sketch No. 203 should be employed, 
and should always be used for syphons which carry silt-bearing rivers. The 





























S YPHONS 


709 


flat upstream and downstream slopes are no doubt more expensive than^the 
vertical drop walls, but the form thus obtained prevents any risk of silt 
depositing. Such syphons are employed in India for carrying off the water 
discharged by rivers which run but once or twice every five years, and are then 
extremely heavily charged with silt. As silt deposits never give trouble, the 
type may be adopted with confidence whenever choking of the syphon by silt is 
to be apprehended. Downstream erosion, however, is likely to occur, as the 
energy of the issuing water is but slightly dissipated. The drop wall shown in 
Sketch No. 203 is usually sufficient in the case of flood channels ; but in a 
canal or river which flows constantly, pitching with brickwork, or concrete 
blocks, may be necessary. 

The drawing shows a syphon constructed of brickwork|’orfmasonry,Jwhich 



Pee her Sy . bhons. Usual Shallow Sy phon. 
--- T ype Sections - - 


Sketch No. 203. —Chenab Syphon. 

cannot resist any great tension. Thus, if it is possible for the syphon to be 
under pressure when the upper channel is dry, it is necessary to place a 
sufficient load of brickwork and earth on top of the syphon arches to equilibrate 
the upward water pressure Thus, the crown of the arches should be at least 
one half of the head of water in the syphon, below the canal or river bed, 

/.<?., d— — (Sketch No. 202). The canal or river bed should also be pitched so 

as to prevent any possibility of the earth load being removed by scoui. In 
modern construction syphons are frequently made of reinforced concrete 
(Sketch No. 204), steel pipes (Sketch No. 205), or other material capable of 
resisting tension. The saving in excavation and masonry then produced by 
the fact that d, need only be as large as considerations of strength render 




































































7 io CONTROL OF WATER 

necessary, is material ; and it is doubtful whether the old masonry design 
should now be adopted. The general form, however, should not be 
altered. 

Sketch No. 205 shows a very neat design employed by the Kashmir State 
in crossing the Tawi river. A steel pipe 5 feet 6 inches in diameter carries 


Sketch No. 204.—Reinforced Concrete Syphon. 

no cusecs for the irrigation of the higher lands on the farther bank of the 
river. The larger discharge of 480 cusecs which irrigates the lower lands is 
carried across in the 10 feet by 7 feet 7 inches masonry arched opening, the 
bed level of the canal being dropped by a fall just above the river crossing, in 
order to prevent internal pressure being brought to bear on the arch. Were 
steel plating relatively cheaper, there is little doubt but that the whole work 
would be constructed of steel piping. The ample dimensions of the masonry 


Circumf- ReinP ^"centres. Orcumf-Reint % B "6 "centres. 


internal. 


External. 



























BRIDGES 


7 11 

are necessary owing to the character of the river, which is extremely torrential, 
with floods amounting to 150,000 cusecs. 

Level Crossings. —The levels of a river and canal are sometimes almost 
identical. In such cases (especially if the river and canal are approximately 
equal in size), a level crossing is adopted. This consists of two regulators, one 
acioss the river downstream of the crossing, and one across the canal down- 
stieam of the river. The Bengal type of regulator (Sketch No. 190) is usually 
employed. The river is usually dry, and ample warning of the approach of 
floods is possible. In cases where the river flows for long periods, and where 
it is necessary to take its water into the canal, the river regulator may be 
provided with falling shutters, and can be worked in conjunction with the canal 
regulator, just as the weir and regulator at the headworks of a canal are 
handled. The extra cost entailed in the construction of the regulator so as to 
enable it to retain 13 or 14 feet of water, in place of 6 or 7 feet, must be 
carefully balanced against the value of the water thus rendered available. 



Bridges over Canals. —The construction of bridge work, or masonry 
arches, does not come within the scope of this book. In canals (and especially 
where the soil is tender and silt is carried in the water) the proportions of the 
bridges require consideration. 

The rule :—Clear waterway is equal to the bed width of the canal plus the 
full supply depth, has been found advantageous in such cases ; and any marked 
obstruction of the waterway tends to induce scour, and a consequent deposition 
of silt lower down the canal. The circumstances thus produced are liable to 
become permanent in character. Thus, pitching of the character indicated in 
Sketch No. 206 is employed. The sketch refers to a case where the velocity 
is about 5 feet per second. At smaller velocities, a shallower toe wall and a 
smaller breadth of pitching (say 5 feet in width) are advisable in all cases where 
silt and scour are determining factors. 

Regulators for Bratich Ca?ials >.—The design of these works follows the same 
rules as for head regulators. The head of water sustained does not usually 
exceed the full supply depth in the main canal. 

As a rule, it is desirable to disturb the proportions of silt and water existing 
in the main canal as little as possible. Hence the regulator should have ample 
waterway, and the rules given under Bridges may be adopted with advantage. 



































712 CONTROL OF WATER 

Raised sills and arrangements for drawing off surface water are not usually 
required. 

In many cases the openings are closed not by sluice gates, but by means of 
wooden beams. The economy is obvious, and when the beams consist of 



Section 


© 

Ceninino nail 


90' Return Units 
FullSumN.L. 


£ 


Ferried! Face 


- 4 - 

§3 

1.1 


return Ms ^ ^ 


!-- 

1 



Sketch No. 206.—Bridge Pitching. 


needles (i.e. are placed vertically as in Sketch No. 162) the arrangement appears 
to be unobjectionable. Where, however, the beams consist of horizontal bars, as 
shown in Sketches Nos. 207 and 196, the effect will obviously be to diminish the 



proportion of bed silt drawn into the branch canal whenever any beams are in 
place, and the branch is not taking its full supply. This is hardly fair (qua 
silting troubles) to the portion of the main canal below the bifurcation where 
the regulator is situated. Horizontal stop planks are therefore inadvisable, 

















































































FALLS AND RAPLDS 


7 r 3 

unless the slope of the branch canal is far flatter than that of the main canal. 
If this is the case, it may be possible to partially sort out the silt, and to turn the 
major portion into whichever branch is found to be most capable of carrying 
it forward to the fields. In some cases, regulators are built across a canal for 
the purpose of raising the water level locally from time to time, in order to be 
able to supply water to a patch of high land. The advantages thus gained are 
very dearly purchased if the canal carries any silt, as the reach above the 
regulator is alternately a silt trap and a scouring reach. Such works may be 
regarded as radically bad in principle, and should never be constructed where 
any other solution of the difficulty can be found. 

Falls and Rapids. —In the design of an earthen channel it will often be 
found impossible to allow the slope of the channel to be equal to the general 
slope of the ground surface. In the first place, as was discovered during the 
construction of the Ganges Canal, if a large earthen channel be graded at a 
uniform slope equal to the difference of the desired water levels at its head and 
tail, divided by its total length, the velocity is frequently so great that severe 


PiUttini splays at I bus 2 
If- Bed Nidituh'Qmb 


Boulder Sides 
n' 


Spays ell in it (ran 
S nut Bed nid/p 



Section A. 5. 


Bed Nidlh-tinMiedNidb 


P' Stone Grouted 


OS' Grate! 


MS Cdkuldkd 

t ds retaining nails 
V 


1 I S' Stone on Edge 
to' do- on Flat 
0 !> Gravel 


Typical Small Rapid 

/ 'iC* F\t-ar 


Pitching tor 75'on Bed 
do. do- too'on Slopes 


Tf 



alternative Section 


or, IS'Boulders in Lime 
t-S'Hdsonry 
o s' Spalls 

„ .• MU' 6'nails on Vconcrelc flc toc 

alternative Yiatls aboutaouoc. 


Sketch No. 208.—Rapid. 


scouring action, or even total destruction of the banks of the channel, is 
produced. Secondly, isolated patches of relatively higher land nearly always 
exist, which would not be commanded by a channel graded in this manner. In 
the final design of the channel a certain amount of adjustment can generally be 
secured by grading the channel so that the velocity is approximately constant. 
Thus, in place of a channel at a uniform slope, one which is graded in a series 
of short reaches will be obtained, the slope of each reach being approximately 
inversely proportionate to the hydraulic mean radius of the channel, and 
therefore increasing as the size and discharge of the channel decreases. 

It will, however, frequently be found that even this adjustment, or the 
somewhat more complicated method introduced by Kennedy (see p. 753), does 
not produce a channel which commands the country satisfactorily, and is not 
likely to give trouble by scouring its bed. 

The obvious method of improving the conditions is to grade the reaches at 
a smaller slope, and to obtain the total drop required by means of falls, or 
rapids, inserted at favourable points. 

Since a fall or rapid, when judiciously inserted, will often permit long reaches 














































CONTROL OF WATER 


7 i 4 

of channel in embankment to be replaced by a channel at or near to the 
balancing depth, the cost of the required masonry is frequently recouped by a 
saving in earthwork. 

Nevertheless, falls or rapids should be avoided if possible, especially in 
large canals. 

A consideration of the'conditions existing in earthen channels has led me 
to believe that a proposal for a canal which entails many falls or rapids in its 
earlier reaches should be carefully examined, and is probably fundamentally 
incorrect. The most probable error is that the site of the headworks of the 
canal has been selected too high up the river from which it takes out. 

It may, however, be the case that headworks lower down the river are not 
advisable, either because no favourable site for a headworks exists, or (what is 
more likely to prove the case) because any line starting from the lower site 
crosses too many minor drainage channels. 

When a canal, or better still, its minor branches, are approaching their 
ends, the slope of the ground often changes suddenly, especially when nearing 
a river or a drainage. In such cases, a series of falls may be necessary in 
order to drop the water down to the general level of the area close to the 
river. 

Assuming, however, that a fall is justified, the design then becomes a matter 
for consideration. As a general rule, it will be found that the height of the fall 
is but small, 8 or 10 feet being a large value. In the case of small falls it is 
rarely found economical to utilise the water power ; although the turbine 
pumping station on the Huntly Canal (see Engineering Nezt>s, Sept. 3, 1908) may 
be regarded as a pioneer installation, which is well worthy of imitation. Where 
two or more falls exist fairly close together, their union into one fall, with say 
20 to 25 feet available head, may provide a favourable site for power develop¬ 
ment ; although in such cases, a long reach of a canal in bank is liable to 
produce trouble owing to the possibility of excessive percolation causing damage 
to the adjacent lands. 

The actual works necessitated by a sudden drop in a canal may be divided 
into two classes— i.e. falls and rapids. These are very different in their 
properties. 

Speaking generally, a fall should be adopted if any irrigation is effected from 
the reach above its site, as it will hereafter be shown that a fall can be designed 
so as to permit accurate regulation of the water level in the canal. This the 
usual type of rapid does not permit, and rapids are therefore hardly advisable 
except where regulation is not a matter of importance. It is fortunate that this 
discrepancy in the functions of falls and rapids is paralleled by the difference 
existing in the materials requisite for their respective construction. 

As will be seen from Sketch No. 208, a rapid contains an unusual propor¬ 
tion of large stone ; while, in the case of a fall (No. 209 or 210), stone forms only 
a small portion of the material required. Now, as a rule, irrigation hardly 
begins until the canal has left the upper portion of the river valley, where stone 
is most easily obtained. Consequently, it can be stated in general terms that 
rapids are probably advisable on the upper reaches of the canal, from which 
no irrigation is effected. Falls, on the other hand, are required when the main 
canal has begun to split up into branches, and irrigation has commenced. 

It will be found in practice that even soft bricks do not suffer serious 
erosion by water carrying sand, unless the velocity of the water exceeds 20 feet 


NEEDLE FALLS 715 

pei second, or the “silt” contains a large proportion of stones which are 
gieatei than a pea in size. Thus, when the height of the drop in the water 
suiface is restricted to values as small as 8 or 10 feet, actual damage to the 
masonry portion of the work need not be greatly feared. The principal 
difficulty is to prevent the irregular motion of the water as it leaves the rapid 
01 fall from causing erosion of the earth banks of the canal below the fall. This 
side of the question was not at first understood, and the old ogee fall (see Sketch 
No. 158) was designed on the assumption that damage to the masonry works 
was likely to occur. Intense erosion of the banks took place ; which, in some 
cases, became so acute that the masonry was undermined, and the fall was 
damaged. T he design must be regarded as very badly adapted to small drops 
in the water surface. It is still used for drops of 30 or 40 feet or more, such 
as occur in dams of the overflow type. Here it is successful, because the flow 



Typical Punjab Notch Fan mtti Needles in place of Notches 



is not continuous, and the banks of the downstream channel are usually of 
rock ; or, at the worst, of hard gravelly earth. 

For soils such as those in which the majority of irrigation channels are 
constructed, the fall should be designed so as to destroy the energy of the 
falling water as far as possible before it quits the masonry. This is best 
effected by utilising the internal friction of the water. The principle is as 
follows : 

{a) The falling sheet of water is divided into a number of smaller stream 
which interfere with each other. 

ib) A pool, or a water cushion, is formed below the fall, in which the falling 
water eddies and dissipates its energy. 

Where no floating matter occurs in the water a very excellent solution is 
a fall obstructed by needles, as shown in Sketch No. 209. Here, the falling 
waters are split up into thin streams, and their mutual interference thoroughly 


























































7I 6 • CONTROL OF WATER 

destroys the energy generated by the fall. A similar expedient may be applied 
to a rapid with equal success. Where, however, any floating matter occurs, 
obstructions collect on the needles ; and these, if not removed, may block 
the fall, and so cause a breach of the canal. The size of the apertures between 
the needles is such that weeds are quite as effective as branches of trees, or 
large masses of drift. 

As a rule, therefore, such obstructed falls are not advisable ; and Sketch 
No. 210 shows a fall, and Sketch No. 208 a rapid, so constructed that any 
normal drift will readily pass over the crest. 

The details deserve careful consideration. Firstly, taking the fall, let us 
assume that the earth below the fall is very easily eroded (eg. as in the 
conditions existing in the Punjab, or on the Nile, although falls rarely occur 
in Egypt, and even then are only small). In the first place, it is found that 
the falling water should be divided into separate streams, each of which does 
not greatly exceed 200 cusecs even in very large canals. In canals carrying 



Details of Notches 


Rxlii marked R.‘ -S' 
do Jo. 4R.*e' 



□ I! 

lj JV-J / beam 
elevation Han 

Sketch No. 210.—Notch Fall with Road Bridge. 


less than 400 cusecs, there should be at least two, preferably four, notches ; 
and one notch is rarely advisable unless the discharge of the canal is less than 
50, or 60 cusecs. A very good rule is that the top width of the notch (see p. 724) 
should not exceed three-quarters of the depth of the channel. 

In the second place, the breadth of the water cushion should be only slightly 
less than the bed width of the downstream channel. A large volume of water 
is thus secured in which the falling water can expend its energy. The depth 
below the lower bed level §, and length / of this water cushion are usually fixed 
by the formulae : 


_h + d 




where h is the height of the fall and d the fall supply depth of the canal. 

Dyas found experimentally that a bottle was not smashed when passing 

over the fall when & „ a s greater thanVrf VF; 

and, in consequence, he adopted this value with : 

l— 2 V hd 





















































NOTCH FALLS 


7*7 


I do not know the reason why these formulae were abandoned, as the value 
of § agrees very fairly well with the depth of the holes which are frequently 
found below natural waterfalls, but the cisterns of the newer falls proportioned 
by the first rule are floored with ashlar in places where the action of the falling 
water is most intense. An inspection of the dry cisterns of falls which are so 
proportioned causes me to believe that, for materials such as are found in the 
Punjab (which are not good), the rule is close to the minimum safe depth 
(it is usually less than the depth as given by Dyas’ rule), and should not be 
decreased. With better materials, and better soil (as will be seen later), the 
cushion may be diminished in depth, or may even be entirely dispensed with. 
The slope up at i in 2 of the downstream wall of the cushion is important. A 
vertical wall not only sets up waves in the canal and thus favours erosion, but 
prevents the escape of any small stones that may be swept into the cistern. If 
allowed to remain in the cistern, the stones will rapidly produce pot holes, and 
even a piece of broken brick may cause damage under such circumstances. 
For similar reasons, a raised crest wall downstream of the cistern cannot be 
permitted, although it would save excavation and masonry by increasing the 
effective depth of the water cushion. The irregularity in velocity created by 
the raised wall makes itself manifest in the form of intense erosion at a distance 
downstream of the wall equal to one half the bed width of the channel. The 
other details are less important. 

In more resistant soils these proportions may be somewhat reduced. I had, 
however, an opportunity of repairing five falls in the usual Punjab soil, each of 
which carried about 500 cusecs, and in which the following divergences from 
the above design occurred : 

(i) The water fell in one mass into a cistern with a width equal to three- 
quarters of the bed width of the canal. 

(ii) The water fell in two masses into a cistern with a width equal to one-half 
the bed width. 

(iii) The proportions of the cistern agreed with the typical design, but the 
downstream slope was replaced by a vertical wall. 

(iv) As in case No. (iii), but here the wall was raised 1 foot above the bed 
level. 

(v) A fall resembling Sketch No. 210 in all respects, except that the sill of 
the fall had a raised crest (see p. 722) and that the cistern width was three- 
fourths the bed width. 

In the first two cases the downstream erosion had undermined, and produced 
cracks in, the masonry of the fall within less than three years. 

In case No. (iii), the bed pitching immediately downstream of the cistern 
was destroyed, and blocks of stone 2 cubic feet in size (which had been thrown 
in with a view to stopping erosion) showed signs of having been violently 
moved. 

In case (iv), this action was even more violent, two stone blocks being 
broken. Pot holes 1 foot and 18 inches deep occurred in each cistern. 

In case (v) the downstream damage was small ; in fact, not more than 
that which occurred in a similar properly designed fall. On the other hand, 
upstream erosion was very marked ; and the silt thus produced was deposited 
some 5000 feet below the fall, and gave great trouble by blocking the head 
reach of a branch canal. 

I consequently believe that any divergence from these proportions should 


CONTROL OF WATER 


718 

be avoided. When the proportions are adhered to, it will be found that a 
pitching of brick on edge, and brick on the flat suffices to prevent any notice¬ 
able erosion. 

Where the soil is somewhat firmer, Bligh’s rules (see Design of Irrigation 
Works), may be followed. Bligh makes the width of the fall seven-eighths that 



of the bed width of the downstream channel, and gives no water cushion, the 
thickness of the masonry bottom of the fall being represented by fh-rd, and 
its length by 2 (h + d). 

Bligh criticises the Punjab design somewhat severely. The theoretical 
objections which he advances have but little weight. His designs are no 



doubt cheaper than those which are adopted in the Punjab, but they are suit¬ 
able for firmer soil and better material (see Sketch No. 211). 

In really firm soil, falls are but rarely required, since the bed slope can be 
made sufficiently steep to dispense with falls without fear of erosion arising 
from the velocity thus produced. 

In no case have I found good results obtained when the width of the fall is 
considerably less than Bligh’s rule of seven-eighths of the bed width. Any 


































































































RAPIDS 


719 

saving that could be secured by adopting a smaller width would be but small; 
and the risk of downstream erosion is very great, even in the firmest soils. 

The standard design (see Sketch No. 208) of a rapid calls for but little 
remark. The slope 1 : 10 has been arrived at by experience, and (in the soils 
of the Punjab at any rate) a steeper slope is accompanied by excessive erosion 
downstream. The slope is pitched with boulders, or with blocks of lime 
concrete. The drawings usually show the boulder pitching left rough, and 
this roughness appears to be considered advantageous. Actual inspection of a 
well maintained rapid in which erosion has been satisfactorily prevented will 
invariably show that all marked irregularities have been removed, and that 
great care has been taken to smooth the slope by filling all joints and hollow 
places with mortar. 

The actual facts appear to be that the water flowing down the rapid is in a 
state of pulsation, and any stones which project into the stream are sooner or 
later set shaking. This shaking displaces the sand under the stone, and the 
stone sinks slightly ; and when repairs are made the stone is smoothed up and 
brought into line and level by a coating of mortar. If the action is more 
intense, the stone may finally be displaced. Thus, after a few years, the slope 



pitching becomes so smooth that it is frequently difficult to walk on it even 
when dry. This does not seem to render the rapid less efficient, as the 
standing wave that forms at its lower end is quite sufficient to dissipate the 
energy of the falling water. Some of the most satisfactory rapids are found to 
possess a pitching which is more than usually smooth. Thus, any reliance on 
the roughness of the pitching appears unnecessary. Such designs as rapids 
with broken slopes (see Sketch No. 213), or water-cushions, have been 
frequently and exhaustively tested in practice, and all such devices have now 
been abandoned. 

It will be noticed that the typical rapid, like the typical fall, has a width 
equal to the bed width of the downstream channel. A wide rapid is less 
liable to produce downstream erosion than a narrow one, but the condition : 

Width = bed width of channel, 

is by no means so important as in a fall. Erosion below rapids is less regular, 
and is apparently less dependent upon the design than is the case with falls. 

The rules : 

In tender soil, width of rapid = seven-eighths bed width, and 
In firmer soil, width of rapid = three-fourtl\s bed width, 




























720 


CONTROL OF WATER 


may be adopted, and produce rapids which are slightly narrower than falls in 
similar soil. When these rules are adopted an additional amount of down¬ 
stream pitching must be provided, but it is believed that economy in the total 
cost of the work will be secured provided that the rapids are carefully 
maintained. 

Rapids are frequently required when it is necessary to increase the velocity 
of the water in a channel suddenly. Examples occur when an earthen channel 
is followed by a masonry aqueduct, or wooden flume. The general practice in 
the Punjab is to design the aqueduct with a full supply depth equal to that in 
the approach channel, and to provide the increase in velocity necessitated by 
the reduction in breadth that occurs in the aqueduct by means of a rapid. 



Sketch No. 214.—Roughened Pitching. 


The uncertainties affecting the calculations are referred to on page 16, but 
the design of the rapid follows the ordinary rules. 

Prevention of Erosion below Falls and Rapids.— If a fall or rapid 
is left to itself, a pool forms just below the work, and the final plan of the 
channel somewhat resembles the section of a soda water bottle, the fall or 
rapid forming the neck. This form was considered to be correct in former 
days, and the banks of the pool weie frequently pitched, or were even provided 
with retaining walls. The method is still adopted where the water (*.*-. as in a 
canal escape, or in the outlet escape of one of the basins that are used in flood 
irrigation) is discharged into a river or natural water-course. Where, however, 
the water after quitting the fall flows in a canal which has to be maintained 
and regulated, this method is inadvisable, as it is found that a succession of 
pools and constricted necks are formed all the way down the canal. In some 


EROSION 


721 

cases, a series of seven or eight such pools extending for a mile or so below 
the fall has been formed. 

Consequently, the modern practice in canals (and lately even in escapes) is 
to pitch the banks of the canal so as to preserve a section which is just 
sufficient for the normal flow. The pitching is rough, and Sketch No. 214 shows 
a very ingenious chequer work of projecting bricks, which has been found 
extremely effective. 

Bed scour is prevented by cross walls where required. The above sketches 
show the length of pitching. These should be considered as minima lengths. 
No fixed rules can be given ; as, in practice, pitching and cross walls are added 
when considered advisable by the engineer in charge. On an average, it may 
be assumed that about twice the length of pitching shown will eventually be 
required ; some works needing little or no additional pitching, whilst cases exist 
where 300 or 400 feet of brick pitching is ultimately found to be necessary. A 
great deal depends upon the care which is devoted to the maintenance of the 
channel and pitching, and measures should be taken to encourage the deposit 
of silt below the downstream end of the bank pitching by means of fences of 
brushwood, and stakes. 

If a pool of the soda water bottle type has formed below a fall, the fault is 
best remedied by running out banks of rubble stone, so as to define a channel 
of the required size. These banks should not be carried up to the water level, 
as it is desired to encourage the deposition of silt in the pools behind them. 
Thus, banks with a crest 1 foot below the water level will at first suffice, and 
they can be raised as the deposit of silt accumulates behind them (Sketch No. 
161). The principles are now plain. In place of permitting erosion to take its 
natural course, the size of the channel required to carry the supply that flows 
over the fall or rapid, should be calculated, and this channel should be defined 
and shaped by training walls consisting of loose rubble. If erosion has not 
occurred, the banks may be pitched ; and profiles of the bed and banks of the 
correct channel section should be constructed of masonry or stakes and brush¬ 
wood, so as to train the channel to its correct form. When these precautions 
are adopted, silt will rapidly deposit; and where the silt is of a clayey nature 
the roots of plants will bind the silt into a firm mass. 

The Notched Fall. —When a fall, or rapid, is designed according to the 
preceding rules, it will be plain that there will be a draw down of the water 
surface just above the fall. In consequence, the mean velocity just above the 
fall will be greater than the mean velocity in the portions of the canal that are 
more distant from the fall. This increase in velocity may cause local erosion, 
and should therefore be avoided if possible. The drop down and the con¬ 
sequent increase in velocity can obviously be prevented either by raising the 
crest of the fall above the bed level of the canal, or by making the width of the 
fall less than the bed width of the canal. 

The first solution is that usually adopted in the case of a rapid. The second 
solution has been found inadvisable both in falls and rapids, as the banks of the 
canal below falls or rapids which are considerably constricted are found to be 
badly eroded, and the ratio, width of fall is equal to seven-eighths of the bed 
width of channel, is found to be approximately the least that can be adopted. 
Either solution possesses the disadvantage that the depth of the water just 
above the fall is equal to the depth in the canal in uniform motion, for one 
discharge only. 

46 


722 


CONTROL OF WATER 


The equations are as follows : 

Let Q, be the number of cusecs passing over the fall, or rapid. 

Let d, be the corresponding depth in the upstream canal in uniform motion, 
and w, the mean width of the channel for depth d. 

Then, if /, be the length of the crest of the fall, or rapid, the head over the 
fall is given by the equation : 

Q = C 1 /H 1 - 6 

where, C 1 = 3‘4o to 3*50 in the case of a rapid ; and in a fall may be as small as 
2*50 if the sill is flat, and H, is equal to 1 or 2 feet. 

Thus, the crest must be raised to a height x — d— H, above the canal bed ; 

and Q, is very approximately equal to C w*/sd 1,5 , where v — C V rs, is the friction 
equation for the canal, so that: 

Consequently, the crest height will be correct for one value of d, only. The 
variations in C, and w, as d , alters, slightly modify the above equation. If an 
actual case is calculated, it will be found that scour can be entirely prevented 
by a raised crest, but that the difference between ~r+H, and ff, as Q, varies, is 
quite sufficient to cause trouble in the working of a distributary which takes 
out just above the fall. For, if we calculate x, so that x + H = d, when Q, is the 
full supply discharge of the canal, x + H will be considerably greater than d, 
when Q, is say two-thirds of the full supply discharge, and silt deposits are 
likely. If we calculate x, so that x-j-H — d, when Q, is one-half the maximum 
discharge of the canal, then, when tl\e full supply is passed down the canal, 
scour may occur ; and it will be found difficult to give the distributary its full 
supply. 

As an example, consider a channel of a bed width of 20 feet, with side slopes 
of £ : 1, and a bed slope equal to jjjj. Let us assume that the channel is of 
earth, and that it is in fair order {i.e. Bazin’s 7=1*54, or Kutter’s n = 0*0225 
approx.) ; and let us calculate d , the depth in feet of the water in the channel 
when the motion is uniform, and the discharge is equal to Q, cusecs. We also 
calculate H, the head over the sill of a weir 20 feet long, discharging Q, cusecs, 
from the equation Q = 3'5o x 20H 1 " 5 , and H l5 a similar quantity for a weir 
17 feet wide. 

We can then calculate x, and x 1} the various heights of the sill required to 
produce a depth just above the fall or rapid, equal to the depth in the canal 
during uniform motion, from the equation : 


x = d- H. 

We thus obtain : 


Discharge 

in 

Depth in 

uniform 

20-Foot Sill. 

i7-Foot Sill. 

Cusecs. 

Motion. 

H 

X 


X\ 


Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

200 

4*2 

2*01 

2*19 

2*24 

1*96 

140 

3'4 

1*59 

I *81 

r 77 

1*63 

70 

2*2 

1 *oo 

I *20 

I ■ I I 

1*09 

























BALL: RAISED SILL 


723 


Consider the case where Q = 2oo cusecs, and l— 20 feet. Assume that a 
sill 2*19 feet high is erected. Put D, for the depth that now occurs just above 
the fall, i.e. for any discharge we have : 


D = 2’i9 + H. 

We then get : 


Q, in Cusecs. 

1 

d > 

Depth in Canal in uniform 
Motion, in Feet. 

D ’ 

Depth just above the Fall, 
in Feet. 

200 

4-2 

4*20 

140 

3‘4 

378 

70 

2*2 

3' 1 9 


It is plain that the water level is headed up whenever the discharge is less 
than 200 cusecs. Silt troubles are therefore to be feared. 

Similarly, if we consider that Q = 7o cusecs, and that l=iy feet, we get the 
following table, where D = Hid-1*09. 




D, 

Depth just above the Fall, 

Q, in Cusecs. 

Depth in uniform Motion, 

in Feet. 

in Feet. 

200 

4-2 

3’33 

140 

3*4 

2-86 

70 

2*2 

2*20 


So that a drop down exists whenever Q, is greater than 70 cusecs, and 
scour is likely to occur. 

The case selected is purposely somewhat unfavourable, although it is quite a 
practical example. In actual practice, the height of the sill can usually be 
selected so that these local silt and scour troubles do not produce very alarming 
results, and a rapid with a sill about 17 feet high would suffice to secure a 
satisfactory solution in this particular case. If silt troubles are intense, it is 
obviously desirable to give the canal no occasion for offending. 

If, however, a distributary takes out just above the fall, the matter at once 
becomes serious. Whatever height is given to the raised sill, the distributary 
is always fed with water which is abnormally charged with silt. For if scour 
occurs, the distributary receives water charged with freshly eroded matter ; and 
if silt deposits occur, the distributary draws from a silt trap which is full of old 
silt. The results are astonishing. Channels 20 feet in width, and originally 
3 feet deep, have been known to silt up to a depth of 10 inches for a length of 
3000 feet in three weeks, and such cases are by no means rare. As just above 
a fall is otherwise a very favourable location for a distributary head, such 
abnormal silting should be avoided wherever possible. 

These difficulties are obviated by the notch fall (see Sketch No. 210), which 
should always be adopted in falls on canals which carry silted water where a 
distributary takes out just above the fall. 

































fi 4 CONTROL OF WATER 


The calculation of these notches is described by Reid (.Punjab Irrigation 
Branch Papers , No. 2). 

Put Q, as the quantity of water passing over the fall. Let /, be the length 
of the sill of the notch in feet, and l+nx, be the width of the notch at a height 
,r, above the sill. Let y m , be the full supply depth in the channel downstream 
of the fall, and y 0 , be the corresponding depth for the least supply. Also let 
d m , be the full supply depth in the channel above the fall, i.e. the depth corres¬ 
ponding to the maximum supply to be passed over the notch, plus the full 
supply of the distributary. 

Then, as a rule, it is found that good regulation is secured by taking : 

Q 1? the supply corresponding to the depth, 


yo+$(y m -yo)=yi 

and Q 2 , corresponding to the depth, 

j 

yv+l{ym-yo) =y 2 

and proportioning the notch so that it passes the supply Q i? when the depth in 

the canal above the notch is d 1 = —'^, and the supply, Q 2 , when the depth is 

ym 

j d m y% 

a 2 — • 

y m 

Two cases occur : 

(i) The notch has a complete fall, and is never drowned. 


We have : Qi = 5‘35^i 1,6 (^+o , 4«^ 1 ) 

Q2 = 5’35^4 1 ' 5 0M-o'4 ndo) 

It has been found in actual practice that on large canals we 
may put £=078. On small canals, where a slight excess over the 
calculated depth is advantageous, c, may be taken as 070. 

We can thus calculate /, and n. 

(ii) The notch is partially drowned. 

Here, let f, be the difference between the water levels of the two 
reaches, and put, 

e\=yi-f and e 2 =y 2 -f. 

Then, Q x = 8 'Q2c*l 

+ 5 *35^{ ( / + neP){di - e x ) l ‘ 5 + 0*4 n(d 1 - e x ) 2 - 5 } 

A similar equation holds good for Q 2 . 

Here also, as above, c , can be taken as 070, or 078 ; and the equations are 
obvious for the case where the notch has a free fall when Q x , is passing, and is 
drowned when Q 2 , is passing. 

The above equations give the dimensions of a notch which will pass the 
total full supply of the canal. In practice, the notch is usually split up into a 
number of smaller notches, each passing about 100, to 200 cusecs. A very 
usual rule is The top width of each notch should be less than o’8^ ? „. The 
selection of the discharges Q 1} and Q 2 , gives scope for a study of the local 
conditions. As a general rule, it is better to make the notch too large, rather 
than too small, for should the water surface be found to be too low in practice, 





D IS TRIE UTAR Y LOCA TION 


725 

the sill can be slightly raised ; whereas, if the water is unduly headed up, 
adjustment is more difficult. 

Location of Irrigation Channels. —An ordinary map of an area in 
which irrigation is well developed bears a great resemblance to the map of a 
natural river and its tributaries ; but if the contour lines are inserted a marked 
difference is noticed. The river and its tributaries flow in valleys, whereas 
the canal and its distributaries, or small branches, flow along ridge lines. Just 
as each valley (except the very smallest examples) possesses a stream which 
drains the side slopes of the valley, so each ridge line should be covered by a 
distributary which irrigates the side slopes of the ridge. And while in general 
the valley of the main river is the lowest valley, the main canal is usually found 
at or near the highest ridge line. 

Thus, broadly speaking, irrigation systems consist of two portions,—the 
main line and main branches which form the channels by which the water is 
led from the source of supply to the main ridge line, or ridge lines, of the area 



Sketch No. 215.—Good and Bad Location ox Distributaries (after Mackenzie). 

Note. —These sketches are ideal, but the “bad” represents fairly closely the Indian 
practice of 1860-70. The long distributary and its feeders interfere with the natural 
drainage, and therefore water-logging is likely to occur. On the other hand, these* 
feeders permit water to be very rapidly delivered to any point, and the canal staff 
does not need to be experienced. 

The “good” represents modern practice, and most of the older canals have been 
systematically remodelled to this type. Such a system interferes with drainage as 
little as possible. On the other hand, the distribution of water needs systematic care. 

When, in 1905, with considerable experience of waterworks, but with no know¬ 
ledge of Indian irrigation, I received charge of about 200 miles of distributary, I 
came to the conclusion that had the native subordinate staff not been thoroughly 
experienced it would have taken me at least six months to get a real grasp of the 
methods, and I had the advantage of telegraphic communication with, and very 
careful instructions from, my immediate superior. 

to be irrigated ; and the distributary system, in which the canal splits up into 
a series of branches ramifying along all the ridge lines of the irrigated area. 
As a general rule, little or no irrigation is effected from the main line until it 
reaches a ridge line, as the water level is usually not sufficiently above the 
natural surface to permit it to cover the land. This is briefly expressed by the 
statement that the main line “commands” only a small area of land, or none 
at all, as the case may be. The primary object in the location of the main line 
is therefore to reach the main ridge line as soon as possible ; and any irrigation 
that is effected from the sidelong reaches of the main canal is usually 
incidental only. 














CONTROL OF WATER 


726 

As secondary conditions, we must as far as possible avoid deep cuttings, or 
high embankments, or crossing drainage lines and stream channels. It will be 
plain that these objects are also (abnormal local conditions apart) best attained 
when a ridge line is rapidly reached. Thus, the longitudinal section of an 
irrigation canal bears a marked resemblance to the longitudinal section of most 
rivers, the bed slope being flat near the head of the canal (or mouth of the 
river), and growing more and more accentuated as the tails of the distributary 
canals (sources of the tributary streams) are approached. 

No general rule can be given ; but, as a matter of experience, the head 
reach of a canal usually has a slope which is approximately half that of the 
general surface of the land. The design of the distributaries is really a matter 
of trial and error. The area irrigated will determine the volume of water 
carried at each point, and the level of the water in the canal feeding the dis- 



Sketch No. 216.—Relation between Distributaries and Contour Lines. 

Note .—This sketch shows a portion of the Upper Bari Doab Canal. I had in 1909 
selected it as showing what are probably the best laid out distributaries in the Punjab; 
and Mackenzie, who had maps of all the Indian canals at his disposal, has also 
published the complete field map as a good example. 

Personal acquaintance with the locality, and a knowledge of the working condi¬ 
tions, inclines me to believe that the regulation is somewhat more difficult than is 
usual. In fact, the principle has been overdone. This is not very important, as 
it is usually impracticable to follow the theoretical location so closely. 

tributary, and that required to command the area near the tail of the channel 
will fix its mean bed slope. 

Having fixed the gradient, we have next to inquire whether the channel 
will silt, or scour. Kennedy’s principles (when properly applied) enable us to 
answer this question. If it should happen that the ruling gradient is so steep 
as to cause scour to be apprehended, it is necessary to reduce the surface slope 
of the water by putting in falls (see p. 713). The cross-section of each reach 
of the channel and its bed width being thus calculated, we can determine the 
balancing depth, i.e. the depth of excavation, such that the earth excavated to 
form the canal is just sufficient to make the banks. 

It is evident that the canal should be located so that the depth of the 
excavation will, as far as possible, be the balancing depth ; and it is plain that 
where the choice exists it is cheaper to excavate less deeply than the balancing 
depth, and to secure the necessary earth by extra excavation in the canal bed ; 










DISTRIBUTARY BANKS 


7 2 7 

breaches, on the other hand, are less likely to occur if the canal is kept below 
the balancing depth. 

The design of the banks is also important. These are generally constructed 
without any puddle or core wall, and the canal water therefore percolates 
through, especially in the early years before the interstices in the banks have 
been stanched by fine silt. Thus, the quality of the earth must be carefully 
considered. The matter is somewhat more simple than it looks, for in most 
cases it is proposed to carry the water of a river across the alluvial deposits 
which this same river has laid down, so that there is a fairly close relation 
between the quality of the silt carried in the river water and the earth through 
which the channels are constructed. Thus, Kennedy found that the earth 
through which the Bari Doab Canals were constructed never gave trouble by 
scouring, unless the mean velocity exceeded 1*30 v 0 , and a similar relation holds 
good in nearly all cases (see p. 754). 

So also, if the river carries a coarse silt, we may expect that the canal banks 
will, on the average, be constructed of fairly coarse earth. The Punjab silt is 



Bank l Slopes 

B*Pe‘ 


- Bed wm \ U Slopes 
-Excarahon as made 


Sant l Slopes 
S‘pz‘ 


s(n-d) *4-5 = 6 iDS(H-d) Finil ^ SlJf Satiation Stye I i! a tUMfriia-uj-a-M-si r 


© 


lieu Style 



Punjab Condi bank. Sections 

© 


Old Style 


High flood 


iO'M 


Minimum Section 




Hat. Surf. 



Net. Surf, less fan O-Srn. Pelon Hood 

; 


low bard River Bank. Section (reherc Scour is apprehended) 


inerdge SecDM '^SS- r Nat Surf. 

hlxo oat suit me fan ism oelm ftxd e turns i t-tim. Irecoxnj 

flood Banks of River tnie 


Sketch No. 217.—Bank Sections. 


very fine, whilst the earth is nearly as finely grained as is possible. Practical 
experience shows that a bank consisting only of such earth is not safe against 
breaches until the gradient through the bank is approximately equal to 1 in 7. 
Sketch No. 217, Fig. 1, shows the old and new sections adopted in such cases. 

The Nile banks are of the section shown in Fig. 3, and it will be evident 
that the hydraulic gradient is about 1 in 8 ; while, as a contrast, the embank¬ 
ments of the River Po in Northern Italy are as per Fig. 2, and the hydraulic 
gradient is about 1 in 4* 

So long as the branches exceed a size (say 150 cusecs) such that a breach 
would be a serious disaster, it appears advisable to excavate them once for all 
to the cross-section determined by Kennedy’s rules, or whatever local modi¬ 
fication is found advisable. Sketch No. 219 shows the modern Punjab practice, 
and it will be seen that by skilful maintenance the otherwise detrimental silt 
is deposited against the banks and finally produces a very sate section. The 
two insets show how carelessness may produce deposits of silt that do not much 
strengthen the banks or curved banks that increase the roughness of the 

channel. 













































CONTROL OF WATER 


728 

In the case of minor branches of a size such that a breach in the first yeais 
of the canal’s existence may be considered as unlikely to cause much damage 
(and it must be remembered that the flooding of desert land when watei is 
plentiful, is by no means a disaster), the design is somewhat different. 

A large amount of capital expenditure, and considerable after outlay on 
maintenance can then be avoided by constructing these channels as shown in 
Sketch No. 218, Fig. 1. Such banks are weak, and may breach ; they are, 
however, cheap, and scour is unlikely to occur. In the early years of a canal s 
existence the required supply will probably be far less than the designed full 
supply, and the water will probably not rise far above the level AB, and the 
whole area up to CD, will silt up with fine silt, forming a highly impel vious 
bank. During the first clearance of silt, the silt in the area occupied by the 
designed section can be dug out, and can be thrown on the water face ot the 
banks, as shown. The next season’s work will silt solid up to a level about AB, 
and the final outcome (after say four or five seasons) will be the channel shown 
in chain dots. This is flowing in a self-formed bed of highly impervious silt, 

1 .. 1 .* *■' 




Sketch No. 218.—Canal Sections. 


matted together by grass roots, and it will be found that breaches are almost 
unknown in such a channel. 

The advantages of skilled silting are well illustrated by comparison with 
Fig. 2, which shows a channel carrying the same discharge of water not 
containing silt. 

In this Tase the banks cannot very well be formed of earth taken from 
outside the channel, and in consequence the bed of the channel is sunk some¬ 
what below the natural surface, and the “command” is therefore flu* inferior to 
that in Fig. 1, where matters can always be arranged so that the bed of the 
final channel is level with or, if necessary, above the natural surface. 

The early maintenance of channels of the type indicated in Fig. 1, is 
troublesome, owing to numerous small breaches, but after the third or fourth 
year (indeed, in some cases after the first year) the maintenance cost is con¬ 
siderably less than that of a channel as shown in Fig. 2, even although the 
command of the latter may be less. 

The financial advantages are obvious. The channel costs very little until it 
begins to earn a revenue. Again, the first settlers are cultivating virgin soil, do 
























SILT BERMS 


729 


not require silt to enrich their fields, and are not diverted from their agricultural 
development by the labour of silt clearance. Such breaches as do occur 
merely saturate ‘the soil, which requires water, and are usually regarded as 
beneficial. In fact, the one disadvantage of the system is that the cultivators 
are likely to make breaches in order to secure pasturage for their cattle ; and I 
cannot see that this is altogether an evil. 

A Government may consider such damage as an encouragement to settlers, 
whilst a private company should remember that water is cheap in the early 
years, and that rapid settlement is an advantage to all concerned. 

The above discussion assumes that the Kennedy type of channel is 
exclusively used. 

It must, nevertheless, be acknowledged that the adoption of Kennedy 
channels does not tend towards economy in construction. Kennedy channels 


Canal Bed above Natural Surface 


Full Supply 

^ Final Section of Bank 

Ulti mate Bed 

Stake l Brushnood Spurs / 

- 7 raise a as s//r rises. / 

Borrow Pits 7 

KpH Spur lo'nide every !00' p* 10 

Cana! Bed at Balancmo Debth 

full Supply 

- 

ry 

Silt Berm n 'N s ^ 

7/ 



*— 25 ‘ 


Onoinat Bdnk 


full Supply 


The Hump is practical!} a small 



scale High Sank madeltaic nver. 

■ . ... . ' 1 i • 

Bad Section of a Si!t Berm. 


. a 


5 pur 


Spur 


Bad Plan of Berm. 


Sketch No. 219.—Maintenance of Silt-bearing Canals. 


are (comparatively speaking), wide and shallow in form. Hence, even in the 
very largest sizes their construction entails extra expense in excavation ; for it 
will be found that the balancing depth, even in very large canals, rarely exceeds 
5 feet, and consequently mechanical excavation is seldom profitable, while the 
extra width of the canal causes the lead of the excavation to be great, and 
entails a larger expenditure on land. 

Hence, unless the water is known to deposit large quantities of silt, it will 
sometimes be found that the increased capital expenditure is greater than the 
capitalised cost of annual silt clearances, although it must always be re¬ 
membered that the expenditure on such clearances does not fully represent the 
damage done by silt, and that the value of the crops which may be lost by a 
bad supply of water must also be taken into account. 

Command. —The question of the relative level of the water in the minor 
canals, and the adjacent land, is of importance. Silt deposits are liable to 



































73° 


CONTROL OF WATER 


occur at the head of each minor channel, owing to the disturbance of the 
water caused by the bifurcation of the main channel, and also by the regulator 
controlling the supply to the minor channel. These local head reach 
deposits will probably be increased by designing the major channel according 
to Kennedy’s principles. It is therefore advisable to calculate the regulator 
carefully as a drowned orifice (the coefficient of discharge may be taken as 
070 to 075), and to allow a margin of 6 inches in small, and 1 foot in large 
channels, over the calculated head, so that the full supply can be forced into 
the channel, even when the head reach is badly silted. 

The general slope of the channel should be taken so that the level of full 
water supply may be about 18 inches to 2 feet above the level of the adjacent 
land. This, in view of the fact that the channel is presumed to be on the 
highest adjacent land, may at first sight appear unnecessarily large, but it 
will be found advisable for two reasons. Firstly, the channel being a non¬ 
silting one (z>. carrying forward to the fields all the silt that enters it), silt 
will rapidly deposit in the water courses taking out from the channel, and 
these deposits will principally occur close to the head of the watercourse. 
The difference of water level between the canal and the water course should 
therefore be kept high, so as to permit of the full supply being forced into it, 
just as it is advisable to have a margin of available head between the main 
canal and the distributary. 

Secondly, in the present state of the science of irrigation no canal is well 
designed unless it is adapted to the future introduction of modules for the 
distribution of water by measurement. Now, it is very unlikely that any 
practical form will be developed, which does not require a fairly large head for 
correct operation. 

Methods of Field Irrigation (see p. 644).—The methods of field 
irrigation are largely determined by the general slope of the country, and also 
by local custom. A consideration of such methods should not be neglected 
by engineers ; since, when the canal is designed so as to favour the application 
of water in an economical manner, it will be found that the agriculturists 
soon discover the benefits and readily adopt the more economical methods. 
My own experience leads me to believe that even when dealing with a 
conservative population already accustomed to uneconomical methods, three or 
four years’ experience will suffice in order to produce an almost universal 
adoption of better methods. 

The methods adopted by agriculturists when left to their own devices are 
wasteful of water, their weakness principally lying in the lack of attention 
paid to the design of the small channels conveying the water from the 
engineer’s canals to the fields (i.e. the watercourses). An agriculturist con¬ 
siders these channels as necessary evils, and is inclined to make them as 
small as possible. The Punjab Irrigation Department has carried out very 
systematic experiments on the subject, and I have investigated the results 
mathematically, in order to discover the relative advantages of the methods 
of procedure of both parties. Broadly speaking, an engineer can always raise 
a better crop with less water than an agriculturist; while, on the other hand, 
he fails lamentably in taking advantage of local rainstorms, cloudy days, and 
other favourable weather conditions. The table given on page 733 is used in the 
Punjab, and corresponds roughly to Kutter’s n = 0-035, but smaller channels 
are found to be uneconomical. 


COMMAND 


73 1 

it will therefore be evident that the proper function of an engineer is to 
deliver water to the fields in a manner such as to encourage (in fact, force might 
be considered the more correct word) the agriculturist to utilise it to the best 
advantage. The engineer, however, oversteps his proper functions if he in 
any way endeavours to control the periods or quantity of watering. His 
concern is always with the “ how,” and never with the “ when.” 

The area of land which each agriculturist tills is relatively small, being 
about 28 acres in India, and 40 acres in America, and these holdings are large 


yi 

S' 


5 


$ 

a 


Government Watercourse 


r fl. 

Minor 

1 — 1 |—[• - 7 — 

1 1 1 ! 

; 1 | j j 

Private ! Watercourse ! 

i ! 77: 

i i 1 

• 1 

1 1 

Permanent 

1 ! 1 

Eartt) Bank i / toot hiot 

4 Hi 

i! Hi 
*3i ! 

1 1 1 

'I _-_ 1 

• j ! ! ! 

ft. izhiopestpoint in squared 5is piqherthanD. \ If! 

! ! i 7 7 

J5. 

i 7 

/square - H00' * j U00-E7- 78acres ! grass 

Nett\ cropped area about Z7acres. 

1 i 

! i 

! ! i 

is 

1 

i 

/ square *Z5kitas j * POO Pans; eacP\kiari is about 
//)&'* \55'.approximately b\ acre. 


I 

| ! 


Semi 

! i ^ 

..-. ... . ■ ... l 



! ! 

• : 



1 t 

1 1 

i : 

1 1 


B. 

! ! 

1 1 

1 1 

1 I 

J ' - 

a 


Sketch No. 220.—Division of a Square of Land. See also No. 157. 


compared with those of other irrigated countries. We are therefore justified 
in considering that in a well designed system of irrigation water should be 
delivered to at least one point per 30 to 40 acres irrigated. It is plain that 
this point should be the highest spot on the area considered, and even where 
the slope of land is so great that water delivered by a channel at, or about, the 
level of the natural surface of the ground, will flow over the whole area, it will 
still be found economical to insist on delivering water at the highest point, and 
to arrange so that the water level at that point is at least 6 inches above the 
ground level. On the other hand, anything much above 1 foot requires some¬ 
what costly banks. 























































732 


CONTROL OF WATER 


If we were solely concerned with economy in water, there is little doubt but 
that the best results would be obtained by flooding the whole area as rapidly 
as possible, and I have personally obtained very excellent results with a flow 
of 2*5 cusecs (second feet). This volume of water requires a somewhat large 
force of labour to handle it properly, and although a big landowner might 
deal with this volume, and would find it advantageous to do so, the ordinary 
man with 40 acres can hardly be expected to handle much more than one 
cusec ; and, if his watercourses are not in good order, even this quantity will 
tax his energies. 

We should therefore design our watercourses so as to deliver one cusec 
to each plot, and should be prepared to encourage any agriculturist who will 
undertake to deal with a larger stream. Field operations are greatly assisted 
by a systematic division of the area of each holding into plots, each of which 
is separately irrigated. Sketch No. 220 shows the method officially prescribed 
in the Punjab for the division of a 28-acre (accurately 2777 acres) plot. This 
method is well suited to Indian agriculture, and is also well adapted for use 
in other countries where intense culture is practised. But for wheat and 
those crops which require an extensive adoption of machinery, the divisions 
are somewhat small. As a matter of fact, agricultural machinery exists which 
is specially adapted for such cases, but personal experience does not lead me 
to consider that the existing machines are really well suited to the conditions. 
It is therefore at present advisable to lay out the land so as to allow of the 
usual types of agricultural machinery being employed, and the dimensions 
given in Sketch No. 221 show an arrangement which secures a very fair 
balance, as it hampers the machinery but slightly, whilst securing economy 
in water. It is necessary, however, to remark that an irrigated area which 
produces crops such as wheat, can hardly be said to be utilised to its best 
advantage. The proper function of an irrigated area is to produce valuable 
crops which require intense cultivation ; and consequently less valuable food 
crops such as the wheat of the Punjab, or the maize and millets of Egypt can 
only be considered to be economically justifiable when they occupy the 
ground as an inter-seasonal crop, or in rotation with more valuable products. 
Where this is not the case local conditions are backward, and should only be 
regarded as temporary. Great economy in water for cultivation is thus 
hardly necessary ; for, as already stated, in the early years of an irrigation 
scheme waste of water, provided that it benefits the agriculturist, may be 
regarded as justifiable, so long as the custom does not become rooted. 

Design of a Distributary.— The final design of a distributary requires 
a knowledge of the arrangement and position of the field watercourses. 
Similarly, the final design of a branch assumes that the sizes and positions 
of the distributaries are previously fixed. In fact, the final design of the 
whole canal must be regarded as proceeding from the tail upwards. 

The example given below adheres somewhat closely to the conditions which 
are usually found in India. The individual watercourses are perhaps slightly 
larger in capacity than the average of those found in India, but in this respect 
the design is typical of the more advanced Indian practice. The question has 
already been discussed, and there is little doubt that were the Indian agri¬ 
culturists more accustomed to mutual co-operation, even larger watercourses 
might be constructed with advantage, since the capacity of the watercourse 
fixes the rate at which water is applied to each individual field division or plot. 


D/S7RIB U7AR Y DESIGN 


733 


Thus, the larger the discharge of the watercourse, the smaller is the waste 
which occurs by absorption during the actual application of the water to the 
land. The Indian rule on the matter is as follows : 

“ All watercourses which exceed three miles in length are to be considered 
as distributaries, and are to be maintained by the Government.” 

FINAL DETERMINATION OF THE DIMENSIONS OF A DISTRIBUTARY. 


'M t/J 

0 ■*-» 

<L> 

c 



5 O 

(D 

Jm 

cJ 

to g 

< 

5 § 

T 3 

O . 

CJ 

D 

T 3 l.ll) 

5 » 

C 

<D ^ 

omma 

Acre: 

& 

O 

O 

• • • 

3000 left 

1070 

7000 right . 

700 

and left . 

600 

10000 right 

1290 

14000 left . 

1000 

17000 right 

I 33 ° 

21000 left . 

2000 

27000 right 

1500 

29000 right 

T 33 ° 

and left . 

i960 

38000 right 

1800 

40000 tail . 

233 ° 



C/3 

O 

0 


CU 

0 

C/3 

<V 

C/3 

P 

0 

f—T 

0 


O 

W 

<D 

a 

Vo 

Oh 



tn 

U 

O 


0) 

tn 

O 

O 

O 

►H 

tn 

<U 

U 


O 


Vh 

O 

c3 

N 

Oh 



Discharge of Water¬ 
course in Cusecs. 

Nett Discharge of Dis¬ 
tributary in Cusecs. 

Bed Slope. 

Preliminary Cross-sec¬ 

tion of Distributary. 

. Mean Velocity 

E? 

D 

H 

-J 

Absorption at 8 Cusecs 

per Million Square 

Feet. 

Gross Discharge, in¬ 

cluding Absorption. 

Final Section of Dis¬ 

tributary. 

^ . Mean Velocity 

0 

£ 

D 

— 1 
_) 

4 

• • • 

43 *i 


IO X 2*6 

I’OO 

• • * 

47*o 

12 X 2 *4 

1-03 

3'3 

39 * 8 

10 

10 x 2*4 

1*00 

°*4 

43*3 

11 x 2*4 

1*02 

2'2 

35*7 

0 Oh-^ 

9 X 2'4 

0-99 

o'6 

38-6 

10 x 2*3 

1*01 

i *9 

• • • 

11 IT 0 

. .. 

. 


. . . 

. 1. 

• • • 

. 

.. 

3*9 

3 i *8 

ip 0 0 
ng<2 O 

9 x 2*3 

°*99 

o *3 

34*4 

IO X 2*2 

roi 

2 *4 

29*4 

IO M 

H* 

9 x 2*3 

o *99 

o *4 

3 1 *6 

9*5 X 2*2 

I'OI 

3*2 

26*2 

• 

7 X 2-2 

1 "00 

o*5 

27*9 

9*5 x 2 

1*0 1 

4*8 

21 *4 


6 X 2 *2 

o *97 

°*4 

22*7 

7*5 x 2 

I *02 

3*6 

17*8 

up 

6 X 2 " I 

o*97 

o*5 

18-6 

6-5 x i*8 

I’OI 

3*2 

4*7 

9*9 

• • • 

^ 4—> 

N ft <v 
*0 

II 0 

l®g © 

5x1-6 

• • • 

o*97 

0*1 

• • • 

io*6 

• « • 

5x1-6 

• • • 

0*97 

• • • 

4*3 

5*6 

3x1-4 

o*95 

o"6 

5*7 

4 x 1-4 

o*93 

5-6 

5*6 

-(S' 2 2 

|eo 

• • • 

• • 

• 

O'l 

(5-6) 

• • • 

• 

• 


The filling of the table is obvious. The first two columns are obtained 
from the survey of the irrigated area, and the watercourses must be previously 
laid down on this plan. The third column “Cusecs per 1000 acres irrigated,” 
is determined by the depth of subsoil water below the natural surface in the 
areas served by the various watercourses, and is usually constant for the whole 
distributary ; although, in the example given, the allowance is varied in order 
to emphasise the necessity for bearing this condition in mind. The fifth 
column is the sum of these supplies for all watercourses below that Reduced 
distance, and consequently determines the Nett discharge (without allowance 
for absorption) of the distributary between the point considered and the next 
watercourse downstream. The sections of the distributary channel are then 
determined (in the example for slopes of and 4^00) by Kennedy’s 

Graphic Hydraulic Diagrams. The selection is so made that the mean velocity 
is near to (preferably slightly in excess of) v 0 , which is the non-silting velocity 
determined by Kennedy (see p. 754). 

In another locality where Kennedy’s rules are not applicable, the selection 
will usually depend upon economy in earth work. 

The table is purposely made somewhat more complicated than usual. As 









































CONTROL OF WATER 


1 34 


a rule, both the allowance of water per 1000 acres, and the bed slope, are 
constant throughout the distributary. The circumstances selected are, however, 
favourable. Relatively speaking the slope is steep, and hence it is possible to 
obtain Kennedy channels without making the width an unduly large multiple 
of the depth. With flatter slopes, however, it would be found necessary as the 

discharge of the distributary becomes small to reduce the ratio ve l° clt y 


Vo 


to o*95, 0*90, or even to 0*85. No definite rules can then be given, but if 
the fact that the channel carries silt and water is borne in mind, it will be plain 
that such ratios are permissible towards the tail, provided that the outlets of 
the upper watercourses are situated close to bed level; so that the upper 
watercourses draw more than their fair share of silt from the channel. In one 
particular instance, where I was forced to make the ratio equal to 073 for the 
last quarter of the channel, this disproportionate allowance was sufficiently 
marked to cause complaints. In all cases it is plain that no very sudden 
change should be permitted, and I believe that it is far better to grade down 

gradually through say : ^ ean veloc i t y 0*93, 0*90, etc., etc., than to 


Vn 


produce a sudden drop in the ratio, such as : roo, roo, roo, 0-90, etc. 

The preparation of a table showing the bed level and the water surface 
level at each watercourse outlet is now easily effected. It is, however, 
necessary to observe that the changes in depth must be assumed to be 
produced not by a rise in the bed but by a drop in the water surface. Thus, 
the difference in bed levels between the points R.D. o, and R.D. 14,000 is 
14x0-25 = 3-5 feet, but the difference in water surface levels is : 

14x0-25-}-(2*4 — 2‘2) = 37 feet. 

Similarly, the total fall in the bed in the distance of 40,000 feet is : 

14 x0-25+ 26x0*275 = 10-65 feet, 


but the drop in water surface is : 

io- 65 + (2*4— 1-4)= 11-65 feet. 

It will be noticed that the absorption is calculated on the basis of eight 
cusecs per million square feet of wetted perimeter, and the gross discharge of 
the distributary as tabulated in Column No. 10 is greater than the sum of the 
watercourse discharges. The corrected section is shown in Column No. 11, 
and is obviously sufficiently near to the truth to require no further corrections 
for absorption. The total absorption is 3*9 cusecs in a total discharge of 43-1 
cusecs ; and, as a general rule, it will be found that if an extra allowance of 
10 per cent, be made in the discharge of each watercourse sufficient accuracy 
is obtained. The calculation of a branch canal proceeds on exactly the same 
lines, but it is usual to allow a slightly larger supply per 1000 acres commanded 
in calculating the distributary discharges in order to avoid the necessity of 
previously determining the watercourses. Thus, we find rules such as the 
following : 

When the supply of individual watercourses is calculated as 2’8 cusecs per 
1000 acres, the gross distributary discharge is taken as 3-1 cusecs per 1000 
acres ; and, until local knowledge has been accumulated, these rough rules 
must suffice. It will be plain that the above methods of calculation will usually 




WATERCOURSE ORIFICES 


735 

in practice be applied only when “ remodelling ” existing canals so as to obtain 
the closest possible adjustment between the canal discharge and the local 
conditions. In project work it is usual to design the main branches by treating 
the distributaries in the manner in which watercourses are treated when 
remodelling existing canals. 

r i he final plans of a distributary, or branch, include a tabulation of bed 
levels, natural surface levels and full supply levels at say every 1000 feet. 

r I he quantities of excavation and banking can then be taken out, and the 
irrigation facilities ( e.g . the command and the difference between the full supply 
level in the distributary and the various watercourses) can be calculated. 

The work is laborious, but commonplace. The form adopted depends upon 
local conditions, and my own opinion is that it should include all matters 
connected with the distributary. 

For example : At every 1000 feet interval the bed level should be tabulated, 
together with the following : 

(1) The full supply level. 

(2) The water surface level at any supply which is less than the full, and 

which is frequently delivered. 

(3) The area of excavation. 

(4) The area of the banks. 

(5) The command. 

At every masonry work, or outlet, the following should be recorded : 

(1) The full supply level. 

(2) The command. 

(3) The head through the outlet of the watercourse as defined below. 

(4) The particulars of the work {e.g. bridge of 2 spans, each 8 feet wide, 

piers 14 feet by 2 feet over all; pitched 3 feet above piers, and 

5 feet below ditto). 

Similar particulars should be recorded at each outlet, including the area of 
the orifice, and the discharge. If the work is a regulator, the head for which it 
is designed should be given ; and if a fall, the fall and the dimensions of the 
notch should be stated. 

The ruling principle to be borne in mind is that distributaries are usually at 
least 10 miles in length, and that the engineer should inspect on horseback, or 
by bicycle ; and that the single sheet which he carries with him should provide 
all the information necessary for a decision to be made on the spot. 

The one matter which calls for remark is that a decrease in depth must be 
regarded as producing a drop in the water surface. For example, at R.D. 3000 
(see Table p. 733) the depth is decreased from 2‘4, to 2*3 feet, and this must be 
held to produce a drop of o'l foot in the water level at, or near R.D. 3000 feet. 
This fall is probably caused by the change in velocity which occurs, but its 
existence is undeniable, and if neglected, difficulties will arise. 

The supply to each watercourse is at present measured by an orifice in a 
stone slab. The orifice area is determined by the equation : 

Q = 5 \f h area of orifice, 

where Q, is the supply to the watercourse in cusecs, and /q is the difference 
between the full supply level in the distributary and the full supply level in 
the watercourse. 


CONTROL OF WATER 


73 ® 

In actual practice, these orifices are not fixed in place until irrigation has 
been carried out for some two or three years. The delay is in some respects a 
disadvantage, but in actual work it is found that the opportunity given for local 
investigations regarding the necessity for an increase or decrease of the supply 
(by such factors as unusually absorbent soils, or peculiar methods of irrigation) 
justifies the delay. I do not give standard drawings of the outlets which are 
employed, because the selection of the design and the materials used must 
entirely depend upon local conditions. It must, however, be realised that these 
outlets are constructed by dozens, if not by hundreds, so that their design is a 
matter which deserves careful consideration. 

Modules. —These are instruments for the supply of water by bulk, and are 
analogous to town water meters. The advantages to all concerned are obvious, 
an agriculturist who pays a rate of so much per acre irrigated has no personal 
interest in economising water, whereas if he pays a rate per 1000 cubic feet of 
water delivered, each economy effected in applying the water to the cropped 
area is his own gain. 

The obvious methods are a recording gauge and a weir, or a vaned wheel, 
fixed in a channel of known dimensions, whose revolutions are recorded. The 
practical difficulties are: (a) any such instruments are too costly ; (< b ) except in 
North Italy and parts of America the average agriculturist will steal water, 
tamper with instruments, and has public sentiment to support him in this atti¬ 
tude ; (c) in general the mean slope of the ground is so small that any device 
entailing a large loss of head is unpractical. 

Thus the problem will not be solved until some instrument is discovered 
whose records cannot be stolen or falsified, which, if tampered with, invariably 
delivers less water than when in proper order, and which works under a head 
of say o*5 foot as a maximum. 

I was employed by the Punjab Government to experiment on two forms of 
module, the Kennedy and the Gibb. Both, I believe, fulfil these conditions. 
Being proprietary articles I do not describe them. The Kennedy I consider 
the better, but this statement refers only to silt-bearing waters. The Gibb 
retains nearly all the silt in the water in the canal, and therefore alters the 
regime for the worse. This may be an advantage in clear water canals, but I 
have no practical experience of the case. When standardised I believe the 
Gibb will be the cheaper ; at present its accurate erection and calculation is 
very tedious, while the Kennedy can be ordered in fixed sizes and put in place 
by an untrained mason. Also the Kennedy can be examined and seen to be 
working correctly merely by reading a gauge. 

Surveys Preliminary to Irrigation.— The quantity of water which it 
is desired to supply to the land can be estimated from the observations which 
have already been given. The following figures (which, when possible, should 
be supplemented by direct observation) permit an estimate of the losses in 
transit from the river, or other source of supply, to be made. The capacity of 
each individual channel of the system can thus be estimated when an accurate 
survey of the irrigable area has been made. It is not proposed to discuss the 
methods adopted in such surveys. Broadly speaking, the country must be 
mapped with an accuracy comparable with that attained by such bodies as the 
British Ordnance Survey, or by other Government services. Practical experi¬ 
ence in checking the levels given by Ordnance surveys and good maps of 
irrigated districts enables me to state that the levels (although not the topo- 


ABSORPTION 


737 


graphy) are probably more accurately determined by irrigation engineers. As 
rough rules it may be stated that the level of the ground surface should be 
determined to a tenth of a foot at every corner of a series of a fifth of a mile 
squares, in plain country ; and that the accumulated errors must be carefully 
balanced. I have twice had to work across a boundary of levelling operations 
where the reference datum on one side of the boundary was 30 miles distant 
from the reference datum on the other side. The difference was not very 
great, and the original levelling work must have been very accurate, but the 
trouble entailed was enormous, and in one case led to what might have proved 
a serious defect in the supply. Wherever possible it is therefore advisable to 
select ridge lines as the boundaries of the operations of the various levelling 
parties. 

In a country with a more accentuated topography, such difficulties are less 
likely to arise, but the ground level will then have to be determined at more 
closely spaced points. 

Absorption , or Leakage from Channels or Reservoirs. —The leak¬ 
age from an unlined channel, or reservoir, is so entirely dependent upon local 
circumstances, that any general figures for its value must be regarded as mere 
indications of its possible magnitude. 

It is of course possible to obtain a theoretical formula, by the process em¬ 
ployed in the investigation of percolation under a dam or weir. But this seems 
useless, since the leakage occurs over so large an area that it would be im¬ 
possible to ascertain the average permeability of the soil accurately. The same 
difficulty occurs in the original investigation, but in that case we need not con¬ 
sider the permeability at a distance from the work, for although this may 
largely influence the total leakage, it cannot materially affect the stability of the 
dam. The statement is illustrated by certain early British reservoirs, where 
the dam is constructed according to the best British practice, with puddle walls 
carried deep into impermeable strata, and is therefore probably as little liable to 
leakage as any human work of an equal area can be. The reservoir sites, 
however, are crossed by a geological fault, and the reservoir is consequently 
rendered practically useless by local leakage along the line of the fault. 

Some writers on this subject have given sketches showing the theoretical 
paths of the leakage water. Reasoning on these lines, some investigators have 
arrived at rules such as the following 

“ A canal on the top of an embankment is less leaky than one in a cutting,” 
etc. 

I cannot quarrel with their mathematical reasoning. If the slopes of a bank 
are to be considered as impermeable boundaries because they do not visibly 
sweat, or leak water, the proposition hardly needs mathematical demonstration. 
•I do object to the idea that water does not leak across an earth surface because 
it never appears in a visible form on such a surface. Actual calculation shows 
that, quite apart from the rank growth of vegetation which is often found on the 
outer slopes of canal embankments or earthen dams, evaporation from a bare 
earth surface is quite sufficient to dispose of all the leakage water that reaches 
it from the canal. 

It is generally found that canals in bank do leak less than those in cutting, 
owing probably to the fact that the rolled earth forming the banks is more 
water-tight than the unrolled earth which usually forms the banks of a canal 
in cutting. 

47 


CONTROL OF WATER 


73 8 

The only factors that are sufficiently powerful to overcome local differences, 
such as care in construction, height of the bed above subsoil water level, etc., 
are the character of the soil, and the amount of silt deposit that forms on the 
bottom of the channel or reservoir. 

The following figures represent the observed leakage (including evaporation 
from the water surface) from certain French navigation canals, reduced to 
cusecs per million square feet of wetted perimeter. The figures usually refer to 
the summit level of these canals and are therefore probably greater than would 
usually occur. This opinion is confirmed by the fact that most of the figures are 
obtained from reports concerning proposals for remedial measures. It is also 
believed that nearly all these canals are supplied with water which has been 
stored in reservoirs, and therefore contains very little silt. It is quite certain 
that (except for two doubtful cases where the canal takes out from the Rhone, 
and may therefore receive silted water) the water is always extremely clear 
when compared with the water usually occurring in irrigation canals. 


Fissured rock 
Chalk 
Gravel 
Alluvial soil 


maximum 270; 
„ 270; 

„ 60; 

r 44 ; 


minimum 28 ; 

„ 8 ; 

>> 5 } 

„ 1*5; 


average 90 

5 > 48 

v 40 


For very fine soils such as occur in the Punjab, we have the following 
values (Kennedy, Indian Irrigation Congress , 1905), which refer to water 
carrying much silt : 


Main line of Bari Doab. 4000 ' 
cusecs discharge. 6 feet deep, 

) Average, 

97 

cusecs per million 

constructed in shingle and 

I 


square feet. 

sandy soil. 

Do., Sirhind. 7 feet deep, con- < 
structed in sandy soil, but the 
subsoil water level is nearer 

) 

| Average, 

9 ° 

cusecs per million 

to the bed level than in the 
case of the Bari Doab. j 

( 


square leet. 

Branches, 1000-3000 cusecs. In 1 

| 



good loamy soil. No sandy 

Average, 

2'2 

cusecs per million 

soil. Side slopes silted, but 1 
no bed silt. J 

Do., Sirhind. All sandy soil. No ) 

f 

1 Average, 

5’2 

square feet. 

cusecs per million 

side silt, or bed silt. J 

Distributaries of Bari Doab. 300- \ 

1 

Minimum, 

2*3 

square feet, 
cusecs per million 

1000 cusecs. Conditions as ( 
in branches, but some fine silt j 

Average, 

3'3 

square feet. 

j 5 

in bed in a few cases. J 

Maximum, 

4’4 

3 3 

( 

” Minimum, 

5 -o 

cusecs per million 

Do., Sirhind. Sandy soil. J 

1 

Average, 

8*o 

square feet. 

35 


. Maximum, 

12*0 

3 > 


INDIAN ABSORPTION 


Distributary Branches, 0*5 to 3 cu- 
secs discharge. All conditions. 
Some quite new, with no silt. 
All in loamy soil. 

Do., Sirhind. All conditions. Sandy 
soil. 


Fields. First watering. In loamy 
soil. 


Do. Dry or moist. In sandy soil 


739 

( Minimum, 3*3 cusecs per million 

square feet. 

Average, 9-4 

Maximum, 30 ,, 

{ Minimum, 7 cusecs per million 

square feet. 

Average, 22 
Maximum, 80 

Minimum, 5-5 cusecs per million 

square feet. 

Average, 8 

Maximum, 16 

' Minimum, 12 cusecs per million 

square feet. 

Average, 21 
l Maximum, 60 


5 5 
55 


l 


55 

55 


55 

55 


Judging from the comments passed upon Kennedy’s statement, these values 
are lower than is usually the case in India ; but it must be remembered that the 
subsoil water level in the Punjab is generally far deeper below the canal bed 
than elsewhere in India, while the soils are finer in texture. Hence, it is prob¬ 
able that the silt had stanched the beds in many cases. Kennedy’s figures 
are, however, confirmed by the value of yi 5 cusecs per million square feet lately 
obtained on the Ibrahimiya Canal (Egypt), and in this case the canal would 
not be considered well silted in the Punjab sense of the term. 

The figures for the Punjab may be taken as fair averages, and do not, like 
the French figures, refer to abnormal cases; since the discharge of all the 
channels is systematically measured. 

There is of course little doubt that the depth influences the leakage, and the 
formula : __ 

Cusecs percolation per million square feet — Cl depth in feet, where for the 
Punjab C is 3*5, has been proposed by Dyas. This formula is useful as show¬ 
ing the effect of marked variation in depth when other conditions are unaltered. 

The general results may be summed up as follows : 

(i) Guillemin states that at the first filling of a new canal a volume equal to 
that of the canal should be provided for initial leakage. 

(ii) The average loss in those sections of a canal which are not unduly 
leaky may be considered as about 4 to 8 cusecs per million square feet, when 
all possible care is taken to minimize losses. As the canal deteriorates by age 
(silt being assumed not to be deposited), this quantity increases to double after 
some five to ten years. 

(iii) For an old canal where silt has never been deposited, or where it has 
been removed, such values as 20 to 40 cusecs per million square feet are 
possible. 

In channels in rocky and fissured soil, these losses may be doubled, or 
trebled ; but it must be remembered that such abnormally leaky sections cause 
trouble, and are therefore more frequently studied, and the figures relating to 
them are more frequently quoted. 

In some channels the water table of the surrounding ground is sufficiently 




740 


CONTROL OF WATER 


high to cause the channel to act as a drain. Here, no loss occurs, and ground 
seepage replenishes the canal. For example, in the first eight miles of the 
Sirhind Canal it is believed that seepage into the canal occurs at the rate of 
about 5 cusecs per million square feet. 

(iv) In canals carrying muddy water some stanching by deposition of this 
mud in the cracks and fissures of the soil always occurs, even though silt is not 
deposited in the channel. Kennedy’s values may be taken as correct, and the 
usual allowance in the Punjab for leakage at the rate of 8 cusecs per million 
square feet of wetted perimeter is ample. The canal will probably become 
less leaky as it ages, but any scour may cause the leakage to increase 
suddenly. 

Lining of Irrigation Channels .—The figures given above show 
that in a large canal system the absorption losses, between the canal head 
and the fields, may reach 50 per cent, of the total volume entering the canal, 
and rarely fall below 20 per cent. This loss, as it tends to raise the subsoil 
water level and encourage waterlogging and alkaline soils, is directly detri¬ 
mental. 

Thus linings to stop percolation have been frequently proposed. Earthen 
channels lined with concrete or rendered with cement, and iron pipes form the 
standard systems of distribution in Southern California. In my own practice, 

I have usually found that wherever the water is lifted more than 20 or 30 feet 
similar linings (of the main channels at any rate) will always earn interest on 
their cost by the diminution secured in the fuel bill. 

In gravitation and large pumping schemes, however, such linings are too 
costly. 

The University of California and the Punjab Irrigation Department have 
carried out many experiments. The linings tried include concrete (lime and 
cement), cement rendering, oiled paper, mixtures of light and heavy oils with 
gravel and dry earth, puddle clay, etc. 

The only effective linings appear to be the concretes, rendering, puddle 
clay and oiled paper. The last deteriorates with age, and the last two, unless 
made too thick to be economical, are very easily perforated and rendered less 
efficient by animals trespassing on the channels to drink. 

The following figures may be useful : 


Loss in unlined Californian channels = 9*4 cusecs per million square feet 


Loss in channels lined with 
2^-inch cement concrete 
2^-inch lime concrete 
1-inch cement mortar 
3^-inch puddle clay . 
oiled paper . 


= 1 * • 


= 3'i 
= 3*4 
= 5*2 
= 3 to 5 


of water surface area. 


55 


55 


>5 


55 


55 


55 


55 


55 


55 


The puddle clay does not appear to have been good puddle, but there are 
very few irrigation districts where good puddle is available. 

Leakage of Reservoirs. —One favourable circumstance exists in the case 
of a leaky reservoir. There being no current to remove silt, stanching of the 
percolation passages takes place ; and, unlike a flowing canal, the leakage of a 
reservoir will decrease with age. 

Further than this, it appears impossible to make any statements. Modern 
studies show that the evaporation from the water surface of a large reservoir is, 


RESERVOIR LEAKAGE 74I 

considerably less than (usually about §) that which is observed in ordinary 
evaporation pans. 

Now, engineers have been accustomed to apply the results of evaporation 
pans in order to obtain the loss from large reservoirs, and no discrepancy which 
is so extensive as to arouse suspicion has yet been noticed. It would therefore 
appear that the leakage from reservoirs is generally small, and that it does not 
probably exceed a depth of i foot annually in the case of a good reservoir. 

It must be remembered that in dry years when the reservoir is drawn down 
below its normal level, percolation occurs from the ground into the reservoir. 
Herschell and F tely have estimated this at as much as io per cent, of the 
volume of the reservoir. 

A safe and practical rule appears to be as follows : 

Allow for evaporation and leakage combined the quantity reported as 
evaporated from a free water surface, i.c. from a small evaporation pan. 

The real difficulty is that the total leakage is probably less than 2 per cent, 
of the volume received by the reservoir ; and usually we cannot accurately 
measure such volumes to 2 per cent., the probable error being about 5 per 
cent. 

The following figures represent the allowances for leakage plus evaporation 
which are usually made in practice : 

Allowances are rarely made in Great Britain, but 2 feet per annum seems to 
be a maximum. 

In Germany, r64 feet (0-5 metre), or occasionally 2*46 feet is allowed. 

In India, from 6 to 7 feet; or where reservoirs are known to leak, 10 feet 
has been allowed, and 13 to 15 feet has been observed under unfavourable 
circumstances. These allowances are usually stated to refer not to the year, 
but to the interval between the end and the beginning of two successive wet 
seasons. 

In Australia, 6 feet is allowed, but this is insufficient in the hotter 
districts. 

In South Africa, the usual allowance appears to be 7 feet per annum; and 
this refers to valley reservoirs in mountainous country, so that the conditions 
are favourable. 

In the Eastern United States, 40 inches used to be allowed, and in the 
Western arid tracts estimates are based on a value of 8 to 10 feet per 
annum. 

Regulation of an Irrigation System. —The figures given during the 
discussion of the irrigation duty of water will render it plain that the 
agricultural requirements of a cropped area are variable. Quite apart from 
such climatic conditions as falls of rain or unusually hot spells of weather, 
land invariably requires water to be supplied at a greater rate during the 
ploughing season than later on when the crops are growing. 

Similarly, the available supply in the river, or other source from which the 
water is drawn, may vary from day to day. 

The adjustment of supply to demand therefore forms a very intricate pro¬ 
blem, which deserves the best efforts of all concerned, since the success 01- 
failure of the system largely depends on the efficiency of this adjustment. 
Putting local conditions aside, it is plain that in a season when the demand 
or the maximum available supply was, say, three-quarters of the maximum 
quantity which the canal can carry, it would be futile to distribute this 


742 


CONTROL OF WATER 


diminished quantity of water pro rata among the individual branch canals, so 
that each carried about three-quarters of its maximum supply. / 

The correct distribution is plainly obtained by shutting down certain branch 
canals, the combined capacity of which is about one-quarter of that of the 
whole system entirely, and running the remaining channels full bore. Thus, 
any difficulties caused by variations in the water level are prevented. As a 
general principle, a channel from which irrigation is effected should always 
carry something between o'9 and ri of its designed maximum supply, or else 
be bone dry. 

For this reason, the areas which are commanded by the larger channels 
(i.e. the main canal and the three or four largest branches) should not be 
irrigated directly from these channels, but from small branch canals taking off 
from the main channels, and in some cases running for long lengths not more 
than ioo feet distant from the parent channel. (Sketch No. 216.) 

The preparation of a systematic table showing the periods during which 
each individual channel receives its full supply is a matter that can only be 
arrived at by long experience. The principles are obvious :—The preliminary 
local investigations give full information regarding the permissible interval 
between successive waterings, and this interval must form the basis of the 
table, since each individual irrigation channel must receive its full supply at 
least once during this interval. During the early years of the system careful 
studies of the available supply and of the normal demand must be made ; and 
finally, after some five or six years have elapsed, a fair working schedule can 
be laid down. This schedule will require modification from time to time, as 
the irrigated area increases, or as the staple crops change. The existence of 
such changing conditions forms the only real reason for the services of an 
expert engineer on an old and well maintained canal, and it is therefore plain 
that irrigation engineers who aspire to be more than supervisors of small 
repairs must consider their position mainly dependent on the efficiency with 
which they contrive to utilise the available water to the best advantage. 

The watercourses taking out from each small distributary of a canal system 
must also be regulated on the same principles during the period over which it 
receives water, and a table of the times during which each individual farmer is 
entitled to use the full supply of the watercourse which irrigates his fields must 
be drawn up. The days of the week, or the hours of the day form convenient 
and unmistakable divisions. As a general rule, so long as the distributary 
receives water, each watercourse should be open, and should be permitted to 
take its full supply. Any attempt to close off individual watercourses is usually 
considered unjust, and invariably leads to “ unauthorised irrigation,” and the 
manufacture of “ legal crimes ” is an unprofitable affair. 

Alkaline Soils. —A soil may be considered to be alkaline when it contains 
a sufficient quantity of soluble salts to interfere decidedly with the growth of 
crops under circumstances which favour this interference. Consequently, the 
term covers a very extensive range of conditions, varying from soils covered 
with layers of common salt, some 2 or 3 inches in depth (capable under 
favourable circumstances of being utilised commercially), to those which contain 
distributed throughout their top 3 or 4 feet a quantity of soluble salts which 
is just sufficient to damage delicate plants when concentrated into the top 2 
or 3 inches of the soil. 

The salts which usually render a soil alkaline are sodium chloride, sodium 


I 


ALKALI 


743 


sulphate, and sodium carbonate, but damage has also been traced \to mag¬ 
nesium sulphate, and chloride, and to calcium chloride. The most dangerous 
alkali is sodium carbonate (the so-called black alkali of the United States), 
since a far smaller quantity of this salt suffices to render a soil alkaline, than 
any of the others (with the possible exception of calcium chloride). The 
practical problems relating to the removal of all these salts, however, are more 
01 less identical. It must be realised that once water is applied to an alkaline 
soil, reactions transforming the original sodium chloride into say sodium 
carbonate, and calcium chloride, are not only possible, but actually take 
place under favourable circumstances. At present the exact conditions are not 
well known, except that the dangerous black alkali, sodium carbonate, can be 
more or less rapidly transformed to the less harmful sodium sulphate by the 
action of powdered gypsum in the presence of water. The chemical reaction 
is expressed as follows : 

Na 2 C 0 3 + CaS 0 4 ==CaC 0 3 + Na 2 S 0 4 

As calcium carbonate is very insoluble under all conditions, the reaction is 
fairly certain. On the other hand, such reactions as : 

2 NaCl + CaC 0 3 = CaCl 2 + Na 2 C 0 3 

although theoretically possible, depend (under practical conditions) on such 
matters as the temperature and the amount of water present, and are therefore 
by no means certain to occur. 

Practically, therefore, an engineer can be satisfied with regarding all alkaline 
soils as alkaline without drawing any distinctions as to the chemical composition 
of the salts present, and will find that the practical methods either for removing 
alkalinity, or for preventing its occurrence, are not markedly affected by the 
chemistry of the alkali. The chemical composition of the alkali is known to 
have a decided influence upon the time and quantity of water required to re¬ 
move it. As yet the matter has not been exhaustively studied, and only relative 
values can be given. 

Soils which are rendered alkaline by sodium chloride (and probably all 
other chlorides) are relatively easily reclaimed. Sulphate alkalis are somewhat 
less easily removed, but cannot be regarded as difficult to deal with. Sodium 
carbonate is a far more difficult proposition. It appears to render the soil less 
permeable, as may easily be observed by adding a few drops of a solution of 
sodium carbonate to a cubic foot of sand and testing the permeability both 
before and after the addition of the salt. In consequence, the soil appears to 
be capable of choking drain pipes and entering into gravel beds in a manner 
which leads me to believe (although I have been unable to detect the effect 
microscopically) that the individual grains of the soil are broken up. While 
soils which are heavily charged with sodium carbonate have been reclaimed 
and rendered fit for cropping, I consider that the process is rarely, if ever, 
economically profitable. Dressing with gypsum (as ’already indicated) appears 
to be a necessary preliminary. 

The engineer’s classification of alkaline soils is as follows : 

(a) Soils which are naturally alkaline. 

(b) Soils which are artificially alkaline. 

Soils belonging to the first class are those which, prior to irrigation, contain 
sufficient alkali to prevent growth. It is of course quite possible that this 
alkali is a relic of former irrigation. 


744 


CONTROL OF WATER 


The soils of the second class are at first capable of supporting the growth of 
crops ; but they contain (either equally distributed throughout the depth of the 
soil, or obtained from the water used for irrigation), a sufficient quantity of alkaline 
salts to prevent crop growth if concentrated in the upper layer of the soil, i.e . 
the upper i, to 3 inches depth. 

The problem of irrigation in connection with alkaline soils therefore consists 
in : 

(i) The reclamation of soils of class (a). 

(ii) The treatment of soils of class ($), in such a manner as to prevent their 
becoming alkaline. 

The reclamation of alkaline soils is a very simple process in principle. The 
soil is covered with water which dissolves the soluble salts, and this water is 
drained off, carrying away the salts. The details are by no means simple. 
Alkaline soils rarely contain much above 2 per cent, by weight of alkali, and 
were it possible to obtain a solution even approximately saturated, a watering 
of about 4 inches depth should be sufficient to remove the alkali in the top 
3 feet of soil. As a matter of fact, the last remnants of the alkaline salts 
are very difficult to wash away. The process actually consists in removing 
sufficient salts from the top layers of the soil to permit the growth of some 
plant (e.g. Panicum crusgalli, or some varieties of clover), which is more than 
usually resistant to the action of alkaline salts. Having thus obtained a 
covering to the soil, so as to prevent abnormal evaporation, the remainder of 
the alkali is washed down by the water used for irrigating the first crop, as it 
percolates to the drains. 

The most easily reclaimed land is that which is alkaline by nature, e.g. the 
beds of dried-up salt lakes, such as occur in the Western United States, India, 
Egypt, and elsewhere. In such cases, it is sufficient to dig drains about 66 feet 
apart, and of such a depth that the drainage water stands about 1 foot 3 inches 
to 1 foot 6 inches below the soil level. The earth excavated from the drains is 
thrown out on either side so as to form banks to retain the washing water, as 
is shown in section in Sketch No. 221. 

The great difficulty usually found in such work is to obtain a sufficient fall 
to ensure good drainage. The problem is that of irrigating low-lying land with 
large quantities of water, and yet preventing waterlogging. The two con¬ 
ditions are to a certain degree antagonistic. 

The natural slope of the soil is rarely sufficient ; and, in consequence, the 
drainage water has frequently to be pumped out artificially. The larger drains 
must therefore be very deep close to the pump, in order to obtain a correct fall. 
It will therefore be found that one pump cannot economically drain much more 
than 2500 acres. The pumps may be proportioned so as to deal with 1 cusec 
per 150 acres during reclamation, although 1 cusec per 250 acres will suffice to 
keep the reclaimed land properly drained. Unless ample water is available, the 
extra pump capacity only permits a slightly more rapid reclamation. 

The rate at which reclamation proceeds depends almost entirely upon the 
permeability of the soil. It will be found that where previous to reclamation, 
the soil has been trodden on, or has otherwise been rendered hard {eg. foot¬ 
paths, or places where materials have been deposited) it remains alkaline long 
after the surrounding soil has been reclaimed. 

The following sketch (No. 221) shows the methods developed by Anderson 
and Sheppard (see P.I.C.E., vol. 101, p. 189) at Lake Aboukir. 


RECLAMATION OF SOILS 


745 


The large fields A B C D are 3280 feet long (1000 metres) by 984 feet wide 
(300 metres). The main drains and irrigation canals run along A C, and B D, 
as shown in section at E. Along A B and C D, run the secondary drains, as 
shown at F ; and an irrigation canal of equal cross-section is dug down the 
middle of the plot. * 

The minor drains are usually about 2’3 feet deep, with a bottom width of 
o' 83 foot, but vary with the nature of the soil. Consequently, the plot is cut up 
into twenty smaller plots, each 328 feet wide by 492 feet, drained by a minor 
drain, and surrounded by small banks which permit them to be flooded to a depth 
of 1 foot, to 18 inches. 

The slope of the drains is usually less than but where the slope of 

the ground permits, steeper slopes are adopted. 

The general conditions are favourable. The soil consists of about 2, to 3 




!*• 

1 


on da/ 

V 

Drain 

► -»- 




5 

1 

1 

1 





1 

e 

1 * 

i® 

! 

^ Sec 

wdary 

(ana! 







1 

1 

1 

1 

1_ 

: 

'■ 

r 

R 

J 

_L_ 



h 

1 r 5 

1 

I 





K- 

1 

i 

_ L . 



1 

1 

1 

1 

1 



- 528 - 




r 

_ 




- 3280 

•4 



—i 

1 

1 

l 





Plan 


drain 


Road 


Cana! 



Sketch No. 221.— Reclamation of Alkaline Land at Lake Aboukir. 


feet of loamy clay, underlain by a stratum of sand, which affords a very 
efficient subsoil drainage. The plan was successful on the more easily re¬ 
claimed portions of the soil, but at the present date (1910), when the last 
remnants of the area are being reclaimed, a far closer spacing of the minor 
drains is found requisite, and the average size of a plot may be taken as about 
170 feet by 400 feet, instead of 330 feet by 500 feet. 

The average quantity of salt removed in the early days was about 8 lbs. 
per cubic foot of water pumped. This may be considered as very good work. 
At present, similar details cannot be given ; but it is probable that owing to the 
great amelioration affected in the whole area, not much more than 2 lbs. of salt 
per cubic foot of water is removed when the quantity which is used for re¬ 
clamation is alone considered. 

The above methods, combined with wider or closer spacing of drains (accord¬ 
ing to local circumstances), will usually suffice for the reclamation of any soil. 




























































































CONTROL OF WATER 


746 

A very fair estimate of the necessary spacing of the drains, together with 
their depth, can be made by observing the effect of two parallel drains on the 
slope of the subsoil water between them. 

The drains must be sufficiently deep and close together to keep the subsoil 
water level say 1, or 2 feet below the natural surface at the points farthest 
removed from them, and when cotton and other delicate crops are put in this 
depth must be increased to 3 or even 4 feet by deepening the drains or con¬ 
structing extra drains. 

A more rapid reclamation can usually be effected by means of shallow 
cross drains, which split up the plots into smaller areas. I have noticed that 
practical agriculturists in Egypt and India are quite capable of making these 
cross drains themselves ; and from their intimate acquaintance with each field 
they obtain better, and more economical results, than any regular spacing such 
as an engineer will lay out can give. 

The engineer’s business may be considered as finished once he has put 
in the drains shown in Sketch No. 221, and has designed them of such a size 
that the normal stoppage of the pumps ( e.g . at night) does not permit the 
water to rise higher than one foot below ground level. The details depend 
upon the staple crop, and must be adjusted in accordance with its peculiarities. 
The best results are of course obtained by first cultivating a crop such as 
Panicum crus galli, or coarse rice, later barley, and waiting some years before 
deeper rooted crops (such as wheat, or cotton), which are more easily affected 
by alkali, are sown. 

It will be plain that the principles here laid down might be modified. 
Thus, in some cases, open drains have been replaced by a system of covered 
tile drains, as used in England for draining agricultural land. A certain 
economy both in water and time was thus effected at Sakalous (see Barrois, 
Irrigations en Egypte). The method, however, is costly, and in certain 
cases near Cawnpore (“ Private Letter from the Director of Agriculture”), the 
drains were rapidly choked by particles of the soil, which appears to have been 
unusually fine in texture. 

So also, reclamation has been attempted by flooding large areas, and 
draining off the water, after a period of ten, or twenty days, when saturated 
with salt. The process is tedious, costly in water, and the banks are liable 
to damage by wave action. So far as I am aware, permanent success 
has never been attained, although the method may prove useful provided 
that systematic drainage is carried out as soon as crops can be grown on the 
land. 

In all reclamation work on soils of this class the engineer must bear in 
mind that the land should be handed over to the agriculturist as rapidly as 
possible. As soon as a crop of even the coarsest quality can be persuaded 
to grow over the whole surface of a plot, the further progress of reclamation 
entirely depends on the standard of the cultivation which the land receives. 
The engineer can damage the land by neglecting the drainage channels, or 
by giving a bad water supply. But once a plot of land has been reclaimed 
sufficiently to support a crop which is capable of resisting a little alkali, the 
most careful drainage and washing will produce but little progress unless 
supplemented by careful cultivation. The further improvement is apparently 
entirely due to diminished evaporation produced by the shade afforded by 
the crop. Such operations as mulching, surface-hoeing, and green manuring, 


AGRICULTURAL RECLAMATION 


747 

produce rapid improvement, and should be adopted in bad cases, even if not 
necessary for the crop actually on the ground. 

In Egypt and in India little difficulty is experienced in persuading 
agriculturists to rent and cultivate a plot which has produced a crop of 
coarse rice, beerseem (Egyptian clover), or Panicum crus galli. The leases 
should of course contain provisions preventing the obstruction of drains, or 
other interference with the drainage works. 

Soils belonging to the second class become alkaline through the salt 
contained either in the soil, or in the irrigation water, being carried up 
to the surface of the land, and concentrated there by evaporation. 

Although the natural content of alkaline salts in the soil has a certain 
effect, all water for irrigation contains sufficient salts to render the soil 
alkaline, if continually applied in excess, and allowed to stagnate on the soil 
and evaporate. We may therefore consider that if more water is applied to a 
soil than is required for vegetation, combined with the quantity which can be 
drained away through the lowest layers of the soil, the soil will sooner or later 
become alkaline. 

Where the soil itself contains an appreciable proportion of alkaline salts, 
the action will be more rapid. If the soil is naturally very alkaline to start 
with, one or two seasons of irrigation may finish the process. Over-irrigation 
will render any soil alkaline in time. 

It will be plain that the process is as follows :—Capillary action 
raises the excess water with its quota of dissolved salts to the 
surface. Evaporation then removes the water, and the dissolved salts 
are very rapidly concentrated at the surface, and stop, or impede plant 
growth. 

The best method of preventing such action consists in drainage with a view 
to removing the excess water. Prevention of evaporation, although of secondary 
importance, is also very helpful. 

The worst damage is caused by the application of a greater quantity of 
water than can be disposed of by vegetation and percolation. Therefore, 
accidents apart, the less permeable soils are those which most rapidly become 
alkaline. For this reason, the reclamation of soils rendered alkaline by over¬ 
irrigation, is a far.more difficult problem than the reclamation of naturally 
alkaline land ; since drainage difficulties are increased by the greater im¬ 
permeability of the soil. 

Precautions against alkalinity are consequently far more important than the 
reclamation of land which has become alkaline. 

As a rough index, the depth at which the subsoil water level lies below 
the natural surface of the ground is most easily ascertained ; although, as 
already stated, this does not allow for the effect of variations in the perme¬ 
ability of the soil. Orders exist in the Punjab to the effect that when the 
depth of water below soil level is less than 25 feet, only 25 per cent, of the 
land is to receive canal water each year, the remaining irrigation being 
effected from wells. When the water is more than 25 feet below soil level, 
and less than 40 feet, the permissible quota of canal irrigation rises to 
40 per cent. When more than 40 feet below soil level, the quota reaches 
75 per cent. 

I am not aware that these rules are ever enforced, and it may be stated 
that any rigid insistence would be inadvisable. They may be taken as 


CONTROL OF WATER 


748 

representing the percentage of area which it is desirable to irrigate when 
canal water is first introduced. Even so, it must be understood that the 
limitations apply to very large areas. Consequently, zones where the water 
is less than 25 feet below soil level, at the initiation of canal irrigation, 
may be considered as exposed to the danger of waterlogging not only by local 
irrigation, but also by percolation from large areas higher up the canal, where 
the subsoil water is more than 25 feet below the ground level. 

As a matter of fact, good crops are raised, and irrigation up to 75 per cent., 
and even no per cent, of the area of the land (allowing for double crops) 
goes on in places where the subsoil water level is only 6 feet below soil level, 
provided that : 

(a) There is a good drainage, provided by natural stream channels or 
artificial drains. 

(b) This intense over-irrigation, and high subsoil water, are local, and 
extend only over a small area, so that the subsoil water slopes are steep, and 
subsoil drainage is therefore good. 

It can generally be stated that such limited irrigation as is indicated above, 
under Indian conditions {i.e. corresponding to 3*1, 2’4, and r6 cusecs per 1000 
acres of gross area according to the depth to subsoil water) does not give rise 
to any very marked and continuous increase of the subsoil water level year 
after year. The alkaline soil question in the Punjab is (comparatively speaking) 
a very minor one, thanks not so much to the limitations of the percentage of 
the area irrigated, as to the economy in water exercised by the irrigators. 
While local limitations are badly required, no universal waterlogging has 
occurred when the water is supplied in quantities equal to those stated above, 
even although occasionally, and on isolated estates, a larger quantity has been 
allowed, and the subsoil level is close to the natural surface. 

The question is far more acute in Egypt. Here, in place of quantities of 
water as above mentioned, the supply for “dry” crops (corresponding to Indian 
conditions), is about 8 cusecs per 1000 acres ; and for rice about 16 cusecs per 
1000 acres. The slope of the country is much flatter, and, in consequence, 
the natural drainage channels which generally suffice in the Punjab are inade¬ 
quate, and artificial drains with a capacity of 3, to 5, cusecs per 1000 acres have 
to be constructed. 

Taking the case of the early American irrigators, who used 25, to 30 cusecs 
per 1000 acres, it is not surprising to find that virgin land was very rapidly 
rendered alkaline. Two years usually sufficed in unfavourable cases, and ten, 
to twelve years was almost the maximum period of fertility. On the other 
hand, some of the very carefully irrigated orchards of California, although 
undrained, and lying in hollows, such that the subsoil water is but 8, or 9 feet 
below the natural surface, show no signs of alkalinity, in spite of this accumu¬ 
lation of unfavourable circumstances. Salvation here is probably entirely due 
to the lining of the channels (see p. 740). 

The principles are therefore obvious. When the first signs of alkalinity 
appear, a drainage system should be laid out, and should be extended as neces¬ 
sary. Every possible means for securing economy in water used for irrigation 
should also be employed. 

As a matter of practice, when land has once become thoroughly alkaline 
through over-irrigation, it is usually found less costly to abandon the land and 
irrigate new tracts. This is not a desirable solution of the difficulty, but the 


SIL T 


749 

statement serves to emphasise the importance of taking preventive measures 
as soon as any alkalinity becomes apparent. 

There is a fair amount of evidence to show that if land becomes alkaline, 
and is at once reclaimed by washing, it will be found to have deteriorated in 
fertility, the salts essential for plant life having apparently been removed with 
the alkali. Thus, in Egypt, such lands are often treated by warping with silt, 
in the hope of restoring their fertility by the manurial value of the silt. 

Lands which have been alkaline for a long period, and are then reclaimed, 
do not appear to be thus prejudicially affected to any very marked degree. 

This is not easy to explain, as very little is known about the chemistry of 
such soils, but the matter must be borne in mind when such questions are 
dealt with. 

Silt. —The term silt is a convenient expression for all non-floating sub¬ 
stances carried forward by water flowing in rivers and canals, and may be 
contrasted with drift, which includes all floating substances. 

From an engineer’s point of view, two classes of silt exist, in all rivers which 
carry silt. These are : 

(i) Bed silt, which is rolled along the bottom of the river, rather than 
carried forward. 

(ii) Lighter particles of silt, which are carried forward in suspension in the 
water, as turbid matter, or suspended silt. 

If the journeyings of individual particles could be traced, it would probably 
be found that there were very few which were not sometimes included in the 
bed silt, and at other periods were suspended in the water; yet, the general 
characteristics of a sample of bed and suspended silt are widely different. 

The factor which determines whether a particle performs the greater part 
of its travels in the form of bed or suspended silt is evidently the relation 
between its size and the velocity of the water near the bottom of the channel. 
If this velocity (as discussed on p. 488) is large enough to lift and suspend the 
particle, it will (except for certain short periods between jumps) be lifted off 
the bottom of the channel and will be carried forward. Whereas, a somewhat 
larger particle will be rolled forward as described in the above reference. 
Hence, the larger and coarser particles of the silt form the bed silt, and the 
finer particles are carried forward in suspension. Consequently, bed silt is 
coarser and more gritty than suspended silt, and may be said to be a sandy 
material; while the suspended silt is (comparatively speaking) clayey. Rivers 
exist where the term gravelly might be substituted for sandy, and then of 
course the suspended silt would be mainly sandy in nature ; but the relative 
distinction remains, and once this distinction has been pointed out, there is 
very little doubt as to the class to which a deposit should be assigned. 

The term “rolling,” can hardly be considered to correctly describe the 
manner in which bed silt travels. When a channel is examined which is 
heavily charged with silt, it will be found that the bottom usually forms a series 
of steps rising about T in 20' and then dropping on the downstream side at 
1:1, much like a flat sand dune. It would therefore appear that the motion 
of the particles of bed silt is probably as follows ; the entire upper layer moves 
up the long slope, and then falls down to rest at the bottom of the short slope, 
so that each wave moves forward by means of an internal motion of pai tides 
from back to front of the wave, in a manner similar to sand dunes under the 
influence of air currents. 


CONTROL OF WATER 


75° 

The silt content of the water of a river is produced by the erosion of the 
catchment area by the river and its tributaries. In a canal or irrigation channel, 
which does not receive small tributaries, it will be plain that the silt content 
is entirely due to the two following sources : 

(a) Silt derived from the river or reservoir supplying the canal ; which I 
shall call “ original silt.” 

(b) Silt which the water has eroded from the banks or bed while in the 
canal ; which I shall call “derived silt.” 

Precautions against silt troubles consequently have the two following objects : 

(i) To pass forward or remove the original silt contained in the water as 
drawn from the source of supply of the canal. 

(ii) To prevent the occurrence of derived silt, by stopping erosion of the bed 
or banks of the canal. 

If the headworks of the canal are properly designed, the original silt will 
mainly consist of suspended silt. A considerable proportion of the small 
amount of bed silt which is taken into the canal may be removed by silt traps, 
or escapes. On the other hand, derived silt contains a larger proportion of 
bed silt; and, since erosion may occur at any point, it is difficult to provide 
effective silt traps and escapes. Consequently, the prevention of erosion is 
very important, since, so far as my experience goes, bed silt invariably gives 
trouble. Suspended silt, on the other hand, may be regarded as a favourable 
factor, as it rarely produces trouble, and can be caused to deposit itself so as to 
diminish leakage and strengthen weak places in the canal banks. 

It is well known that erosion occurs if water travels at velocities which 
exceed certain limits. It is quite impossible that such erosion should con¬ 
tinually prevail in an earthen channel, as it would ultimately destroy the 
whole channel. Thus, the erosion which is detrimental to the maintenance of 
earthen channels is accomplished at velocities which are less than the limits 
spoken of on page 495, and is principally conditioned not by the absolute 
magnitude of the velocities, but by irregularities and sudden changes in 
velocity. It is therefore extremely important that the channels should be 
uniformly graded, and that they should be correctly proportioned to the 
quantity of water which they are required to carry. The systematic design of a 
channel on these lines is detailed on page 733. It may be assumed that such a 
channel (provided that it is not required to carry quantities varying greatly 
from those for which it is designed) will, in virtue of its correct proportioning, 
be liable to but slight erosion. 

The principle is best illustrated by the case of the Ibrahimiah Canal. In 
former years this canal silted very badly. The silt was not originally contained 
in the water as it entered the canal from the Nile during the low water season, 
but was derived silt, produced by the erosion of the banks in the upper length 
of the canal where the floods of the Nile annually deposited a fresh supply. 
The annual quantity of silt removed has now been reduced from 600,000 cubic 
metres, to 100,000 cubic metres, by the construction of stone groynes which 
prevent the high flood waters from eroding the banks to a section which would 
be too large for the normal discharge of the canal during the low water 
periods. 

So also, Sketch No. 222 (adapted from Buckley’s Irrigatio?i Works of India) 
shows upstream, a canal head taking off at too large an angle from the river. 
Consequently, the flow of the canal is set oscillating from bank to bank, and 


HEAD REACH ALIGNMENT 


75 1 


alternate patches of scour and silt (analogous to the deeps and shallows of a 
natural river) occur. In the downstream canal head, the water enters the 
canal in a fair curve, and the revetment of stones round the head guides the 
water in so regular a fashion that scour below the revetment is improbable. 
The flow remains tranquil ; and, as a result, the banks are not attacked. 

The large scale plan of the Rupar Heaclworks (see Sketches Nos. 163 and 
200) illustrates a somewhat similar theory. In this case the head reach is 
actually located so as to be directed somewhat upstream. An even more 
marked upstream direction has been proposed by Willcocks for the head reach 
of the Hindan (Mesopotamia) Canal (see Engineering , May 31, 1910). The 
advantages gained by designs such as these last two are somewhat doubtful. 
The Sirhind Canal silted badly (sec p. 659). The principle should be kept in 
mind, especially when an inundation canal, or a canal unprovided with a 



“ raised sill ” head regulator is being designed, but it is probably inadvisable to 
adopt such locations if they entail deep cuttings. 

If a river carries but little silt, and that in a suspended state, and if the bed 
of the canal is also well above the bed of the river, such precautions combined 
with careful proportioning of the cross-sections of the individual leaches of the 
canal will banish silt entirely. Thus, in cases where the initial content is not 
large, and erosion does not occur, the rules are simple, and are as follows : 

(i) The mean velocity must not exceed a certain value ; which in the case 
of the most easily eroded alluvial soil, may be taken as 3 3° feet per second, 
and for more tenacious soils rises to 3-50, 370, or even 4-00 feet per second. 

(ii) The mean velocity must not fall below certain other values, which are 
those necessary to carry forward the major portion of the silt found in the river. 
As preliminary rules we rpay say that the canal should carry all the suspended 
silt, and about three-quarters of the bed silt found in the river, the proportion 
obviously depending on the care taken in locating the head reach. 












CONTROL OF WATER 


75 2 

For example, Willcocks (. Egyptian Irrigation ) gives the following rules for 
Egyptian canals, the headworks of which are located in accordance with the 
principles now discussed. 

Mean Velocities. 

2*3 to 3'3 feet per second (070 to 1 metre per second) :—No silt is 
deposited. 

i'97 feet per second (o'6o metre per second) :—07 metre depth of silt is 
deposited, i.e. about one-sixth or one-eighth of the area of the canal 
section is silted up during the flood season. 

1*64 feet per second (070 metre per second) :—1 metre of silt is 
deposited. 

1'33 feet per second (070 metre per second) :—mud is deposited. 

Hence, a velocity exceeding 3*3 feet per second produces erosion of the most 
easily eroded Egyptian soils ; which agrees with the figures for Punjab soils. 

With a velocity less than 17 foot per second, the suspended silt is not 
carried forward. 

It is consequently plain that a velocity of 27 to 3 feet per second is 
the best. 

The above figures refer to canals the beds of which are from 12 to 15 feet 
(37 to 4*6 metres) above the bed of the river, and which take out in situations 
similar to the downstream canal head (see Sketch No. 222), or, as Scott 
Moncrieff (A J ote on Sharakiin 1882) (see also Willcocks, ut supra, p. 76) states : 
“ The practice of the Arab engineers was to align their canals under the 
following rules : 

(i) “The offtake shall be taken off the deep water of the Nile when it is 

running along the bank from which the canal is taken, and the canal 
axis shall be as nearly as possible a tangent to the general curved 
sweep of the Nile’s central current in the curved reach.” 

(ii) “ When the canal must be taken off from a straight reach, the Arab 

engineers take it off at a very acute angle to the Nile’s axis.” 

(iii) “The Arab engineers attach much importance to having deep water 
in the Nile at the offtake, and are always ready to abandon any 
canal head that takes off at a point in the Nile where a sand bank 
is forming. I consider that they find from experience that coarse 
sand which rolls along the bottom of the Nile bed does not enter 
the canal unless the Nile bed has become silted up by a sand bank 
to nearly the level of the canal bed.” 

The above rules can be summed up as follows : 

(i) Keep the Nile bed silt out of the canal. 

(ii) Prevent the formation of bed silt in the canal by stopping erosion of 

the banks either by groynes, or by pitching; or better still, by keep¬ 
ing the mean velocities sufficiently low to prevent erosion, and 
designing the canals so that sudden changes in velocity which 
produce eddies do not occur. 

The bed silt being but a minor factor, the rules for the lower limit of the 
velocity can be summed up in the single statement : 

(iii) Keep the velocity sufficiently high so as to move forward the sus¬ 

pended silt, together with the little bed silt which has entered. 


KENNED Y’S LA W 


753 


The conditions are somewhat different in the Punjab. At least three out of 
the six rivers are of the same order of magnitude as the Nile, but their bed 
slopes near the canal headworks are from to -toVcn pl ace of T1 ^ 00 , in 
the Nile. The rivers are consequently shallower. Thus, in spite of all the 
provisions for regulating the rivers, and skimming the'clearer water (see p. 660), 
it is found impossible to prevent a certain amount of the river bed silt from 
entering the canal. In fact, personal observations lead me to believe that 
every Punjab canal receives initial silt in quantities which are comparable to 
those occurring in a very badly situated canal on the Nile, where Scott 
Moncrieffs condition No. (iii) is entirely disregarded. In such cases, the bed 
silt is the most important factor, and merely to prevent erosion in the canal 
itself is not sufficient to obviate silting. We must so proportion the canal that 
the initial bed silt is not deposited, but is passed on to the fields. 

Our knowledge of the precautions necessary in order to keep channels 
fairly free from silt deposit is almost entirely due to the investigations of Mr. 
R. G. Kennedy (Graphic Hydraulic Diagrams , and P.I.C.E ., vol. 119, p. 282) 
on the Bari Doab Canal. As, however, his principles have been found valuable 
on other canals in the Punjab, where local conditions differ very greatly from 
those existing on the Bari Doab, and have stood the test of sixteen years’ 
practical use, it seems advisable to carefully describe both these conditions, and 
Mr. Kennedy’s observations. 

The Bari Doab Canal receives water from the Ravi River, a snow-fed 
Himalayan stream, which is in flood during the greater portion of the hot 
weather (May to September), and is then intensely turbid, rolling heavy 
boulders along its bed ; while surface velocities exceeding 20 feet per second 
are frequently observed. In the cold weather (October to April), the river,— 
except for freshets of infrequent occurrence,—is a clear water stream. During 
the hot weather the supply of water in the river far exceeds the requirements of 
the canal. Nevertheless, irrigation continues during the whole of the flood 
season, and it is only rarely that any closure of the canal for the rejection of 
silted water is possible ; whilst the headworks are so constructed that the 
engineer in charge has but little chance to select the less heavily loaded portions 
of the water. 

We are therefore entitled to assume that the Bari Doab Canal is fed for six 
months with water which is more heavily charged with silt than that which is 
usually admitted into Punjab canals. On the other hand, a clear water season 
lasting six months, is unusual on other Punjab canals. 

It is, however, very probable that the average (over the whole year) volume 
of silt per unit volume of water is very much the same as it would be were the 
headworks of the Bari Doab (like those of most other Punjab canals) situated 
somewhat lower down the river, where the stream is less torrential in regime. 
It would then be possible to reject a certain quantity of the more heavily silted 
water during the hot weather, as the relatively less torrential river would be 
under better control. On the other hand, during the cold weather the river 
would carry more silt than higher up its course at the same season, as the 
originally clear water of the cold weather season picks up the silt which is 
deposited in the intermediate course during the hot weather floods. 

Mr. Kennedy’s observations were mostly made on branches and minor 
distributaries of the Bari Doab, situated at least 50 miles below the head- 
works. The turbid and clear water periods are by no means clearly defined in 

48 



754 


CONTROL OF WATER 


these cases, as some silt is deposited in the intermediate channels during each 
period of turbid water, and is picked up and swept forward during the period of 
clear water. In a general sense the action is similar to that which has been 
described as occurring in the natural river channels of the Punjab. 

Records of the character of the water do not exist ; but, judging from my 
own observations (taken after Mr. Kennedy’s principles had been systematically 
applied), it may be assumed that the period of turbid water in these channels 
lasted some eight months, and was followed by a period of four months of more 
or less clear water. The nett effect, therefore, was to produce in every channel 
under Mr. Kennedy’s control, a period of about eight months during which silt 
was deposited in the channels, and a succeeding period of approximately four 
months during which the channels were scoured. The circumstances were 
consequently very similar to those prevailing close to the headworks in other 
Punjab canals. 

In most cases, the result was a constant increase in silt deposits, and had 
not the channels been cleared each year, they would have been more or less 
rapidly silted up. 

Mr. Kennedy discovered twenty-two channels in which, year in, year out, 
the deposits during the silting period were scoured out, and were swept forward 
during the corresponding clear water period ; and as a nett result these twenty- 
two channels were unaffected by silt deposits ; eight other cases in which the 
nett silting or scour was small were also found. After very exhaustive investiga¬ 
tion of the whole circumstances, Mr. Kennedy concluded that these channels 
were characterised by the fact that the mean velocity of the water bore a certain 
relation to the depth. Hence, he deduced the following law : 

v 0 — 0-84^° ,C4 

Whence, if 

d = i 234 5 67 89 10 12 feet. 

7/0 = 0-84 1-30 1-70 2-04 2-35 2-64 2*92 3-18 3-43 3*67 4-12 feet per second. 

Where : 7/ 0 = the mean velocity in feet per second in a channel that neither 
silts nor scours (a Kennedy channel) (see p. 727). 
d— the depth of channel in feet. 

Mr. Bellasis has observed that the expression 

v 0 — I-05 Vd 

represents the actual observations nearly equally well. 

This description of Mr. Kennedy’s observations is purposely intended 
to disclose the apparently slight foundations of the rule. When the rule 
became well known, they were systematically applied to determine the form of 
the cross-section of the channels on the whole of the Lower Chenab Canal 
(approximately 2,000,000 acres of irrigated land), and to a large portion of the 
Lower Jhelum Canal (approximately 600,000 acres of irrigated land). The 
conditions affecting the silt deposits in these two canals differ greatly from those 
which prevail on the Bari Doab. 

The Jhelum silt is finer than that of the Bari Doab, but the clear water 
periods rarely last more than a month. 

The Chenab silt is somewhat coarser than that of the Bari Doab, but the 
clear water period lasts about two months. 


KENNED Y'S LA W 


755 


The general effect of adopting Mr. Kennedy’s rules has been a large 
decrease in silt clearances on all three canals. A similar decrease in silt 
clearances has also been effected on other Punjab canals. 

These rules have been thoroughly tested, as they have formed the basis for 
nearly all remodellings of the Punjab canals for the last eight years. Following 
the usual custom of a Government service, it may be said that they are now 
applied somewhat blindly. While this method is not so advantageous to the 
interests of the Government as a more elastic system, it has at any rate secured 
a very interesting large scale test of the laws affecting such channels. 

A consideration of all the information which I have been able to obtain, 
combined with the detailed results of my own experience in preventing silt 



deposits in about 200 miles of small channels (which had been designed with 
no attention to Kennedy’s rules), has led to the following conclusions : 

(i) The duration of the clear and turbid water periods has but little influence 
on silt deposits when the rules are properly applied, and a channel can be 
designed which will carry turbid water the whole year round, without silting. 

(ii) On the Punjab canals, bed silt is in motion all the year round, whether 
the water is clear, or turbid. While the motion is more rapid in periods of 
clear water, there is little, if any, difference in the volume carried forward. 
Probably, therefore, in periods of turbid water, the bed silt is in motion over a 
greater depth. 

(hi) Mr Kennedy’s rule, that the least velocity at which silt is not deposited 

is given bv the equation : 

5 ' V 0 = cd»'«\ 


is correct for all classes of silt that occur in the Punjab. 

Jlie value £ = 0*84, however, is peculiar to the Bari Doab Canal ; and slight, 


































CONTROL OF WATER 


75 6 

but quite noticeable differences may be observed not only on the different canals 
of the Punjab, but also on the various reaches of the same canal as we go down 
the canal. If a sample of silt is collected from the bottom of a canal, and is 
tested by the grading tube described on page 758, it will be found that c, is very 
approximately proportional to the percentage of silt of which the velocity of fall 
in still water is greater than o’10 foot per second. The value ^=0*84 corre¬ 
sponds very fairly well with a silt in which 40 per cent, of the grains fall more 
rapidly than o‘io foot per second. This last rule is only approximate, but the 
differences which I have observed (although quite apparent in careful experi¬ 
ments), are never sufficiently great to cause a channel designed by these rules 
to silt up to such an extent that any noticeable deposit is produced in a period 
of one year. The further clearance necessary in the second year to shape the 
channels so as to produce a truly non-silting channel is but small. 

Thus, if even one channel on a new canal is found to work properly, and 
to be unaffected either by scour or by silting, it is only necessary to observe 
its mean velocity and depth in order to obtain c , and then the preliminary 
design for the non-silting sections of all other channels on that canal is reduced 
to a very simple calculation (see p. 768). 

(iv) The bed silt in a channel designed according to Kennedy’s rules, 
moves far more rapidly and uniformly than in a channel carrying the same 
quantity of water, but with a smaller mean velocity in proportion to its depth 
than is given by Kennedy’s rules. Thus, if at any point in a Kennedy channel, 
the motion of the silt is disturbed, and local silt deposits occur, these deposits 
will be far more intense than those which are produced by a similar disturbance 
or obstruction in a channel which is not designed according to Kennedy’s rules. 

Kennedy channels are therefore somewhat more easily put out of regime 
than other channels, and are liable to heavy local deposits of silt. In many 
cases, the cause is easily recognised, since a sharp curve in the channel, a 
bifurcation, or a bridge, are well known to be disturbing influences, and the 
Punjab rules of design provide for such eventualities. Certain less easily 
recognised disturbing causes also exist, such as a patch of hard clay projecting 
above the general bed level, or an almost buried tree. Consequently, while 
the volume of silt that is deposited in a Kennedy channel is relatively small 
the channel must be very carefully inspected, and Kennedy’s rules are often 
considered useless by engineers whose ideas of careful inspection are derived 
from experience of ordinary channels. 

I must remark that many engineers in the Punjab who have given quite as 
much consideration to the question, and who possess greater experience than 
myself, disagree with me as to rule (i), while other engineers may consider 
rule (iii) as an unnecessary refinement. These gentlemen, however, usually 
have experience of only one canal, and very few of them have enjoyed the 
opportunity for systematic observation which was my lot for nearly three years. 

It appears to me that the application of Kennedy’s principles to all canals 
carrying silted water must become universal, and it seems necessary to explain 
why they have not as yet been discovered and applied outside the Punjab. 

In the first place, it must be recognised that Kennedy’s rules do not in any 
way minimise silt deposits, but rather the reverse : they merely alter the place 
where the deposits occur. The silt is no longer dropped in the channels, and 
removed during the yearly clearance, but is carried forward and deposited on 
the fields, or in the small field watercourses. This is no doubt a far easier 


SILT GRADING 757 

place to deal with silt ; and under the conditions obtaining in the Punjab, the 
lesult is to shift the labour of silt removal from the staff responsible for the 
maintenance of the canals, on to the agriculturists, who find that their water¬ 
courses silt up more rapidly than was previously the case. 

The silt of the Punjab canals frequently possesses fertilising properties, and 
is very rarely absolutely injurious to crops. Thus, the Punjab agriculturist is 
well content to undertake the extra labour entailed, fully realising that he 
thereby obtains a more certain supply of water. 

In Southern India, however, the silt is of a more sandy nature, and the 
general size of the grains is far greater than in the Punjab. No agriculturist 
can therefore be expected to view the prospect of the continual deposition of 
such silt upon his fields with equanimity. Consequently, in Southern India and 
in similar cases ( e.g . most of the United States’ silt-bearing waters, other than 
those of the Colorado River), a servile application of methods adopted in the 
Punjab would be inadvisable. 

Nevertheless, I believe that many advantages can be obtained by the 
application of Kennedy’s principles so as to secure that the silt is mainly 
deposited in selected channels where land suitable for the disposal of such 
deposits is available. Such selected channels might be regarded as silt traps, 
and could either be systematically and continually cleared, or could be con¬ 
structed in duplicate, so that the channels could be alternately closed off and 
cleared without interfering with the regular supply of water. 

In Egypt, as has already been explained, owing to the flatter slope of the 
river, and its relatively deeper bed, it is usually possible to exclude nearly all 
the troublesome bed silt. The general slope of the land is also so flat that, 
if bed silt enters the canal in large quantities, it is almost impossible to obtain 
a mean velocity which is sufficiently great to carry it forward. 

General Principles. —We may divide silt-bearing rivers into the two 
following classes : 

(a) The Egyptian, where the slope of the river is flat. 

(b) The Punjab, where the slope is (comparatively speaking) steep. 

The dividing line may be roughly taken as slopes which are flatter or 
steeper than 75V0. 

In the first case, coarse silt ( i.e . silt which falls in still water at a velocity 
greater than o - io foot per second), is not very abundant. It will be found that 
it is usually possible to prevent any large quantity from entering the canal. 
Such coarse silt as enters the canal will usually (the canal being obviously 
graded at a slope which is at most only one-half that of the river, say at the 
steepest yo^oo)> be deposited close to the head, and can be removed. The 
canal water being thus deprived of the initial silt, any further silting is entirely 
prevented, provided that erosion does not occur. 

The Egyptain rules have already been given. 

So far as I am aware, the figures for other localities of a similar character, 
differ very slightly from those for Egypt, but an observation of existing 
channels will easily disclose any small differences. 

The second, or Punjab class, can be recognised by the fact that samples of 
silt taken from deep channels of the river contain an appreciable percentage 
(say over 20 per cent.) of grains which fall in still water with a velocity exceed¬ 
ing crio foot per second. The slope of the river varies from t0 soW? 



75 8 CONTROL OF WATER 

larger percentages of coarse silt usually occurring in those rivers which possess 
the steeper slopes. It is then impossible to prevent an appreciable quantity of 
coarse silt from entering the canal. The slope of the canal being about one- 
half that of the river, it will be possible to pass this silt forward to the fields, 
provided that the canal is proportioned according to Kennedy’s law. Con¬ 
sequently, the important factor is the value of c , in the equation : 

v 0 =cd? M 

This is best ascertained by a direct observation of the mean velocity and 
depth of a channel which is known not to silt. In default of such expeiience, 
samples of bed silt may be taken, and the percentage of coarse silt, as above 
defined, can be observed, and c, can be calculated by the rule : 

C84 p 
40 


where p, is the percentage of coarse silt (see p. 768). 

Either method may lead to erroneous results, for the following reasons. 

A channel which does not silt may be so situated that the conditions are 
unusually favourable (eg. its head may be very well placed on a deep channel 
of the river), and may carry less silt than is the case with the channels of the 
proposed system. Thus, the silt deposited in the bed of such a channel should 
be carefully classed and compared with the silt which is normally found in 

o ‘84/ 

the rest of the channels which take out from the river. The rule 

is founded solely upon experience gained in the Punjab, and may be too high 
for rivers in which the average content of silt per unit volume of water is less 
than that in the Punjab rivers, or too low for rivers which carry a larger. 
proportion of silt. My own experience, however, leads me to believe that if 
Kennedy’s principles are intelligently followed, the first designs for the cross- 
section of a channel will be so close to the required form that the silt deposit 
during the first year will give but little trouble. Consequently, the true form 
can be obtained, and the channel can be constructed during the clearances 
which are necessary at the end of each season owing to the growth of weeds. 

Grading of Silt. —Sketch No. 224 shows the silt classifier used in the 
Punjab (see Punjab Irrigation Branch Papers , No. 9). The glass is graduated 
into divisions, having a volume of o’ooi cubic foot. One-tenth of a cubic foot of 
silt is thrown into the water, and the intervals are noted at which the falling 
sand fills the tube up to the first, second, third, etc. marks. Let us assume 
that the first grains reach the bottom of the tube in 26 seconds, and that the 
tube is filled to mark No. 10 in 65 seconds. Then, the heaviest grains fall 
6'5 feet in 26 seconds, or, have a velocity of o’25 foot per second, and 10 per 
cent, by volume of the individual grains fall with a velocity greater than 
o*io foot per second. This fact is expressed by the notation 10 per cent, of the 

silt is of the grade *-. 

The apparatus is simple, and for that very reason the results obtained by 
its use do not possess the accuracy that can be obtained by the use of upward 
flow graders. The observations, however, can be taken by comparatively 
unskilled men, and the apparatus consequently deserves to be used in practice. 
It will be seen that by a systematic use of such an apparatus the engineer may 




SILT DEPOSITS 759 

expect to im p r ° ve his designs. In our present state of ignorance concerning 
silt deposits any further refinements are useless, and even detrimental if their 
adoption decreases the number of observations. 

The following figures are taken from the above report on the River Sutlej 

Velocity Tube 



Water Surface 


Escape 

Rubber Ring 

Graduated Glass 

Rubber "Ring- 
Set Screw 


Sketch No. 224.— Silt Classifier. 


and the Sirhincl Canal, which is fed from this river, but they may be considered 
as typical of all Punjab rivers. 

By actual experiment it is found that suspended silt (even in a canal which 
is silting heavily) rarely contains any grains that fall with a greater velocity 
than 0*20 foot per second ; and, for the most part, the velocity of fall is less 






















76 o CONTROL OF WATER 

than o'io foot per second. The following gradings occur in the Punjab rivers 
when in flood : 

PERCENTAGES. 


Grade °'° 5 

O'IO 

Grade 

O 20 

0‘20 

Grade- 

0-30 

Grade °'° 5 

OIO 

O'IO 

Gra<3e 0-20 

Grade °’ 20 
0-30 

5 ° 

5 ° 

0 

66 

34 

0 

6 5 

3 ° 

5 

44 ' 

42 

14 

3 8 

37 

2 5 

• • * 

• • • 

• • • 


although ioo per cent, of grade is more usual, and always occurs when the 
river is not in flood. 

The deposits on the river bed during the cold weather or low water season, 
close to the head of the Sirhind Canal, are of the following character: 


O'OO 

Grade- 

0-03 

Grade —f 
0-05 

OTK 

Grade —^ 

O’IO 

O'IO 

Grade- 

0'20 

Grade 

0-30 

26 

14 

5 ° 

' 7 

3 

8 

2 

57 

28 

5 

48 

IO 

37 

5 

0 

48 

10 

3 2 

10 

0 

3 ° 

IO 

46 

11 

3 


The grading of the deposits in the canal is best exemplified by the following 
table : 


Locality. 

Grade 

O'OO 

O'IO 

Grade 

O'IO 

O '20 

Grade 

'0'20 
k_ 

0-30 

Grade 

°‘ 3 ° 

0*40 

Grade 

0-40 

o'6o 

Main Line— 






10,000 feet below head . 

4 

5 ° 

3 ° 

9 

7 

^Sj^OO 5 > 5 ) 

7 

65 

21 

4 

3 

20,000 ,, ,, 

5 

53 

28 

7 

7 

25,000 ,, ,, 

6 

5 2 

28 

7 

7 

Branch Line— 




150,000 feet below head 

28 

56 

1 2 

4 

0 

170,000 „ „ 

29 

57 

11 

3 

0 


The above figures are confirmed by many other results. A certain propor¬ 
tion of the grains are of local origin, being derived from the adjacent banks 









































































MOTION OF SILT 


761 

and bed of the canal, which was silting badly at the time at which these 
observations were taken. 

Hence, the following points are fairly obvious : 

(' a ) Grains of a grade are rapidly moved along the canal. 

(0 Grains of a grade are hardly moved at all, and therefore : 

(c) [ he silt which gives the greatest trouble is the grade and the 

°' 3 ° 

quantity of this grade entering the canal is a very close measure 
of the amount of troublesome silt. 


A study of samples taken from Kennedy channels suggests that, in such 
channels the demarcation between bed silt and suspended silt differs somewhat 
from that given by the above figures, which refer to a canal which was silting 
heavily. The matter is not of great importance, but my own experiments show 
that some Kennedy channels pass forward appreciable percentages (5 to 10 

per cent.) of sand of a grade This property is advantageous to the canal 

engineers, but I doubt whether it will prove permanently satisfactory to the 
agriculturists who have finally to receive and dispose of such coarse silt. 

Silt Traps .—In all canals it is found that the first reach below the head is 
subject to relatively large deposits of silt. The cause is obvious :—The change 
of the direction of the motion of the water as it enters the canal creates a 
disturbance which lifts silt from the river bed, and this lifted silt is drawn into 
the canal. 

As an example :—On the 28th July 1896, in the River Sutlej, 10 cubic feet of 
water just below the regulator contained o'oo2 cubic foot of suspended silt, of 
the following grades : 

0*05 o*io 


Grade . 
Percentage 


O'lO 


5 ° 


0*20 


5 ° 


Ten cubic feet of water drawn from the canal just below the regulator 
contained 0*004 cubic foot of suspended silt, grading as follows : 


Grade . 
Percentage 


°'°5 

0*10 

0*10 

0*20 

74 

2 I 


0.20 

°' 3 ° 

5 


The first sample was taken from water flowing at a velocity of about 3 feet 
per second, and the second from water which was flowing at a velocity of about 
2*5 feet per second. Thus, a priori, we might expect the second sample to 
contain a smaller quantity and a finer quality of silt. The difference is due to 
the fact that the water in the second sample had been passed through the 
openings of the canal regulator, and had there attained a velocity of 3*5 to 4 
feet per second. This, per se , would not entirely explain the difference, but 
in addition this increase and decrease in velocity had produced swirls and 
vortices in the water, so that silt was picked up from the bed of the river in 
front of the regulator. 

The action can be observed at and around any bridge pier. The nett result 










762 


CONTROL OF WATER 


is that the first sample in reality represents the suspended silt in the river, while 
the second sample represents a mixture of the suspended silt and the bed silt 
in the river. Consequently, the vital importance of preventing the river bed 
silt from ever Approaching the canal head is obvious ; and it should be 
remembered that these observations were obtained when the water was drawn 
in over a sill raised 3 feet above the river bed. 

The nett result, therefore, is that before the water in the canal can have the 
same silt content as the river, each 10 cubic feet of water must drop about 

o'oo2 cubic foot of silt of the grade ——and about o'ooo2 cubic foot ot the 

grade Similar figures could be obtained for all rivers, and the above 

0-30 

example is by no means an uncommon one ; although the extra amount 
of silt is probably greater than that which is found in the more favourably 
situated canals. 

Putting aside the temporary extra loading of silt caused by the disturbance 
produced by the change in direction which occurs at the canal head (and also 
by the regulator if one exists) it is probable that most canals are not capable of 
carrying so large a proportion of silt as the river from which they take out. In 
the head reach of the canal the quantity of silt in the water is changed from 
that which prevails in the river, to that which the slope and dimensions of the 
canal permit it to carry. Thus, not only is all the silt which has been 
temporarily picked up dropped in the head reach of the canal, but also a 
certain portion of the silt which is normally carried forward by the water of 
the river. 

The quantities of silt thus deposited may be enormous. For example, in 
the month of July 1896, the deposition in the first 14 miles of the Sirhind Canal 
was at the rate of 0*55 cubic foot of silt per 1000 cubic feet of water passed down 
the canal, and far larger figures occur (see Punjab Irrigation Papers , No. 9). 
It will, however, be found in every case that a well defined distance from the 
canal head exists beyond which this silt of adjustment is not at first deposited 
in marked quantities. I say at first,—because, if the silt is permitted to 
accumulate at the head of the canal, sooner or later this head deposit will begin 
to move down the canal. I am not therefore definitely prepared to state 
whether the limited length of canal inside which the main deposit occurs is 
caused by some physical law of silt deposit (eg. is determined by the relation 
existing between the mean velocity of water in the canal, and the rate at which 
silt particles fall in water moving with this velocity) or, is in reality dependent 
upon the length of time during which the silt has been accumulating, and is 
therefore essentially an artificial matter, more or less under human control. 
Personally, I incline to the former view, for in cases where the canal has been 
neglected and more than the normal quantity of silt is deposited, the deposit of 
silt does not usually extend farther down the line ; but the whole mass moves 
bodily forward, and a wave of deposited silt travels slowly down the canal. 

This observation, however, cannot be regarded as conclusive ; since, when 
such waves are observed, there has usually been a change in the method of 
drawing water into the canal, and it is uncertain whether the wave is not 
caused by the endeavours to clear the canal. 

The distance within which the major portion of the silt is deposited is of 
great practical importance, since this knowledge enables us to fix the most 




HEAD REACH DEPOSITS 


763 

suitable sites for silt traps and scouring escapes. I regret that I am unable to 
give any definite rules for determining the distance. In rivers which carry so 
fine a silt as that which is found in the canals of the Punjab, it is measured in 
miles ; being about 14 miles in the case of the Sirhind, and about 10 in the 
case of the Jhelum Canal. While, in rivers carrying coarser sand, as in 
Madras, it appears to be about four miles ; and in the case of gravel or 
boulders, about half a mile. 

Broadly speaking, the finer the silt, and the wider the canal, the greater is 
the distance, and the above figures refer to canals 100 to 200 feet wide. 

In certain cases, as in inundation canals, or flood water canals, and in rivers 
such as the Nile, where the canal head has no regulator to set up disturbances 
in the w T ater, and where the first reach of the canal takes off nicely from the 
river (so that no unnecessary disturbance occurs), and above all where the bed 
of the canal is situated well above the river bed, it is possible to prevent a large 
quantity of harmful silt from entering the canal. In these cases, the canals 
usually run dry after the flood is over, and the small deposit of silt that has 
occurred can be dug out. Usually, however, some, or all of the three con¬ 
ditions given above must be violated, and disturbances occur in the motion 
of the water. Silt is then inevitably drawn into the canal, and the means of 
removing it, or minimising its effects must be considered. 

The most efficient method of clearing away this deposit of “adjustment” 
silt, is to admit (in seasons when the river water carries less silt than is usual) 
water in excess of that which is required for irrigation, and to pass off this 
excess by means of a special escape. The effect is obvious :—The cleaner 
water, which moves at a higher velocity than usual, picks up the bed silt; and 
this temporarily suspended matter is carried away with the escaping water 
(see p. 702). 

The details of the process require some consideration. In the first place, it 
is the bed silt, or rolling silt, that causes such deposits. Thus, although a very 
turbid water u-sually carries a large proportion of bed silt, the turbidity of water 
as judged by the eye is by no means an infallible index of the quantity of bed 
silt, especially as relatively clear water often carries a certain quantity of un¬ 
usually coarse grained bed silt, and may therefore be extremely undesirable for 
scouring purposes. Consequently, every opportunity should be taken to secure 
samples of the bottom layers of water, and the engineer in charge should 
accustom himself to rely upon the results of such samplings, rather than on an 
inspection of the upper layers (for that is what judging a water by its visible 
turbidity really amounts to). 

Secondly, the escape sluices should be designed so as to draw water from 
the bottom of the canal, rather than from the top ; and raised sills and similar 
kindred devices such as are used in regulators are out of place in escapes. 

It is also obvious that unless the canal is completely closed below the escape, 
a silt wave of the character already described may be set up, and part of the 
temporarily suspended silt may be carried into the canal below the escape, and 
dropped there. 

Clear water periods in a river obviously coincide with low water periods. If 
the capacity of the canal, as compared with the low water flow of the river, is 
large, it may be impossible to spare clear water for scouring purposes, since the 
more urgent demands of irrigation absorb all the available supply. 

For these reasons, escapes have now grown somewhat out of fashion, and 


764 


CONTROL OF WATER 

the newer Punjab canals, when compared with the older ones, are badly 
provided with escapes. In Egypt also, scouring escapes are not employed. 
Nevertheless, wherever an escape exists, and clear water is available, the 
engineers in charge are very glad to make use of it. I therefore considei that 
escapes should be provided wherever the canal crosses a drainage or small 
stream at such a relative elevation that the water can be rapidly run oft. The 
floods of the stream can then be relied upon to carry away the silt. On the 
other hand, escapes discharging into long, artificial channels, only change the 
location of trouble. Such escapes are rapidly rendered useless by the escape 
channel silting up, while any further discharge of silt and water merely floods 
and deteriorates the low lying land near the escape. 

The usual mistake made in the location of escapes is that they are placed 
too close to the head of the canal. Escapes have proved most successful in the 



Sirhind Canal (referred to above), and the most effective escape is situated 
12 miles below the head. 

As a general rule, no escape which is not removed from the headworks at 
least three-quarters of the total length of the adjustment section (in which silt 
is deposited) will keep the canal free from silt. The ideal design would be one 
escape at half, and another at i 4 times the length of this section below the 
canal head ; and if a choice must be made between the two, the lower escape 
is the better one to select. 

For the above reasons, the sand trap has been largely adopted ; and proves 
most effective in the case of silt which is somewhat coarser than that which is 
usually found either in the Punjab, or in Egypt. In small canals (say not more 
than 40 feet in bed width) the sand trap shown in Sketch No. 225 will catch 
most of the sand as it rolls along the bottom of the canal; and, if correctly 
designed, a small extra quantity of water may be regularly admitted into the 



































GRAVEL DEPOSITS 765 

canal, and can be as regularly passed out with the entrained sand, by means of 
a sand trap. 

Careful observation of the working of such sand traps permits me to say 
that the farther apart they are spaced the more effective they will prove. An 
ideal design would provide about ten, spaced 500 feet apart, over the second 
mile of the canal, in cases where the natural length in which deposits of silt 
occur is four miles. 

The necessity for discharging the mixture of sand and water into some 
natural watercourse, where floods can carry the accumulation away, usually 
renders such a distribution of traps impracticable. Nevertheless, this plan 
should be adhered to as closely as possible, and traps in the first quarter of the 
adjustment length will not prove highly efficient unless there is an unusual 
proportion of large grains in the sand. 



These upper traps should therefore be designed for coarser silt, and the 
proportions shown in Sketch No. 225 are best suited for coarse sands, while 
those of No. 227 will remove finer sands and silt if necessary. 

In wider canals, it is usually difficult to draw the sand which falls into the 
middle of the trap, to the sides. I therefore consider that it will be advisable 
to take advantage of all places where streams are syphoned under the canal, 
and to provide central orifices so as to draw off the sand from the centre. The 
installation at Ventavon, on the Durance (see Genie Civil , Dec. 31, 1910), is a 
good example of this method. The river is extremely torrential, carrying gravel 
and boulders, and these are drawn off from the decantation basin by means of 
12 orifices discharging into tubes 1-97 foot (o’6 metre) in diameter. The design 
is interesting, but it must be realised that the second and smaller regulator (see 
Sketch No. 226) would be a mistake, were it not that the canal below it is lined 
with concrete, and the mean velocity of the water exceeds 6 feet per second, 














CONTROL OF WATER 


766 

which is amply sufficient to carry forward any sand suspended by the eddies 
caused by this regulator. This sand is later removed by an ordinary sand trap 
at the lower end of the canal. 

In cases where the canal is unlined, and where the velocity in consequence 
cannot greatly exceed that normally prevailing in the river, the best method 
appears to be that practised on the Bari Doab Canal, where the first 3000 feet 
of the canal are double, and the water is alternately passed down each channel, 
while the other is being cleared. I am, however, inclined to believe that the 
entry of gravel into a canal must usually be regarded as evidence that the area 
of the waterway through the regulator at the canal head is insufficient. In the 
Bari Doab Canal, measures have been taken to provide a less turbulent method 
of entry by means of bellmouth orifices in front of the sluices. The present 
insufficiency of waterway is due to the fact that the canal now supplies some 60 
per cent, more water than it was originally designed for, and were it designed 
de novo the regulator sluice area would probably be made at least 60 per cent, 
greater. 

It must be remarked that proper mechanical appliances for excavating and 



transporting gravel would possibly prove cheaper than this design, under 
ordinary conditions. In the Bari Doab labour is relatively cheap, and the 
gravel and sand excavated in the clearances is required for making concrete, 
and other repairs. Consequently, these materials are more cheaply procured 
than if special excavations were made in the river bed. 

In cases where most of the large gravel can thus be kept out of the canal, it 
will usually be found that the smaller rounded gravel which enters the canal 
can be removed by one or two sand traps. Since such gravel is rounded, and 
rolls easily, central escapes are usually not required. 

On the Bari Doab, the sand which enters the canal and is not caught in the 
first 3000 feet is dealt with by means of scouring escapes. The fact that the 
canal head is situated on a torrential river, while the land irrigated is very flat, 
causes the silt deposits on this canal to be extremely complex in character 
The real lesson to be learnt is that the head is too high up the river, and should 
have been located lower down, where only coarse sand and clay are carried by 
the stream. As a rule (as is the case at Ventavon), when the river is torrential, 
the canal can be given such slopes and mean velocities that coarse sand is 
carried to the fields without difficulty. The canals of Lombardy which take 





































KENNED Y’S LA W 


767 


out from rivers with a steep bed slope, and are provided with gravel and sand 
traps, illustrate this principle ; and I was surprised to find how little attention 
is here paid to silt problems, once such traps have been set to work. 

When designing escapes, or silt traps, it must always be remembered that 
it is necessary to catch the bed silt alone. Turbidity of water is mainly pro¬ 
duced by clayey silt, and I am not aware of any case where clayey silt is not 
wanted ; in fact, personally speaking, the more clayey turbidity existing in the 
water, the better I am pleased, as it is required to stanch leaks, to form berms, 
and to fertilise fields ; and provided that these objects are secured, the slight 
deposits produced are amply compensated for by the counterbalancing 
advantages. 

Physical Basis of Kennedys Rule .—The physical meaning of 
Kennedy’s rule seems to have been somewhat misunderstood, and doubts have 
frequently been expressed as to whether such a “ peculiar ” law can have any 
true physical foundation. The actual facts are that Kennedy channels are 
channels which carry a certain amount of silt as well as water. If we refer to 
Deacon’s studies of the laws of the transport of sand by water (see p. 488), we see 
that q , the quantity of silt which is carried forward per foot width of the canal, 
may be represented by the equation : 


q—kv n say. 

The quantity of water carried per foot width of the canal is :—Q=w/, where 
d, is the depth of the channel. 

Now, in a Kennedy channel, taking the average of the year’s flow, we find 
that: 

Where /, represents the ratio between the quantity of water and the quantity 
of silt that enter the channel in a year. 

E 

Consequently we get:— kv n —pvd , or v n ~ 1 — -^d. 



Thus, Kennedy’s form of the relation between v , and d , might be theoreti¬ 
cally deduced. If we accept Kennedy’s figures we find that : 

11 = 3, if Vo— I'o^d 0 ' 5 ; 
or, 7z = 2*56, if z/o^o-Sqzf 0,64 ; 

are respectively taken as the algebraic expressions of Kennedy s obsei vations. 
The matter can be still further tested. Kennedy (see P.I.B ., Paper No. 9, pp. 
ii and v) believes that a Kennedy channel carries a quantity of silt in suspen¬ 
sion ranging from xxVo to ^yoo °f ^ ie volume of its watei dischaige. In 

addition, a quantity varying from xsooo to ffoooo °f tlie v0 ^ ume tlie water 1S 
rolled along the bottom in the form of bed silt. The larger ratios seem to 
occur when the water is clear, and the smaller ratios when the water is turbid, 

and heavily charged with mud. 

We may thus assume that ^ = o‘ooo 16Q, is a fairly probable average lelation 

between the silt and the water volumes. 

Thus, since a cubic foot of silt weighs about 125 lbs. (the figure is doubtful, 


CONTROL OF WATER 


768 

as values ranging from 140 to 80 lbs. have been observed), we may say that q , 
is about o'o2 lb. per cubic foot of water ; or that in a 100-cusec channel, 2 lbs. of 
silt are swept forward every second (the exact figures are absolutely immaterial, 
for the present discussion is concerned with relative quantities only). Now, 
picking out the non-silting channels, as given by the intersection of the lines 
representing v 0 , and 100 cusecs, from Kennedy’s Graphic Diagrams, we find 
that: 


• 

Slope. 

Bed Width 
in Feet. 

Depth 
in Feet. 

Mean Velocity 
— v 0 , in Feet 
per Second. 

Lbs. of Silt swept 
forward per Second 
per Foot Width 
of the Bed. 

O "0002 

22*5 

2*65 

1*57 

0*098 

O '0002 2 5 

15*3 

3*35 

1*85 

0*130 

0*00025 

12*3 

373 

I '95 

0*162 

0*000275 

10*1 

4 ‘° 5 ' 

2*11 

0*198 

0*0003 

87 

4*35 

2*16 

0*230 

o * ooo 35 

7 *o 

4*80 

2*29 

0*284 

0*00040 

57 

5 *i 5 

2 *40 

°‘ 35 ° 


The last two columns permit of a curve (Sketch No. 228) being plotted for 
the Bari Doab silt, similar in character to that given by Deacon for Liverpool 
sand. Other points on this curve can be constructed by taking any other dis¬ 
charge (say 50, or 1000 cusecs), and tabulating in a similar manner. In this 
way the plot of v, and S, is prepared, where S, represents 

o’02 discharge 
bed width 

l 

and is consequently approximately equal to the silt discharge per foot width of 
the channel, measured in pounds per second, and v = v 0 , is the mean velocity 
in a Kennedy channel. The points do not fall accurately on a continuous 
curve, but seem rather to be included in a narrow zone. Nevertheless, the 
general resemblance to Deacon’s results is quite evident. When the values of 
log v, and log S, are plotted certain irregularities manifest themselves. The 
wider channels (say 50 to 100 feet bed width) are apparently slightly more 
efficient carriers of silt than the narrow (say 5 to 20 feet bed width) examples. 
This probably arises from the fact that the wider channels observed by Kennedy 
did actually carry somewhat more silt per cubic foot of water than the narrower 
ones. 

Buckley (Irrigation Cha?mels) gives certain additional information concern¬ 
ing non-silting velocities. 

In Sind the rule, v 0 —\ (Punjab v 0 ) = o'63d 0 CA has been officially adopted. 

In Burma a table of non-silting velocities which is very close to, 

v 0 =o’gid°’ 57 , 

has been used with success. 

While in Egypt it is stated that, 

v 0 — t (Punjab v o ) — o^6d 0 - e4 . 



















769 


NON-SILTING VELOCITIES 


My own short experience is rather adverse to this last rule. 

_ O n summarising these rules and Deacon’s figures and Thrupp’s curves, it is 
quite plain that some relation of the form 

v 0 — cd n 

always obtains, and I believe it is also true that: 

The coarser the silt, the less the value of and that the value of c, 
increases in proportion to the volume of silt per unit volume of water. 




' >. 


/ 


S 

c. 

ix-. 


1 



_ 


1 

/ 


. 



1° 



i , ■ 1 •• • 


J 

M 

/o 


Jo 


0/ 

/ 0 


« 



O </ 

/o 



CO 

.. 


0 y 0 

O/O 

- 


<5 

0 y 

r./ 

'0 

- 



y 

y 

' 




Sketch No. 228. —Relation between Mean Velocity and Quantity of Silt 
swept forward in Kennedy Channels. 


The physical facts underlying the rules given for the velocities of rivers 
which carry pebbles or boulders (see p. 492) are now fairly obvious. The mean 
velocity must increase with the depth, not because the increase in depth in any 
way prevents scour or prevents detritus from being swept forward, but because 

49 











































CONTROL OF WATER 


7 ' 7 ° 


the increase in depth causes the quantity of detritus swept forward per foot 
width of the channel to increase in the same ratio as the depth (in actual fact, 
rather faster than the depth, owing to the increase in mean velocity produced 
by the greater depth), because the ratio of silt carried forward to water discharge 
must remain constant. 

In this connection, the very interesting small scale experiments by Seddon 
{Trans. Assoc, of Eng. Soc ., 1886, p. 127) deserve notice. Here, the channels 
did not carry silt, but were merely permitted to erode the sand bed in which 
they flowed until no sand was carried forward. The results obtained indicate 
that the channel became shallower and broader as the slope increased ; and 
that the mean velocity remained constant for all slopes, i.e. v — C^rs, was 


t / 2 


constant, and therefore r , and (very approximately) d, varied as where v, is 

practically equal to the velocity required to move the sand. This law is in 
striking contrast with Kennedy’s. I believe that it is the lack of appreciation 
of the fact that a channel which carries silt cannot have the same form as one 
which has eroded its bed in silt until it ceases to carry silt, which has caused 
Kennedy’s rules to be regarded as purely empirical. Certainly, in my own 
case, this confusion existed long after I had learnt from practical experience 
that the rules were reliable. 

Regarded from this point of view, Kennedy’s rules are rules for the design 
of a channel with a double purpose, the top portion carrying water, and the 
lower layers carrying silt. 


*A 


CHAPTER XIII 
MOVABLE DAMS 

Movable Dams. —Advantages—Conditions affecting the design—Selection of types of 

dam. 

Flashboards. —Applicable in the regulation of rivers. 

Shutter Dams. —Not adapted to rivers carrying boulders—Dangerous when over-topped. 
Trestle Dams. —Limits of height of water retained—Vertical needles versus horizontal 
gates—Difficulties caused by drift. 

Bear Trap and other Mechanical Dams. —Necessity for careful design. 
Calculation of Bear Trap Dams. —Faults of older examples. 

Old Type of Bear Trap.—Parker Type of Bear Trap. —Stresses in the leaves— 
Stiffness of leaves. 


Movable Dams. —The advantages of a dam which can be utilised to retain 
water for an indefinite period, and yet rapidly removed so as to leave the 
channel across which it is erected free for the escape of flood water, are 
obvious. Thus, movable dams are frequently employed in the regulation of 
rivers during their low water stage, either in the interests of navigation, or in 
order to divert the low r water flow into a canal, or into another branch of the 
river. They also prove useful for temporarily closing the escape weirs of 
reservoirs, since the available storage capacity of the reservoir can thus be 
greatly increased, while the escape weir is rapidly made ready for the passage 
of floods by removing the dam. 

The design of such dams is in a very chaotic condition, and a mere 
enumeration of the various types would be as tedious as useless. I have given 
a great deal of study to existing examples, and am unable to see any valid 
reason for the adoption of more than three, or at the most four types. 

The selection of the type of dam depends upon the following conditions : 

(i) The height of water to be retained. 

(ii) Whether the dam has to be erected when water is flowing over its 

base, or when its base is deeply immersed in the backwater below 
the dam ; or merely lifted after the flood has ceased and the base 
is left dry. 

The details of design are largely influenced by the quantity of silt carried 
by the river, by the frequency of floods, and by the rapidity with which the 
river rises. 

As will be shown later, when the river carries boulders or is subject to 
frequent and sudden rises, certain types of dam which would otherwise be 
suitable, cannot be employed. 

771 



772 


CONTROL OR WATER 


The four types are as follows : 

(i) Flashboards. 

(ii) Shutters. 

(iii) Trestle dams, either with needles, or sluicegates. 

(iv) Bear trap, and other mechanical dams. 

(i) The ordinary dashboard type is suitable for all cases where the head 
held up does not exceed 5 feet, although, if the height is more than 4 feet, 
shutters will probably be more efficient. This type is simple in construction, 
and can be used in all cases, for although boulders may damage the flashboards 
and their supports, these are cheap and are easily replaced. Flashboards are, 
however, difficult to replace until the water has fallen to the level of their base, 
and are therefore best adapted to high dams or escape weirs, over which the 
water flows but rarely. 

(ii) The shutter, or dashboard on fixed hinges, type, as developed in India. 
This is suitable for heads up to 8 feet (although if the head greatly exceeds 
6 feet difficulties arise in working), and may be considered as applicable to 
very large rivers, provided that they do not carry much gravel. 

Shutters can be lifted and put into place when the backwater level is 2, 
or even 3 feet above their base. They are therefore suitable for the crowns of 
low dams which are frequently submerged. 

(iii) The trestle type of dam. This type is but little affected by gravel or 
boulders, unless these are of such a size that the masonry and angle irons are 
destroyed by impact. Trestle dams are suitable for heads up to 11 feet, and 
under favourable circumstances 15, or 16 feet of water can be retained. If 
machinery is employed for lifting the trestles and placing the needles, greater 
depths of water can be retained, although I am unaware whether a greater 
depth than 20 feet has yet been dealt with. 

Trestles can be lifted and the needles put into place wherever the water 
level stands. • They are therefore suitable for bars or dams which are 
permanently under water. 

(iv) The bear trap, or other mechanical dam. These are suitable for condi¬ 
tions similar to those under which the trestle type is used. They are more 
costly, and are at present not capable of retaining a greater depth of water. 
Consequently, it is unlikely that they will be adopted except in rivers which 
are subject to such sudden floods that a shutter or trestle dam could not be 
dropped with sufficient rapidity. In such cases, a mechanical dam appears to 
be necessary, although previous to erection it is advisable to consider whether 
timely warning of approaching floods cannot be obtained by means of regular 
reports of gauge readings on the upper portion of the river. In countries where 
labour is scarce or inefficient, a mechanical dam may prove advantageous, as 
it dispenses with the more or less numerous staff necessary to work the non- 
mechanical types. A study of existing examples of movable dams does not, 
however, favour this idea, and it will usually be found that the mechanically 
operated portion is but a small fraction of the total length of movable dam in 
any installation, so that the necessary staff is not greatly diminished. 

Thus, unless local conditions are peculiar, a short length of mechanical 
dam is usually employed as a relief valve for dealing with small and sudden 
fluctuations of the river flow. Longer lengths of trestles and flashboards are 
relied upon to pass the larger and slower variations. 


SHUTTERS 


773 


Regarded in this light, a short length of bear trap dam permits a long 
length of trestle, or shutter dam, to be employed with the best efficiency, since 
the water level can with safety be kept just a few inches below the top of this 
portion of the dam, the bear trap being relied upon to pass off any sudden 
rise during a period of sufficient duration to permit the trestles or dashboards 
to be dropped. 

Flashboards.—These have been discussed on page 402. They are equally 
applicable to the partial regulation of rivers. It will be plain that in river 
regulation flashboards must be supplemented by sluices, or movable dams, 
because once they have fallen, re-erection cannot take place until the height 
of the river has abated some 3 or 4 feet. 

Consequently, flashboards are best adapted for cases where the river has 
a marked and well-defined flood season, followed by an equally well-defined 
low water period. They are then used to block the flood channels, and the 
water level in the low season is kept a little below their top. All regulation 
of the river in the low water season is effected by a manipulation of the sluices 
or movable dams, and the flashboards are only moved when unusual floods 
occur. Broadly speaking, we must provide a sufficient area of sluices and 
hinged dams to deal with the annual maximum low water flow (or at least 
three-quarters of this maximum). The large excess of the maximum flood 
over the annual maximum of the low water season can then be dealt with by 
the flashboards. 

Shutter Dams.—This type of movable dam is generally hinged at the base 
(see Sketch No. 229), where it joins the fixed portion of the dam. The real 
distinction between a flashboard and a shutter dam, however, lies in the fact 
that flashboards are intended to be over-topped, and are designed to fall 
automatically when the over-topping exceeds a certain height. Whereas, if 
shutters are over-topped, they are likely to be damaged. Shutters which are 
hinged at their base, or are otherwise capable of being guided into place, can 
be raised while the water is flowing over the dam, even though the depth over 
the fixed portion of the dam is from 4 to 5 feet. On the other hand, flash- 
boards cannot be put in place until the depth on the fixed portion of the dam 
has become small (say 1 foot or 18 inches at the most). 

The hinging or other guiding arrangement at the base of the shutters is a 
disadvantage, since in streams which carry many stones of fist size, or greater, 
these stones are liable to lodge in the spaces in which the hinges and guide 
• or supporting rods, work. So far as I am aware, no shutter type has 
yet proved really successful in such cases. Otherwise, this type has shown 
itself capable of dealing with far more exacting conditions than any other 
movable dam. 

Several dams exist in India which are more than 4000 feet in length, and 
which hold up water to a height of 16 feet, of which 6 or 7 feet is retained by 
the shutters. The few troubles which occur have never been attributed to 
any defect in the shutters. 

Sketch No. 229 shows a typical Indian shutter, which is dropped by releasing 
the curved horizontal lever. The raising of the shutter is effected by a hand 
crane, which hooks on to the smaller (hanging) loop on the upstream face of the 
shutter. Trained men can raise and set these shutters with ease in 5, 6, or 
even 7 feet of water, provided that the backwater below the dam is not so high 
as to interfere with the working of the crane. 


774 


CONTROL OF WATER 


The dropping of these shutters is perfectly easy, provided that they are 
not over-topped. If once over-topped, it is almost impossible to get them 
down, although this has been effected with some risk when the river did not 
rise rapidly after over-topping the shutters. If the shutters are over-topped, 
and the rise of the water continues, the dam will probably be destroyed, not 
so much by the impact of the water falling over the shutters, as by cross¬ 
currents induced along the dam from the portion where the shutters are up, 
towards that where they are down. These currents set up eddies, which 
rapidly undermine and destroy the dam. 



Sketch No. 229. —Indian Steel Shutters and Wooden Flashboards. 


Consequently, many designs have been prepared for automatically dropping 
the shutters. As a rule, these designs consist of a projecting bevelled arm, 
which is forced down by the fall of one shutter, and sets the next one free. 
Sketch No. 230 shows a non-automatic shutter that can be opened even when 
over-topped. 

Automatically falling shutters are at present in the experimental stage, and 
are consequently not given in detail. It must be remembered that the shock 
produced by the simultaneous fall of a long length of shutters is a severe trial 
for a weir, or dam. 

Experience in India suggests that over-topping of shutters is rarely, if ever, 
due to any cause except carelessness, and it may therefore be inferred that a 




























































































1RESTLES 


77 5 

staff which has become lax enough to permit the shutters to be over-topped 
would also sufficiently neglect any automatic falling gear to preclude the 
possibility of its working when required. 

Trestle Dams.—Trestle dams are especially indicated when the dam has 
to be closed when there is an appreciable backwater below it; In such cases, 
the problem is best solved by a series of trestles, or horses, hinged at their 
base to axes parallel to the flow of the river. These trestles are raised to a 
vertical position, and are then used to support a series of vertical needles, or 
horizontal sluice boards. The total height of water that can be retained is 
fixed by the weight of one of these needles. It is found by experience that 
wooden needles of sufficient strength, and say 4 inches wide, are too heavy 
for a man to handle if the depth of water retained greatly exceeds 9 or 10 feet. 



Eleven feet may be regarded as the maximum depth of water retained, unless 
machinery is used to remove the needles. The weight of the needles may be 
somewhat reduced by providing an intermediate supporting bar hung on 
chains. This additional complication has not found much favour, except in 
cases’where the needles are but rarely moved, say once a year at the most. 

Where horizontal sluice gates are employed, differences in water level 
greater than 11 feet can be maintained, but as the head increases these sluices 
become very heavy, unless the trestles are spaced close together. The trestle 
dam at Suresnes ( A.P.C ., vol. 18, 1889, p. 49) retains 17*2 feet (5*27 metres) 
of water, and this is nearly the maximum that can be dealt with. Sketch 
No. 231 shows the dimensions. 

A study of Sketch No. 231 will show that owing to the close spacing 
(1 metre = 3*28 feet) of the trestles, the sill has to be raised somewhat above 
the base of the trestles. In a stream like the Seine, which normally 







































776 CONTROL OF WATER 

carries clear water, this is of little importance, but in a silt-bearing stream the 
sill should be as low as possible. Hence, when down the trestles should not 
lie over each other, and their horizontal spacing should therefore be very nearly 
equal to their height. When this is the case, it will be plain that the pressure 
on a horizontal sluice gate of a span equal to the height of water retained, is 
so great that unless the head is very small (say 6 or 7 feet) a man cannot move 
it. For silt-bearing waters, therefore, vertical needles are generally employed. 
These are made of wood, and if tapered off at the. ends, a trained man can 
handle them provided that the head does not exceed 13 feet, each needle being 
about 4 inches wide (Pontoise dam, see Tra?is. Am. Soc. of C.E.,x ol. 39, p. 459 )’ 
For greater heads, machinery must be employed in order to place the 
needles. In these cases, the needles are usually 2 to 3 feet wideband made 




Plate 

hk , 

Sketch No. 231. —Suresnes Trestles. 

of wood, stiffened by steel angles. Heads up. to 20 feet are thus dealt with, 
and there is no reason to suppose that this is the maximum possible (see 
ibid., p. 490). . ' 

It must, however, be remembered that accumulations of drift are unhealthy, 
and must be avoided in thickly populated localities. Needles are very badly 
adapted to such cases, for, although it is perfectly easy to let off small excesses 
of water by propping a few needles forward of the general line of the dam, 
drift will not readily pass through the narrow orifices thus formed. .With 
sluices, on the contrary, the water and the drift are easily passed over the top 
of the dam by opening a few of the upper sluices. For this reason sluice, gates 
mounted on wheels have been proposed. The difficulties are great, for if the 
bearings are of the ball-bearing type, they will rapidly rust; and roller bearings 
are liable to jam if the trestles move relatively to each other in any degree, 































































BEAR TRAP DAMS 


777 

Bear Traps and other Mechanical Dams. —It is quite impossible to 
enumerate the various forms of these dams which have either been adopted, 
or proposed. In essence all these dams consist of two leaves fixed to hinges 
in the bed of the river. These leaves (with connecting leaves or “ idlers ” in 
some types) form a closed chamber, into which water can be admitted under 
pressure. This pressure water opens out the leaves, and the dam is thus 
raised. When it is desired to let the dam down, the pressure water is with¬ 
drawn, and the dam falls by its own weight. 

The outlines of chief types are shown in Sketch No. 232 and are the original 
u Bear Trap,” and the Parker and Lang modifications. The Lang type is 
obviously best adapted for rivers carrying silt and drift, as the idler leaf 
prevents these being caught between the leaves. Our present knowledge does 
not permit us to state whether the Parker modification has any real advantages 
over the original bear trap. It is probably used more frequently, but, as will 
later be seen, the facts are that a badly designed bear trap will refuse to rise, 
whereas a badly designed Parker dam refuses to fall. It is plain that this 
difficulty is easily obviated by such expedients as weighting the leaves. 
Whereas, a dam which refuses to rise is not easily lifted up. For this reason, 
therefore, the adoption of the Parker type in preference to the simpler bear 
trap may only indicate that the ordinary designs of both types are badly 
proportioned fundamentally. 

Calculation of Bear Trap Dams. —The older examples of this type of 
dam were badly proportioned, and a study of the excellent results obtained by 
some (if not all) of the newly erected and scientifically designed dams built by 
the United States Army Engineers, leads me to believe that the capabilities of 
these dams are at present greatly underestimated. 

The failure of the older examples was principally caused by the two follow¬ 
ing faults : 

(i) The relative proportions of the leaves of the dam were such that the dam 
was liable to stick, and consequently failed to rise, or fall as the case might be. 

(ii) The leaves were insufficiently rigid in a longitudinal direction. Hence, 
it was possible for one end of the dam to rise, while the other end remained 
down. This produced strains, and consequent leakage. 

It cannot be said that sufficient experience has yet been accumulated to 
enable these difficulties to be entirely overcome. The following analysis must 
be regarded as a preliminary sketch, but so far as I am aware, all dams to 
which similar principles have been applied work fairly well. 

All of the older dams which have proved notorious failures have been found 
to be defective when tested by these rules. 

The proportioning of the leaves has been investigated by Powell ( fourn. of 
Assoc, of Eng. Soc ., vol. 16, p. 177), who deduces the following results : 

Old type of bear trap (see Sketch No. 232, Figs. 1 and 2). 

Let X, be the length of the upstream leaf. 

Let Y, be the length of the downstream leaf, and let the distance between 
the hinges be represented by Q. 

Let Z = X + Y —Q, be the overlap of the upstream leaf on the downstream 
leaf when both are lying flat. 

The critical positions are as follows : 

(i) When the dam lies flat, and begins to rise under a head //, say. 

(ii) When the dam is raised to its greatest height, and begins to fall. 



CONTROL OF WATER 


(i) Let us consider one foot length of the dam. The head //, may be consideied 
as produced by the difference in level of the water surfaces above and below 
the dam. The most unfavourable assumption, therefore, is that the pressure 
caused by h , feet of water acts downwards on the whole of the leaf X, and 
upwards on the whole of the leaf Y, and on that portion of X (j.e. a width 
X —Z) which is not covered by Y. 

Let Pj, be the downward pressure at the end of the leaf Y. 

Then, taking moments about the upstream hinge; P 1 (X-^-Z) = 62'5^z(x— j. 

The upward pressure on the leaf Y is : P 2 = JY// 62’5. 

_Z“ 

Therefore : P, =7?Po, if Y — and in order to have a reserve of force 

n[X — L) 

to overcome friction, it is plain that n , must be less than i. 


Thus, we can obtain Z, in terms of X, and Y, and putting Q = i, so that X, 
is now equal to : 

Length of upper leaf 
Distance between the hinges 

we find X, and Y, in the forms : 


X= V(i —^)Y 2 —2(1 -\n) Y+1 


Y = 


i — In 


/ X 2 j/ n y 
i —n V i—« 4 Vi^z' 

n= i ; Y = i —X 2 

n=o-8 ; Y=3- LJxF+a : etc. 


h 2 


Sketch No. 232.—Diagrams for Movable Dams. 


& 

* 


1 



Pc 

- 


*■ 

iZT 


© ■ . / fe** Hater Level 


Cham Leaf 


For example : 


























PARKER TYPE 


779 


Thus, for an assumed X, we can calculate Y. 

The height to which the top of the upper leaf rises (i.e. the head of water 
which the dam can hold up) is given by the equation : 

H 2 = Y 2 sin 2 / 3 , where cos /3 = ^zzY4-(i — \n). 

Finally, if we make H, a maximum for a given value of zz, by expressing H, 
in terms of Y, and differentiating, we obtain the following equation : 



whence we can express X, Y, and H, in terms of zz. 
Thus, when H, is a maximum, we obtain : 


When zz = o-8 Y = o’682i X = o'5239 H=o*333, 

When zz = 075 Y = o'68ii X = o*5i44 11 = 0*323, 

and so on. 

(ii) In order that the gate may fall, the angle between the leaves should be 
greater than 90 degrees, say 100 degrees, or more. If zz, be less than 1, this 
condition is always satisfied. 

In some of the earlier examples zz, was greater than 1, that is to say, the 
gate could only rise when the pressure below the leaves was greater than that 
on the upper side of the upstream leaf. Such designs should be avoided. 

In successful gates it is found that: zz = o*8o, to 0*85, at the most. It is 
doubtful whether zz, should be less than 0*75, lest the dam should be run up too 
rapidly, and a shock should be produced. The amount of friction between the 
leaves and at the hinges is evidently important, and the more silt in the water 
the less should be the value of zz. 

The Parker Type of Bear Trap Dam.—In this case let the distance between 
the hinges be equal to unity, and in this unit let (Fig. 4): 

X, be the length of the downstream leaf (which is now the upper leaf when 

the dam lies flat). , 

Y, be the length of the lower upstream leaf, and Z, the length of the 
intermediate two-hinged leaf. 

Then: X+Y-Z=i. 

When the dam is raised to its greatest height: 


cos <p = 


X 2 + i-(Y + Z) 2 
2X 


where is the angle which the leaf X, then makes with the horizontal. 


Also Z = \ {V 1 + X 2 —2X cos (f) — (1 — X)}. 

Y=£ {V1 +X 2 —2X cos <£ + (i-X)}. 

Therefore, YZ = £X (1 —cos <£). 

Also, g, the distance between the top of X, and the upstream hinge when 
the dam is partially opened, and X, makes an angle a with the horizontal, is 
given by : 


(T‘ 


2 =i+X 2 - 2 X cos a 


and if 0 be the angle between Y, and Z : 

Z 2 -f- Y 2 —g 1 
C0s 3 YZ • 







780 


CONTROL OF WATER 


Hence, (1 —cos 8)(i — cos <f>)~ 2(1—cos a), 

so that d can be calculated when a and $ are given. 

The critical positions of this type of dam occur when it is falling ; so that the 
pressure inside the dam is atmospheric, or at the most that due to the back¬ 
water, while the upstream faces of the leaves Y, and Z, are exposed to pressure 
caused by water which may rise as high as the top of the dam. 

Resolve the forces caused by these pressures, as shown ; where P 5 , and P G , 
act in the direction of Y, and Z, respectively, and the other forces are 
perpendicular to the respective leaves. 

Taking moments about G, we get the following equation for the equilibrium 
of the leaf X : 

P 2 cos y — P 5 sin y = o. 

Similarly, since P 3 and P 5 acting at L are equivalent to P 4 and P 6 acting at 
the same point; we have resolving along P 4 , 


P5 = —Ps cot 8. 

sin 8 

Or, substituting for P 5 , 

P 4 — P 3 cos 8 — P 2 cot y sin 8 = 0. 

If there be no backwater, denoting the various depths as shown in Sketch 
No. 232, 

P 2 = ^ 3 Z P 3 = P 3 Z P 4 = P 3 Y + ^ X Y. 


Therefore : 


(r + i) y+2 (Y — Z cot 8) — Z sin 8 cot y = o. 


In practice y is best obtained graphically, but if necessary we can calculate 
the angles x, and \fs from : 

# 

sin a , . 1 Ysin 8 , . 

sin x= -, andsm\//‘ =-; and y = x~4 r ' 

r £ £ 

The critical position will be found to occur when the dam is falling, and is 
just about to reach the horizontal position. 

In actual practice ~ will then have a certain limiting value depending upon 

/z 3 

the area of the passages available to pass water around the dam. Powell, 
however, assumes that and l z 3 , then vanish simultaneously, which is a less 

favourable case. Consequently, his assumption that: 


P2 cos y—P 5 sin y = o, 

in place of P 2 cos y— nV 5 sin y = o, which is similar to the equation used to 
investigate the old type, will lead to a satisfactory dam. 

In the final calculations it would nevertheless appear advisable to make 
certain that when a — 5 degrees or 10 degrees say, there is sufficient overplus of 
downward pressures to overcome friction. Bearing in mind that initial friction 
is always greater than moving friction, and that silt deposits have a certain 
sucking power which prevents the dam from starting, but is not very active in 
stopping motion when it has once begun, we may believe that a dam is more 
likely to refuse to start when nearly down than to cease closing up just as it 
gets flat when motion has once started. 




STRENGTH OF DAM LEA VES 781 

■H ll 

Evaluating the indeterminate fractions -T, and sin 0 cot y for the case 0 = o, 

4 ' l 3 

we get: 

V- , »~ x - 

"3 Vi(l — COS (p) — Z 

» -> | f, • _ . t ' - 1 f v : • 

and, sin d cot y = - 1 ■■ =» 

Y— V^(i —cos 4 >) 

Substituting these values in the above equation, we finally obtain : 

(i —X) 3 — 2|(l — COS 0 )(l —X) + (i—COS (f)) 2 = o. 

This equation can be solved by the ordinary rules, and X, having thus been 
determined, Y, and Z, can be calculated. 

Where the dam is exposed to a backwater, the critical position will be found 
to occur when the dam is falling, and its crest is just level with the backwater. 

In the general case, when the leaf Z, is only partially immersed in the 
backwater, we have : 

p 2 =P 2 m + / ' 2 p 3 =p 2 z -| 2 

6 Z o Z 

P4-P2Y. 

In the critical position it is found that M = Z, and N = o. 

So that: Y —Z cos d —Z sin d cot y = o, which, expressed geometrically 
gives, 

angle KJG = d —«. 

v sin(d — a) . ’ . h . , 

sin d H 

The best solution is most easily found by calculating a series of values of 

h 

X, Y, Z, and H, for assumed values of 0 and 

The above investigations can only be regarded as a preliminary sketch. 

Before the proportions of a dam can be finally determined, the local con¬ 
ditions must be investigated, and the possible value of the pressure liable to 
arise inside the dam must be determined. It is fairly plain that if an artificial 
head can be produced (e.g. by accessory stop planks, or reservoirs) which is some¬ 
what greater than that retained by the dam when just about to rise, the leaves 
of the dam may be shortened. The economy thus secured may justify the 
expense. 

The effect of leakage through the hinges in diminishing this internal head 
must also be investigated. 

The friction of the hinges and possible deposits of silt also require 
consideration. 

The dimensioning of the leaves is evidently a problem which is somewhat 
akin to that of a bridge under moving loads. The forces producing the 
stresses for given values of 0 and « have been written down. The maxima 
bending moments and shears can be determined, but the algebraic expressions 
are complicated, and it is best to draw the position of the leaves for, say every 
10 degrees of increase in a, and measure h u h 2 , and // 3 . The bending move¬ 
ments and shears can then be calculated by the usual formulae, and their 








782 CONTROL OF WATER 

maxima values can be selected, and the sections of the leaves dimensione 
accordingly. 

In this connection, however, the stiffness of the leaves along the length of 
the dam deserves investigation. As already stated, in many existing dams the 
end where the pressure is applied may rise, and the other end remain down, 
owing to the diminution in pressure produced by leakage as the water travels 
along the inside of the dam. 

The matter has been investigated by Bowman {Trans, of Am. Soc. of C.E., 
vol. 39, p. 609). By a calculation similar in principle to that made by Powell, 
but which takes into account the weight of the gates (but not the friction at 
the hinges, for which reason I do not give it) Bowman finds that a pressure of 
about 35 lbs. per square foot, say 7 inches head, is required to cause a certain 
bear trap dam (old type) to begin to rise. 

It is found from actual experience that if such a dam be more than 50 feet 
long, and insufficiently stiff in a longitudinal direction, one end is likely to rise 
and the other end to stay down. Bowman therefore infers that in actual 
practice the 7-inches head occurs at one end of the leaf, but gradually dies out 
to o, at the other end. He therefore investigated the deflection of a cantilever 
under a load of p lbs. per inch run at its end, which gradually diminishes to o, 
at the inner end. The equation is : 

dfy - P ( y‘2__-0\ 
dx - 2 2EIV 3// 

where p in this case is equal to : 

35 X width of leaf in feet ,, . , r . 

—-- : —- lbs. per inch run of the beam, 


dy 


and l — 50 x 12 = 600 inches. 


Integrating, since—=0, when x = l and y = o, when x = o; we get 

IQ 

the maximum deflection, 8 = — ~~ where I, is the moment of inertia of a 

120 Lb 

section of the leaf by a plane parallel to the direction of flow of the river. For 
the actual case considered 8 — 1*84 inch, so that the leaf is obviously sufficiently 
stiff. 

Bowman’s paper forms a very valuable example of the detailed calculation 
of the forces acting on a dam as it rises. The general proportions agree very 
fairly well with Powell’s rules. The omission of all friction renders the figures 
less accurate than could be wished, but there is little doubt that certain of the 
assumptions partially compensate for this error. Reference may also be made 
to Willard’s {ibid., p. 573) investigation of the Lang type of dam. This is 
very complex, and a comparison with Powell’s results, indicates that the 
Parker type is preferable in all cases. Consequently, the calculations are 
not given. 






r 


CHAPTER XIV 

HYDRAULIC MACHINERY OTHER THAN TURBINES 

The following discussions must not be considered as intended to provide 
all the information required for the complete design of any hydraulic machine. 
The constructional problems are almost entirely ignored; and the most 
important of all hydraulic machines—the piston pump—receives no discussion. 
The circumstances under which hydraulic engineers generally work justify 
this action. Assuming that a hydraulic engineer possessed the requisite 
knowledge and experience of the working properties of metals to permit him 
to produce a first-class design, it is extremely improbable that he would have 
access to the tools necessary for its construction. Thus, in nearly all cases, a 
trained mechanical engineer will be associated with the design. Under these 
circumstances, any hydraulic engineer who interferes with the mechanical 
details merely creates friction and assumes an unnecessary responsibility. 

I have personally worked with excellent mechanical engineers who stated 
that: “ Such large pipes are always exposed to intense pressures, and therefore 
the thickness of plating should be increased by 50 per cent.” These large 
pipes were actually exposed to less than one-half of the pressure sustained by 
pipes of equal thickness and smaller diameter which the mechanical engineers 
had already installed. The facts and theory were therefore hopelessly 
erroneous. Nevertheless, on investigation the pipes as designed were found to 
be somewhat less rigid than they might be, and the extra weight of metal was 
finally applied, not in increased thickness, but in the form of stiffeners. 

A knowledge of the theory of hydraulic machinery is really useful under 
the following circumstances. An existing machine works satisfactorily under a 
certain head and when utilising a certain volume of water. It is desired to use 
this machine under a different head, and when utilising a different volume of 
water. A little consideration will show that a knowledge of the friction losses 
in the machine, as installed, will permit the efficiency of the machine to be 
predicted under the new circumstances with a fair degree of accuracy. The 
pressure and velocity at any point in the machine under the new circumstances 
can then be calculated ; and the stresses produced in its various members can 
be estimated, as also the necessity for alterations in the loading of the valves, 
or other details. 

This work is undoubtedly best performed by a hydraulic engineer, and 

should also be carried out when purchasing hydraulic machinery. The 

following chapters are therefore devoted solely to this problem, and as a rule it 

is assumed that the coefficients of skin friction, which, in practice, will also 

include losses of head at bends and obstructions, are determined by previous 

783 


CONTROL OF WATER 


784 

observation. The problem is therefore somewhat more simple thaii that which 
occurs when designing a new machine. 

The first two sections, however, are devoted to a consideration of the 
hydraulic properties of enlargements and contractions in pipes, and the loading 
and motion of valves. Similar questions concerning bends have been discussed 
on page 28, and the uncertainties there disclosed form the greatest defect in 
the following theories. 

Valves and other Obstructions in Pipes. —Approximate theory—Valve in circular 
pipe—Sluice in a rectangular pipe—Cock, or throttle valve. 

Circular Diaphragm in a Circular Pipe. —Sudden contraction in a pipe—Fire 
nozzles. 

Sudden Enlargements in a Pipe. —Borda’s rule— Baer’s experiments—St. Venant’s 
rule—Practical rule—Large scale experiments—Labyrinth packings. 

Losses of Head at Gradual Enlargements, or Contractions.— General theory— 
Loss by friction. 

Andre’s Experiments.—Effect of Character of previous Motion of the Water.— 

Practical calculation for a conical enlargement—Application to other than conical 
enlargements'—Gibson’s experiments on more rapidly diverging cones. 

Motion of Valves. —Utility of the investigation. 

Motion of a Pump Valve. —Shock at closure—Values of v —Coefficients of resistance for 
valves—Coefficients for a valve just before closure—Spring loading. 

* ; ’ • . •' ; i > ' i > i . i • • j • * , •) ) > • 17/0 ff y 

Symbols connected with Valves and Enlargements. 

A and a (see p. 795). 

A 0 is the area in square feet left vacant by a valve or other obstruction in a pipe. 

A p is the area in square feet of the unobstructed pipe. > 

Aj, A 2 (see p. 793). 
c (see p. 790). 

c c is the coefficient of contraction of the area A 0 considered as an orifice subject to 
suppression of contraction by the upstream portion of the pipe. 

C is the coefficient of discharge of the same orifice. 

<zf 1} d 2 (see Sketch No. 236). 

h 0 is used for the loss of head in feet when the velocities at the points between which h 0 
is measured are the same. 

/q, h 2 (see p. 793). 

H 0 is used for the loss of head in feet when the velocities at the points between which 
the loss occurs differ and this difference is taken into account. 
h m is the pressure in feet of water at the smallest cross-section of a diverging cone 
(see p. 797). 

2 0 

H = —- (see p. 797), lif and ha (see p. 799). 

2 S ,, • 

K (see p. 797). ... , . 

I (see Sketch No. 236). 
m (see p. 787)* 

A 

n — T^- (see p. 7S9). On p. 796 n is a number. 

Ap ^ . * f 

Q, the_quantity of water flowing through the valve or other orifice in cusecs. 
r~ An (see p. 790). 
s (see p. 796). 

Vj, is the velocity in feet per second in the unobstructed section A,, of the pipe. 
v, is used for the velocity in the smaller pipe where there are two pipes. 
v m is the velocity at the smallest cross-section of the path of the water or the diverging 
cone considered. 

These and all other vs are defined by the relation, Q = zA., with appropriate suffix. 

5 is the vertical angle of a conical enlargement (sec Sketch No. 236). 

i*a coefficient in the equation h 9 = 

ri and rjd (see p. 799). 
p (see Sketch No. 236). 



OBSTR UCTIONS 


735 


SUMMARY OF FORMULA 
Theoretical formula for head lost at an obstruction : 

~ Vp)~'Vp 


k 0 = 


2 d 


Relation between C and f: 
C = — 

w Vi- 

Head lost at a valve : 

— Q“ 
c-a 0 -2^ 2^ 

Sudden contraction of a pipe 

2 2 


= V/_A 2L _\2 = ^2 
2 Y \ AA 0 ) s 2^ 


(see p. 787). 


7 / 1 \ zv 0 0-0418 

, £ = 0-582 + - ■ . 

V J 2g I - I - r 


Fire nozzles: 


^ 0-0429 

0=0-571 +- ±-?. 

J I’l-r 


Sudden enlargements in a pipe : 


H . = taz^! or -i 


zv - v 2 




H 0 = - 


2g 

St. Venant’s rule : 

, (^i-^ 2 ) 2 1 V 
2 ^ 9 2 / 

Labyrinth packings, with n enlargements 

. ■ Q 2 n + 1 

ho — _ 2 * 

2^ a- 

Gradual enlargements: 

(a) Corrected for friction only : 


(but see p. 795). 




K: 


O 9 

4 g 


C 2 tan^ 


(I-K) (see p. 797). 
where v — CsJdi. 


(b) Correction for friction and divergence loss : 


*1 = 




! - V % V m 2 - V 2 


29 


-y= 


2 CT 


(i-K-ija) 


Table of 77 and rja (see pp. 799 and 800). 


Valves and other Obstructions in Pipes.— Our knowledge of the 
head lost at these is mainly due to Weisbach (Versuche iiber der Ausfluss 
des Wassers). His experiments were small scale, and effected by observing 
the time taken to pass a given quantity of water through the system of pipes 
and valves experimented on. The values are therefore mean values for a head 
varying from about 3 feet downwards. Despite the fact that the observations 
were very carefully conducted, comparison with such modern experiments as 
exist on a larger scale leads me to believe that the numerical results are by no 
means exactly applicable to larger pipes, although it is highly probable that 
they form a guide to the general effect of the obstruction. 

There is a certain theory which allows us to test some of Weisbach’s 
experimental results, and which throws some light on the probable applicability 
of his observations to large pipes, and higher heads. 

5 ° 
















CONTROL OF WATER 


786 

Let us consider the effect of an obstruction leaving an area A 0 , vacant in a 
pipe of area A p (Sketch No. 233). The water, which flows with a velocity v Py 
in the pipe, passes the obstruction with a velocity v 0y given by A 0 v 0 —A p v Py and 
issues in a jet the smallest area of which is A 0 c c , where c c , is the appropriate 
coefficient of contraction. The velocity at the “vena contracta ” is then : 


When the water has travelled some little distance along the pipe the jet 
expands, and fills the pipe (the jet being previously surrounded by eddying 
water, or air, according as there is a sufficient vacuum at the vena contracta to 
set free air or not). The velocity then becomes v p . 

The theory given by Borda for the loss of head caused by a sudden enlarge¬ 
ment in a pipe probably applies to the above described motion with far more 
accuracy than to the case actually considered by Borda (see p. 793). The loss 
of head caused by the obstruction is therefore : 


h Avm-Vp? JVy ( A P \ 2 

2g 2g\c c A 0 ) ^ 2g > 


say. 


The “ lost head ” h 0 , can be directly observed as the difference of the 
pressures indicated by the two pressure gauges. 

The case should be carefully distinguished from that shown in the lower 
Figure, where the final velocity v qy is not the same as the initial velocity v p . 
In this case, even if no obstruction existed, and the change of velocity was 
accomplished without any loss of energy, Bernouilli’s equation shows that: 


h p -\- 




2 g 


■Kr 


v n 


2 g 


Hence, H,-, the difference in pressure indicated by the gauges, is com¬ 
posed of: 

qj ^ 2_ tyj 2 

(i) A change in pressure equal to h p — h q ~ ——which is not necessarily 


accompanied by a loss of energy, since the velocity head is increased or 
decreased, as the case may be, by the same amount. 


(ii) A loss of pressure equal to H 0 = 


(v m —v (J y 
2 g 


which, so far as the practical 


requirements of engineers are concerned, is accompanied by a loss of energy. 

In the case shown, v p is greater than v qy so that putting aside the effect of 
the obstruction the pressure at Q, should be greater than the pressure at P. 
Hence, the observed difference Hi, does not fully represent the loss of energy. 

The application of this theory to the values of £ experimentally obtained by 
Weisbach leads to values of c c , which are very close to those experimentally 
obtained on orifices of similar size and under like hydraulic circumstances to 
those formed by the valves and cocks used by Weisbach. 

When it is desired to obtain the value of f for an obstruction in a large 
pipe, or under a head which greatly exceeds 3 feet, it is consequently probable 
that a value of ( which is more applicable to the actual circumstances than that 
given by Weisbach, can be obtained by selecting (in default of special experi- 

C 

ments) the value of - ^g~ or g appropriate to the size of the orifice left free 








STOP VALVES 787 

by the obstruction, and the head under which it works, and calculating from 
the above equation. 

The method is only recommended when direct experiment is not available, 
but it is more likely to lead to correct results than a blind application of 
Weisbach’s figures for a head of 3 feet on an obstruction in a i-inch pipe to 
a similar obstruction under 50 feet head in a pipe 3 feet in diameter. 

Valve in Circular Pipe. —Weisbach ( ut supra ) experimented on a closely 
fitting, thin slide. Kuichling ( Trans. Am. Soc. of C.E. vol. 26, p. 439) on a 
commercial 24-inch stop valve, and Smith {Trans. Am. Soc. of C.E., vol. 34, 
p. 235) on a commercial 30-inch stop valve. Kuichling has discussed the results 
{Trans. Am. Soc. of C.E. , vol. 34, p. 243), and I have followed his method, 
which is to consider the valve opening as an orifice of an area A 0 , equal to 
n times the area of the pipe, and to calculate C its coefficient of discharge under 
the head h 0 , lost at the valve, i.e. : 

Q = Cx A 0 V 2 gh 0 = C n area of pipe V 2gh 0 

Weisbach calculates £ given by : 

(vf = 2gh 0 

where v p , is the mean velocity in the pipe so that: 

Area of pipe 1 
A 0 Vf nf£ 

In commercial valves the valve has to be lifted slightly before any passage 
is opened. Reckoning the lift from this point, we have the following table, 
where : 

Lift 

—:- ; = ffl 

Diam. of pipe 


Smith. 

30-inch Pipe. 

Kuichling. 
24-inch Pipe. 

Weisbach. 

i*57-inch Pipe = o*04 Metre. 

m 

n 

C 

n 

c 

n 

c 


0*1 


0*92 

0*106 

0*98 




0*125 

0*125 

o*88 

0*138 

o*88 

°‘ I 59 

0*64 

97-8 

0*2 


0*84 

0*233 

o*73 




0*25 

0*287 

0*82 

0*296 

0*70 

0 ' 3*5 

077 

r6* 9 7 

0*3 


0*83 

o*359 

0*71 




°'375 

0*443 

0*84 

o*45i 

o*75 

0*466 

0*91 

5’5 2 

0*4 


0*85 

0*482 

o*77 




o*5 

o‘593 

0*90 

0*598 

0*92 

0*609 

1*14 

2*06 

o*6 


1*04 

0*708 

1*19 

• 



0*625 

0*729 

1*09 

o*733 

1*28 

0*740 

1*50 

o*Si 

0*7 


1 '34 

0*807 

1 *61 




o’75 

0*851 

1*60 

°'SS 3 

not ob- 

0*856 

2*29 

0*26 

o*8 


2*08 

0*893 

served 




°'S 75 

0*946 

not ob- 

0*948 


0*948 

4*00 

0*07 



served 






0*9 



0*96l 





























CONTROL OF WATER 


788 


The results obtained with the 24-inch pipe are the most accurate, the 
difference of head on either side of the valve being directly observed ; while 
Smith observed the total head consumed by the valve, and a certain length of 
pipe, and assumed that the head lost by friction in this length of pipe was pro¬ 
portional to the square of the quantity of water flowing, which is somewhat 
doubtful when n is less than 0*50. Neither the theory of Kuichling, nor that 
of Weisbach is absolutely satisfactory, and some of the differences may be 
explained by this fact. 

The losses of head vary from ir6 feet in Smith’s observations, and 97 feet 
in those of Kuichling, at small openings, down to practically nothing when the 
valve is nearly full open. Duane {Trans. Am. Soc. of C.E ., vol. 26, 
p. 464), observed the time taken to fill a certain length of pipe through a 
partially opened valve, and thus obtained the mean value of C, under heads 
varying from a certain maximum down to nothing. 

He gives—C = 075 for a 6-inch pipe, with valve 1 inch open, i.e. rn = o’i66, 
and 71 = o’i24, the maximum head being I2'i feet, and C = 075 for a 12-inch 
pipe, with valve 1 inch open, i.e. m = o’oS3, and n = o'o74, the maximum head 
being 52 feet. 

Graeff {Traite rfHydraulique, Tables, p. 28), gives details of experiments 
with a pipe 0^40 metre in diameter (say 16 inches), with openings ranging from 
0*4 inch (o*ou metre) to 1*54 inch (o'o385 metre), under heads varying from 
52 feet to 131 feet, C, was found to vary between 0795, and o'82o. 

These last experiments seem to show that under very high heads such 
matters as the form of the orifice, which plainly possess a certain influence 
under low heads, no longer affect the coefficient of discharge ; which becomes 
what would be predicted for a circular orifice in a thick wall. 

The valve used by Graeff being some 6 inches thick, it is plain that for the 
orifices experimented on, the “ wall ” can be considered as thick. It is doubtful 
whether in these experiments the jet issuing from beneath the valve ever 
expanded so as to completely fill the pipe. The circumstances of the orifice 
are shown in Sketch No. 233, as the experiments are almost classic and have 
formed the basis of many assumptions concerning coefficients of discharge 
under great heads. 

The value C = 075 to o'8o, may be assumed, and used in all calculations 
where the question is of practical importance, as it is only rarely that we 
require to accurately predict the discharge of a valve except for small openings 
under high heads. 

Sluice i 7 i a Recta 7 igular Pipe .—Weisbach worked on a pipe 1*98 inch x 076 
inch (5*02 cms. x 2*48 cms.), and the opening was always 178 inch wide. He 


gives h 0 = 


where v p , is the velocity in the pipe. 


Area of orifice * , „ 

r- T~- -o' i 0*2 0*3 0*4 07 o'6 07 o'8 0-9 roo 

Area of pipe J y 

C , • .193 44'5 17*8 8*12 4-02 2'o8 0-95 079 0*09 o*oo 

The coefficients of contraction indicated are : 


c c . . . o - 67 o' 65 0^64 0*65 0*67 o*68 072 077 0*85 

and these variations may be explained in general terms by the effect of the 
wider orifice in the earlier stages, followed by that of the partial suppression 
of contraction at the upper edge in the later stages. 



THROTTLE VALVES 


789 

I he theory may therefore be applied, and it would appear that for a similar 
sluice on a larger scale, the coefficients of contraction being smaller, we may 
expect to get somewhat larger values of £. 

Cock or Throttle Valve. —The pipes experimented on by Weisbach were : 

(i) Circular, 1*58 inch in diameter (4 cms.); and 

(ii) Rectangular, 1 ’98 inch x 0*96 inch (5’02 cms. x 2*48 cms.). The coefficients 
in terms of the angle 6 through which the cock or valve is turned, are given 
below ; 6 = o, corresponding to full on : 


d 

Cock. 

Throttle Valve. 

Circular Pipe. 

Rectangular Pipe. 

Circular Pipe. 

Rectangular Pipe. 

Degrees. 

n 

| 

s 

n 


n 

s' 

n 

, 

S' 

O 

I'OOO 

0*00 

1*000 

0*00 

1*000 

0*17 

1*000 

0*26 

5 

0*926 

0*06 

0*926 

0*05 

°*9 I 3 

0*24 

0*913 

0*28 

io 

0*850 

0*29 

0*849 

0-31 

0*826 

0*52 

0*826 

o-43 

T 5 

0*772 

o'75 

0*769 

o*88 

0*741 

0*90 

0*741 

o*77 

20 

0*692 

1*56 

0*687 

1*84 

0*658 

i*54 

0*658 

i*34 


0*613 

3*10 

0*604 

3*45 

o*577 

2 , 5 I 

o*577 

2*16 

3° 

°’535 

5*47 

0*520 

6*12 

0*500 

3*9i 

0*500 

3*54 

35 

0*458 

9*68 

0*436 

11*2 

0*426 

6*22 

0*426 

5’7 2 

40 

°'385 

1 7'3 

°*35 2 

20*7 

0 *357 

10*8 

o*357 

9’ 2 5 

45 

°'3 I 5 

3 1 * 2 

0*269 

41*0 

0*293 

18*7 

0*293 

i5‘3 

5o 

0*250 

52*6 

0*188 

94*5 

0*234 

32*6 

0*234 

2 4*9 

55 

O-lpO 

106 

o*ii6 

309 

o*i8i 

58*8 

0*190 

42*7 

60 

°‘i37 

206 



0*134 

118 

0*137 

77*4 

65 

0*091 

486 



0*094 

256 

0*091 

J 59 

70 



1 


o*o6o 

75i 

0-052 1 

3 6 9 


The original experiments indicate that when n, the ratio : 

Area of free passage _ A 0 
Area of pipe ~ A,, 

is small, the value of £ is influenced by the circumstances of the discharge : eg. 
whether a long pipe succeeds the valve or not, and whether the discharge is 
into air or into water. To judge from Weisbach’s remarks, these differences 
are mainly, if not entirely, due to the flow not being regular under small heads 
such as occurred towards the end of the discharge. It is therefore unlikely 
that these differences will occur when the head through the valve is greater 
than 3 or 4 inches, as will probably be the case in practical applications. The 
values tabulated have been selected from those observations in which this 
irregularity of flow was least marked. 

It would appear that the deflection produced by the throttle valve has very 
little influence on the value of £ compared with the contraction in the area of 
the passage. No deductions as to applicability to larger valves can be 
given. 



























































790 


CONTROL OF WATER 


Circular Diaphragm in a Circular Pipe.— '-Weisbach found experimentally as 
follows : 


Ratio of areas A 0 = nA p 

n = o*i 

0*2 

°*3 

0*4 

°’5 

Approach channel j 
much larger than - 
pipe . . .J 

£=2317 

c c = o*616 

5 ro 

0*614 

19*8 
o*6i 2 

9*61 

o*6io 

5*26 

0*607 

Diaphragm in a cylin-j 
drical pipe . ./ 

£=225*9 
c c — 0*624 

47-8 

0-632 

30*8 

0*643 

7 '80 
0*659 

1*75 

o*68i 

Ratio of areas AJ = nA p 

n= o*6 

0*7 

o*8 

0*9 

1*0 

Approach channel' 
much larger than - 
pipe 

(= 3'°8 

c c = °' 6°5 

i*88 

0*603 

1*17 

o’6oi 

073 

0-598 

0*48 

0*596 

Diaphragm in a cylin-^ 
drical pipe . .J 

£= i-8o 
<r c = 0712 

| 

0*80 

°755 

0*29 

0*813 

0*06 

0*892 

0*00 

1*00 


Note. —In the first case the correction for change of velocities explained on 
page 786 was applied before calculating the lost head. 

The values of c c , agree fairly well with what might be expected, since we 
know that partially guiding a jet after exit increases the coefficient of contraction. 
Hence it is probable that the values of £ hold for larger pipes, but are slightly 
increased. As a matter of fact, we know that the value {= 0*48 (which 
corresponds to the head lost at entry in the ordinary case of pipe flow) is 
increased to 0*505 in large pipes, and this would indicate that c c — 0*584. This 
is about 2 per cent, below the theoretical value, and the difference is probably 
explained by skin friction, as has already been pointed out in the case of 
cylindrical orifices (p. 149). The values of { for larger pipes are probably some 
3 or 4 per cent, in excess of those given above. 

Sudde?i Contraction in a Pipe. —Merriman ( Treatise on Hydraulics , p. 177) 
suggests that the loss of head may be calculated from the formula : 



where v s is the velocity in the smaller pipe, and : 

0*0418 


c — o*;82 


vi— r 


where r (= V n)> is the ratio of the diameters of the two pipes. He gives : 


r— o*o 

0*4 

o*6 

0*7 

0*8 

0*9 

°' 9 S 

1*0 

c — 0*62 

0*64 

0*67 

0*69 

0*72 

0*79 

o*86 

1*00 

£ = °‘ 375 

0*317 

0*242 

0*202 

0*15! 

0*071 

0*026 

0*00 


The rule is founded on the collation of several series of experiments, and is 
therefore quoted. The actual loss, however, appears to be largely affected by 
the circumstances of the prior motion, and the character of the contraction. 





























































CONTRACTIONS IN PIPES 


791 


Merriman’s rule applies best to cases where the velocity is high, and the con¬ 
traction sharp, such as small pipes, coupled up by metallic joints, and convey¬ 
ing water under high pressure. This is probably the case which occurs most 
frequently in practice. 

As a contrast, Brightmore ( P.I.C.E ., vol. 169, p. 323) experimented on 
6-inch pipes, contracting to 4 inches and 3 inches in diameter. 

The experiments on the contraction of a 6-inch to a 3-inch pipe show that 

the loss of head is only very slightly less than —— } so that we may believe 

2 g 


that, due to the pipes being rusted, the orifice formed by the contraction was 
not “ sharp,” and that the loss is therefore that caused by the reduction in 
velocity from that in the 6-inch pipe, to that in the 3-inch pipe. The results 
obtained in the 6-inch to 4-inch contraction are markedly irregular, and cannot 
be represented by any formula. If we put: 


v p — velocity in the 6-inch pipe, 
and v s — velocity in the 4-inch pipe, 


we find, as the mean of several observations, that: 

when v p — 4-2 feet per second. The head lost = 

when v v — 4 feet per second. The head lost = 
when v p = 2*5 feet per second. The head lost = 


°‘ 57 (^— Vp) 2 

2g 

07 3(^8 — v i) 2 

2g 

0-65 {Vs — VjA 1 
2 g 


The matter deserves closer study. For the present, it would appear that 
when the head lost is a quantity measured in feet, Merriman’s value is 
probably the best; but when the head lost is small, and can best be measured 

in inches, the loss is best represented by the expression h =—'^ t,s LJ ^ 


O <X 

<5 


The change of law will probably prove to be more or less intimately connected 
with the critical head phenomena discovered by Bilton (see p. 142). For the 
present it appears advisable to use Merriman’s formula only when the head 
given by his equation exceeds Bilton’s critical value for an orifice of the size of 
the smaller pipe, as we are then safe against an underestimation of the loss. 

Freeman {Trans. Am. Soc. of C.E ., vol. 21, p. 463) experimented on fire 
nozzles. These are orifices at the end of a channel of an area comparable 

. r . ... „ . Diameter of orifice /A„ 

to that of the orifice. Putting r, as the ratio --- ->—?—~i 

& ’ Diameter of pipe V A P 

Merriman (ut supra) finds that the experiments agree very fairly with 
C = 0*571 w here C, represents the coefficient of discharge of the 
nozzle. The tabulation of the experiments is as follows : 


r ... . 

o - 5 

o'833 

0*848 

o-886 

o*95 

1*000 

C (experimental) 

0-634 

0-736 

0-729 

0-742 

o’866 

o'975 

C (calculated) . 

0-643 

0-732 

0-741 

°*77 1 

<>■857 

I "OOO 





















792 


CONTROL OF WATER 


These values are applicable to nozzles of the form shown in Fig. No. I, 
Sketch No. 233. Fig. No. 2 shows a more favourable case, and No. 3 
Freeman’s standard design which produces C = o’95 to 0*97. 

In large scale experiments the difficulties discussed under Enlargements 
(see p. 795) occur, but by no means to so marked a degree. If the edge of 
the contraction is sharp, a vena contracta occurs beyond the contraction, and 
the rules given on page 786 are applicable. (See Sketch No. 234.) 

In practical experiments on a large scale the edge must usually be regarded 
as rounded, and the value 

H =■ ( v *~ v p ) 2 



probably overestimates the loss, provided that the motion in the larger pipe 

has become steady. If, however, the motion is unsteady, the rule 1 ‘^ Vs ~ v p ) 2 

2 g 

is probably more correct, but accurate experiments on a large scale do not 
exist. In some experiments smaller values have been found, but it may be 
suspected that these aie due to incorrect positions of the pressure gauges, or to 
the motion being stieam line (see p. 17). Some experiments of my own, 
wheie A;,, was 8 inches in diameter, and A.s, was 6 inches in diameter, give 

values varying between 1*2, and 1*4 j ; and as in Brightmore’s work 

v. 2g r ) 







































































































ENLARGEMENTS IN PIPES 


793 


the \ allies are apparently accidental, in that duplicate experiments rarely give 
identical results, and the differences are greater than can be explained by 
errors of observation. 

Sudden Enlargements in a Pipe.—Let A 1? be the area of a pipe which 
conveys a quantity of water A^, and let the area of the pipe section suddenly 
alter to A 2 , where A 2 , is greater than A x . 

If the water fills the enlargement, and the pipe continues to flow full bore, 
the new velocity is v 2 , where : 

V 2 & 2 = 7qAx 

If hi, and h 2 , represent the pressures at points in the areas A 1} and A 2 , 
which are at the same level, we have : 


^i + ~ = h 2 +~~ + H 0 , say, 

where H 0 , represents the “ head lost ” at the enlargement. 

Borda has given a theoretical investigation, which shows that there is 
reason to believe that 


h„ - fr ir- 3) 2 

As a matter of experiment, this value of H 0 , is usually slightly exceeded. 
Baer (. Dingler's Journal, March 23, 1907) experimented on pipes where 

A. 

A l5 was a circle of 2 inches (o - o5 metre) in diameter, and the ratio ^- 2 , 
was successively 3, 6, and 11*55. 

The values of ranged from ro5, to 9’28 feet per second in each case. 

Putting H = ——and H' = - 1 -~ t7 ‘ 2 ■ we find that: 

2 Z 2 g 


(i) For ^ = 3. 

(ii) For ~^ = 6. 

(iii) For ^=11-55. 

Ai 


The loss of head is slightly greater than H, and 

is practically, H+a constant, for all values 
of Vi> 

A 

The law is as for = 3, but the constant is slightly 

Ai 

greater. 

The loss is more nearly represented by 
IT — a constant. 


We may therefore state that : 

A " 

When -A is small (say not greater than 3), the loss is very close to H, but 

Ai 

Ao 

slightly exceeds H, and this excess increases as ^r- 2 - increases. 

Ai 

Ao 

When , is greater than 10, the loss is better represented by 
Ai 

A 

IT — a constant, and the constant decreases as — 2 , increases. 

Ai 


St. Tenant states that : 


Loss of head = 


Wi-^2) 2 , 1 v. 


^,2 


9 2 g 


o cr 








794 


CONTROL OF WATER 


Ao 

This rule agrees very closely with Baer’s results for " = 3, although the 

differences are greater than can reasonably be explained by errors in measure¬ 
ment. The rule, however, is quite sufficiently accurate for all practical 
purposes. 

I suggest the following : 


Ao 

If V 2 is less than 2. Then the head lost = H. 

Ai 

A 

If ~ is between 2 and 4. Then St. Venant’s rule may be applied. 
Ai 

A ->h + H' 

If ~ is between 4 and 10. Then the head lost = --■. 

Ai 4 

T C ^9 • 

If -y— is over 10. 

Ai 


Then the head lost = H'. 


These rules are intended to slightly overestimate the loss. 



Tm 

%r 

r 


T — —- 

** 

t 


Pressure ton 
relation 

no definite 
to 4 orh t 

< 

? 






-s- 


Madly indefinite 






Vein. Hi 


Horiiontai Line 

Vdy. l‘ n 



Sketch No. 234.—Pipe Contractions and Motion of a Pump Valve. 


Brightmore ( P.I.C.E ., vol. 169, p. 323) worked with a 3-inch pipe, en¬ 
larging to 6 inches in diameter ; and a 4-inch pipe, enlarging to 6 inches in 
diameter. After correcting for friction and change of velocity in the length 
of pipe between the points where the pressure was observed, he found 
that: 



Then the head lost = H for all velocities lip to -z/g = 3*5 
feet per second. 



Then the head lost = H—o , 04 to o’io foot, for velocities 
up to t/ 2 = 6 , 5 feet per second. 


I consider that the differences are explicable by uncertainties'as to the exact 
value of the friction. 

The whole question is also probably greatly influenced by the roughness 
of the pipes. 


























































LAB YRINTH PACKINGS 


795 


A 

In actual experiments, if the ratio is large, the stream issuing from the 

smaller pipe may move as a jet without mixing with the mass of eddying 
water which lies in the corners of the enlargement. If only a short length of 

pipe, of an area A 2 , occurs, it may then be found that the loss bears no 

n; 2 

fixed relation to —. In such cases, the amount of head lost (or rather, the 

ry or ’ ' ’ 

*v> 

length of the path which must be traversed before the loss is complete), is 
not determined in any way, and although St. Venant’s value, or the value 

771 2 — Vp 

—— ^ " , may be finally attained when the jet has filled the pipe, the distance 

beyond the enlargement where this occurs, depends on accidental circum¬ 
stances. Full bore flow without eddies may be attained in a length equal to the 
diameter of the pipe, or may not occur for 40 diameters or more. In many cases, 
where the enlargement is but temporary, the moving water may flow through 
the enlargement between “banks” of eddying water, with but slight diminution 
of velocity, and consequently with but small loss of head. (Sketch No. 234 
In CassiePs Magazine (March 1907), the head lost in a pipe 9 feet in 
diameter, and 29 feet in length, which then enlarged to 12 feet in diameter 
by a diverging cone 18 feet long, and was followed by 43 feet of piping, 
12 feet in diameter, is given for values of z/ 2 > up to 8 feet per second. The 
results are puzzling, and some error in the friction coefficients may be 
suspected. There is, however, not the slightest doubt that the excess of 
the observed loss of head over that which is given by the usual friction rules 
is very close to : 

V-^2 2 

2 g 

and that no reasonable assumption concerning the values of the friction 

f v _ v \2 

coefficients will permit the value —-— to be obtained. 

The lengths of the pipe are extremely short in proportion to the 
diameters, but until further evidence is available, it is advisable to regard 


2 -V 


as nearer the truth than the usual rule 




n or 


2 cr 
«*» 


ry # 

the larger value — 
in such cases. 

Labyrinth Packings .—These packings are well known, and although they 
are more employed in small apparatus than in large machinery, of late years 
they have been used with great success on a large scale. 

If a , be the area of a narrow passage, and A, be the area of the enlarge¬ 
ments, the theory developed above indicates that for a leakage Q, the head 
lost at each enlargement will be : 


Of (I_jY 

2g\a A/ 


and the energy of the exit velocity being also lost, we see that for a packing 
consisting of n enlargements, and n + 1 constrictions, the total head, or _ 
pressure difference, is : 

O 2 f M r i \ 2 , 1 \ _Q 2 «+1 


\a A/ 

whence the leakage can be calculated. 


_/ n[ 
20-I 


or 

~"S 


a~ 


approx. 








CONTROL OF WATER 


796 


Actually, an allowance should be made for skin friction. 

The experiments of Becken ( Ztschr . D.T.V., July 20, 1907), on a packing 
as per Sketch No. 235, where the circumstances, owing to the zigzag path, 
are far more favourable to loss by shock than in the ordinary packing, show 
that the above theory is fairly close to the truth, but that in practical designs 
the effect of friction is by no means negligible. In actual examples, the 
friction can be taken as proportional to v 2 (although under small differences 
of pressure capillary motion with resistance proportional to v, does occur) ; 
and if /, be the length, and j, the height of the constricted passages, we can 
write : 

Difference in pressure = Q—z (n+i +0*02 —\ 

2i r a~ V s / 

o 

where, of course, both /, and s, may be variable. 

In ordinary cases, s, varies between 9, and 3 thousandths of an inch. 




Shaft or Rofating Motion 


Sketch No. 235.— Labyrinth Packings. 


Losses of Head at Gradual Enlargements, or Contractions.—The usual 

treatment of this somewhat important subject is defective. The application of 
the theoretical principles to the case of Venturi meters has been considered on 
page 79. The draft tubes of turbines, and Herschell’s fall intensifier form 
other practical examples. 

Unfortunately, all the precise experiments upon the subject are on a small 
scale, and very many of them are useless. In the first place, Andres (. Ztchr . 
D.I.V.y Sept. 17, 1910) has plainly shown that the manner in which the water 
enters the enlargement (experiments on contractions do not exist, but the 
effect is probably very small in such cases) greatly influences the loss. Thus, 
if the water immediately before reaching the enlargement is passed through 
a fine mesh sieve, the loss differs considerably from that which occurs when 
the sieve is replaced by a diaphragm containing an orifice, or by an apparatus 
which causes the water to rotate round the axis of the diverging tube. 
Secondly, unless the pressures are so arranged that the vacuum existing at the 
contraction does not exceed a certain value (usually 20 to 24 feet head of water, 

. or 10 to 14 feet absolute, but which is obviously dependent upon the tempera¬ 
ture and the amount of air contained in the water), air will be released from the 
water, which will not therefore entirely fill the tube. Hence, the velocities 
cannot be calculated from the geometrical size of the pipes, and the experi¬ 
ments are useless. 






















CONICAL TUBES 


797 


Thirdly, in small scale experiments, the quantity of water passing is 
frequently such that at some point of its passage the velocity falls below 
Osborne Reynolds’ upper critical velocity (see p. 20). The law of skin friction 
consequently changes, and the experiments are useless. 

The necessity of bearing these conditions in mind is shown by the fact that 
206 out of the 254 experiments conducted by Fliegner are certainly affected 
by one or other of these causes, and possibly even some of the remainder 
as well. 

The theoretical treatment is simple. Let the velocity at the throat (or cross- 
section of minimum area) of a diverging tube be equal to v m , feet per second, 
and let /z OT , be the pressure in feet of water at this point. Then, h , the 
pressure at a point where the velocity is equal to v , is given by the following 
equation : 

<7/ 2_<7#2 

h - h m = 22 —— =H, say, 

and v m , and v , can be calculated from the geometrical form of the mouthpiece, 
when the quantity of water passing is known. 

The corrections for skin friction are uncertain. If the mouthpiece is 
circular in cross-section, and conical in longitudinal section, we find that: 

h - h m = v ™~ v ~ (1 — K) ... (A) 

2 cr 
“<t. 

where, K = —~^ 

O tan- 
2 

where § is the vertical angle of the cone, and v — C Jrs, is the frictional 
equation of the pipe. An equation of similar form, differing only in the fact 
that K, is multiplied by a constant, can be derived when the frictional 
equation is : 

v= A r'Ns 

It is usually stated that C, should be selected so as to correspond with the 
velocity v m , and a size of pipe equal to that of the throat of the mouthpiece. 
This statement does not appear to possess any very reliable experimental basis, 
and I doubt if it can be verified. 

As will later be seen, this detail is not of much practical importance. 

In actual practice, however, a very important distinction exists. If the 
motion is directed from the wider end of the mouthpiece towards the throat, 
the corrected equation is found to represent the experimental facts with 
sufficient accuracy. The fall in pressure indicated in equation No. A occurs, 
and any difference between theory and experiment is quite sufficiently explained 
by uncertainties as to the exact value of C. 

If, however, the motion is reversed, and is from the throat towards the 
wider end, the observed increase in pressure is less than the value calculated 
from the above equation, and the difference is usually greater than can be 
explained by any reasonable value of the friction coefficient. As Andres states, 
the transformation of velocity into pressure is imperfect, and an extra loss 
(which he terms the divergence loss) of head over and above that due to 
friction occurs. 

The experiments carried out by Andres were on twenty-two forms of diverg- 





798 CONTROL OR WATER 


ing tube, with circular, square, and rectangular cross-sections. Of these, nine 
were ordinary conical mouthpieces, and in seven the longitudinal sections were 
so calculated that if Bernouilli’s equation held exactly, the pressure head //, 
would have varied uniformly from one end of the mouthpiece to the othei. 
In the other six, the pressure head would have varied in a parabolic manner. 

Andres defines : 


2^1 


'£> l 


h x 


v 


2 _ 


m 


v 


h hm 


where h x is the observed difference between the pressure at the wider portion 
of the tube, where the velocity is equal to v, and the pressure at the throat of 
the tube, where the velocity is v m . 

Thus, 77 = i, would mean that Bernouilli’s equation was accurately true. 
Of course the influence of skin friction prevents ?j = i,from ever being attained. 


The maximum possible value of h x , is 


Vm — --head lost in skin friction, 




~g 


and then, 77 = 1 — K. 

The best results are invariably obtained with the nine conical tubes, for 
which the mean value of 77 in normal motion is 0720. For the seven straight 
line pressure tubes the mean is o'658, and for the six parabolic tubes the mean 
is o’ 673. I shall therefore merely consider the conical tubes, although varia¬ 
tions in 77 of a similar nature are produced in all forms of tube by alterations 
in the character of the water motion. The character of the water motion is 
fixed as follows : 

The water before entering the diverging tube is passed : 


I. Through twenty fine wire sieves. 

II. Through one similar sieve. 

III. The normal case where there is no obstruction in the pipe. 

IV. The water is passed through three small circular holes in a diaphragm. 

V. The water is passed through a channel obstructed by spirally twisted 

vanes, and thus enters the tube with a rotary motion round 
its axis. 

The effect of these preliminary operations is best illustrated by taking the 
mean values of 77 for all the tubes (conical or otherwise) experimented upon. 

(A) The mean value of 77 for seven tubes, when treated according to the 

method described in No. I, is o - 696, and the mean value of 77 for 
these same seven, in normal motion, is 0761. 

(B) For six tubes, treated according to case No. II, we get a mean 

77 = o’656, and the mean for the same six tubes in normal motion 
is 0727. 

(C) For twelve tubes, treated as in case No. IV, we get a mean 77 = o’Soy, 

and the mean for the same twelve tubes in normal motion is 
0776. 

(D) For eight tubes, treated as in case No. V., the mean value of 77 is 

o'88i, and for the same eight in normal motion it is o‘8io. 

Thus, we see that the more disturbed and turbulent the motion, the better 
is the value of 77 obtained. The high values obtained for a rotating motion 
suggest that the real reason why 77 does not always reach its theoretical value 




DIVERGENCE LOSSES 


799 


as corrected for friction is to be found in the fact that the moving water does 
not naturally fill the tube completely, but that an annulus of dead, or eddying 
water, forms between the walls of the tube, and the jet of moving water which 
issues from the throat. 

The following tabulation shows the results for the six circular conical tubes, 
the symbols being shown in Sketch No. 236. 


d x 

d<± 

l 

-o 

II 

to 

d 

tan — 

2 

_ d x — d.y 

2/ 

77 for Case No. 

v 1 1 e. L i ’ 

Remarks. 

In Inches. 

I. 

II. 

III. 

IV. 

V. 











Surface— 

2*86 

0*62 

10*62 

21*07 

0*105 



0*744 

0*824 

N 

O'. 

CO 

• 

0 

Unpolished. 

1*74 

o*6o 

8*46 

8*47 

0*068 

q 

CO 

Os 

On 

0*871 

0*883 

0*925 

0*989 

Polished. 

1*78 

o*6o 

8*46 

8*70 

0*068 



0*854 

0*861 

0*964 

Unpolished. 

1*77 

0*67 

10*23 

6*86 

0*054 


0*806 

0*838 

0*903 

0*920 

>> 

1*20 

o*6o 

8*46 

4*00 

0*034 

0*890 


0*890 

0*892 

0*928 

Polished. 

1*20 

o*6i 

8*08 

3-88 

0*037 



0*812 

<>■855 

0*857 

Unpolished. 


The final deductions by Andres for the case of a conical enlargement of 
circular cross-section are founded on a discussion of his own experiments, and 
of those of Francis and Banninger, and are as follows : 

*Uy t i _ 7 /^ 

The theoretical increase in pressure being h—h m — H = ■■ - that actually 

observed in normal motion (Case III.) is h v We can account for a certain 

<rH 

portion of the difference H — k ly by skin friction, say hf — -v Andres puts 

C 2 tan* 

2 


h x = H — (hci+hf), and finds that ha = 77, where rj d is a function of 8 only, 
being independent of C, and of v m , provided that the pressures are so adjusted 
that air is not disengaged at the throat, and that Reynolds’ critical velocity is 
not approached at any point in the enlargement (see p. 20). 

The points representing the values of rj d are somewhat irregularly distri¬ 
buted, although not more so than can be explained by the difficulties already 
enumerated. The following table may be used : 

8 = 12° II 0 io° 9 ° 8° 7 ° 6° 5° 4° 3 0 2 0 

ry,{ = o'2o 0*13 0*09 0066 0*055 0*050 0*046 0042 0*039 0*036 0*033 

It will be plain that the smaller C is, the less will be the value of 8 which 

will give the largest value of 77 = yj, and the best design is found by making 


r]d + 


lif 

H 


a minimum, or 77 a maximum. 


It would also appear that a similar equation may be applied to enlargements 
which are not conical. A mean value of 8 or of rj d is selected for each short 
length. This short length is then considered as conical, and 77 is calculated. 
The value of h\ = 77H', where FT is the theoretical increase in pressure in the 
short length, can thus be obtained, and by repeating the process the pressure at 


































8 oo 


CONTROL OF WATER 


any point in the enlargement can be ascertained. Andres states that the results 
of this process agree fairly well with observation. 

A similar law probably holds good for enlargements which are square or 
rectangular in section ; but as these, in practical cases (eg- the wheel or guide 
vane passages of turbines, or centrifugal pumps), generally have a curved axis 
further and more detailed experiments are necessary before any useful rule can 
be given. 

Gibson ( Proc . Roy. Soc ., vol. 83, p. 368) has also investigated this subject, 
using tubes of varnished wood in which: <^1 = 3 inches, d 2 = 1*5 inch. Ihe 
arrangements were by no means so perfect as in Andres’ experiments, but 
for that very reason they resemble those which are likely to be employed in 
engineering practice. 

The results obtained by Andres for normal motion are generally confirmed, 
more especially the most important one that with tubes of circular cross-section, 



at any rate, a conical enlargement is more efficient than any other form. So 
also, i)d is found to depend upon d only, provided that “ the velocity exceeds 
5 feet per second.” 

The following tabulation shows the values of S and rj d for the pipes experi¬ 
mented upon. The differences between this table and that given by Andres 
(which I consider to be the more practical inside its own range) are easily 
explicable by the fact that Gibson used the formula : 



in order to determine the head lost in friction : 


b 

• 

90 ° 

6o° 

5o° 

0 

0 

30 ° 

20° 

1 7\° 

Vd 

• 

o‘6y 

072 

o'6 7 

o’6o 

0-49 

0*24 

0-19 

8 

• • 

i5° 

12 F 

IO° 

7V 

5° 

4 ° 

^0 

0 

rjd 

• • 

0*14 

0*10 

0-073 

0 

d 

to 

0028 

0‘022 

0-013 




















PUMP VALVES 


801 


a = 


firn . _ . 

^ST< see p.803). 


SYMBOLS FOR PUMP-VALVES 


b = 


d-d. 


dh 


(see also p. 805). B (see p. 804). 


c = —, is the velocity of the valve cover in feet per second. 
c s , is the velocity with which the valve cover strikes its seat. 


C = U 


sin 7 mt 


\o 


, is the velocity of the pump piston in feet per second. 


C s , is the valve of C at the instant when c = c s . 

d, is the diameter of the valve cover in feet. 

d x , is the diameter of the orifice in the valve seat in feet. 

E (see p. 804). 


TV 

f = ~cP, is the area of the valve cover in square feet. 

fx — —d-i, is the area of the orifice in the valve seat. 

4 

F, is the area of the pump piston in square feet. 

h, is the lift in feet of the valve cover above its seat. 

^max, is the maximum value of h. 

k 0J is the value of h when C = o. 

v 2 

H = t -A_, is the head lost at the valve in feet. 

i, is the number of guide ribs and s is the thickness of one rib, thus l=ird-is. 

I, is the nett circumference of the cylinder traced out by the edge of the valve cover 
which is free for the passage of water. l=vd or ird- is. 


Ip (see p. 804). 




M v (see p. 804). 


F 

771= —. M 

f , 

n, is the number of revolutions the pump makes per minute. 

P, is the load on the valve in lbs. 

Q, is the delivery of the pump in cusecs. 

S, is the stroke of the pump in feet. 

z\ is the velocity of the water through the area Ih in feet per second. 

z; lt is the velocity of the water through the area f v i.e. v x = ~, but v is not equal to 

O * 

-jj~ (see p. 802). 

a, v (see p. 805). 
k (see p. 805). 

X (see p. 805). 


SUMMARY OF EQUATIONS 


tan X— ~ a 


inf U 


lv if 1 + a 2 


. / 7 mi \ t , 

( 3 ® /' J 


/<„= - 


inf U 


a 


^max — 


mfU 


lv fl+ a 2 


c = 


C,= 


lv 
mXJa 


l + CL 
Tnit 


\/1 + a 2 
U a 

sj I + a 2 


( 7 Tilt \ 

COS-+x| 


c,= 


mV a 
Jl +d z 


c s = mC s = 


7 rnh 


max 


30 


lv J 

-jK 


c s = 0-0055 


FS n 2 
lv 


= 0-0055 


Qn 

lv 


51 



















802 


CONTROL OF WATER 


Valves. —It may at first sight appear that the treatment of this subject by 
a civil engineer is somewhat presumptuous. My excuse is that the necessity 
for some special and definite knowledge on the matter has been forcibly 
brought to my notice by failures in my own designs. I have also found that 
the troubles which occur in pumping machinery may generally be attributed to 
incorrect proportioning of the valves, and an engineer in charge of pumps in a 
locality which is far distant from a regular workshop can at any rate assure 
himself that if his troubles (exclusive of those caused by neglect or careless 
repairs), are not due to errors in valve design, it is extremely improbable that 
his mechanical resources will be sufficiently extensive to permit any remedy. 

I believe that the literature on the subject is exclusively of German origin, 
and that it has not been translated. 

Motion of a Pump Valve.—The ideal case of the motion of a valve through 
which water is being pumped by an ordinary piston pump can be investigated 
as follows : 

'TT'J'lt 

Let F, denote the area of the pump piston, and C = U sin its velocity at 
any time t. 

Let f be the area of the cover (or moving portion) of the valve ; and let 
/z, represent the height of the cover above the valve seat ; or, for shortness, the 
height of the valve opening. 
dh 

Then c ~~t^ is the velocity of the valve cover, or, for shortness, the velocity 
of the valve. 

Let /, be a length such that //z, represents the area which is free for the 
passage of water between the valve cover and its seat, when /z, is the height of 
the valve. That is to say, in a simple, circular valve of d feet diameter, /= 77 z/, 

where f—~~’ 

Let 7/, be the velocity of the water through the spaco between the valve 
cover and its seat, so that //ziz, represents the quantity of water entering the 
rising main. Then plainly : 

¥C = lhv+fc 

where fc , represents a volume of water that passes through the orifice in the 
valve seat, but does not at once get through the valve itself, being temporarily 
stored up underneath the valve cover. 

Now, C = U sin where zz, is the number of revolutions of the pump pet 
minute (2zz = the number of strokes in a double acting pump), and therefore: 


lvh=f sin 

J l 30 dt J 


where F = mf. Thus, /z = 


zzz/U 


W '+(£=)’ 


/ 7rZZ/ \ 

s,n l^T + x) 


, dh_ 
and c=-r: 
at 




TTJl 


h 


V '+(1 


30 

0 cos 

f 7rzz\ 2 v 3 ° 

Iv 30/ 


Iv 30 

/ 7 mt . \ 

+x ) 










PISTON AND VALVE MOTION 


803 


where tan x~~ r. as is easily proved by substituting the values in the 

IV jO 

original equation. 


Let a, denote the small quantity 


fn-n 

Iv 


-tan x- 


Now, the maximum value of /i, occurs when n/ 1 ^+x— — ; 

30 A 2 


and //max = 


mf U mf\J 


approximately. 


lv\'\ + a 2 to 

n O 

When /=o, or — {i.e. at the dead points of the piston stroke), //, is not zero, 
but has a certain value, lh 0 , say, and : 

u h — mf U a _ mf 2 Vnrn 


sin X : 


(/z/) 2 3o 


, approximately, 


Iv+i+a 2 ~” A to 1+a 2 
and when /= — , h = — ho, and is positive. Thus when the piston arrives at its 


?i 


dead point the delivery valve is still slightly open, while the suction valve (on 
the other side of the piston) has closed a little before this instant. 

TT IXt 

So also, h~ o, when-t-X = °; or ) si nce X ]S a sma ^ an gle, we can put 

'' f 

tan x — X) so ^ iat h = o, when 

Thus, the interval between the arrival of the piston at a dead point and the 
closure of the valve is independent of the rate at which the pump runs, and of 
the length of its stroke. This has been experimentally confirmed by Bach (see 
Mueller, Das Pumpen Ventil). 

The velocity with which the valve closes down on its seat is obtained by 
putting : 


cos ^ 


/ nt-K . \ 

^ +x ) =,) 


and is c s = 


mfXUrn _ ml]a 


30/W1+# 2 ^i-f# 2 


The simultaneous velocity of the piston is : 


Ca - 

IT 71 


U sin x = 
Iv 


U a 


1+a 2 


Therefore, c s =? 7 iC s = h ma f-'- — ~h 0 - 

30 / 

Now, put S, for the stroke of the pump. Then, S 

^ FSn 2 n 2 FS n 2 Qn 

Thus, c$ — 7 --— 7- =0*005 5—, 

’ 60 x 2>oto J Iv Iv 


60U 

Tin 


where Q = FS«, is the delivery through the valve in cubic feet per second, that 
is to say, is one half of the delivery of the pump in the case of a double acting 
pump. 

Consequently, we may at once deduce that if a pump with a stroke equal 
to S, is known to work without shock at «, revolutions per minute, when 
delivering Q, cusecs, a pump with valves of the same design will work without 
shock, provided that its^stroke, speed,'and delivery are such that; 

« 1 2 S 1 = « 2 S, orQ 1 « l = Q«, 


















804 


CONTROL OF WATER 


The great importance of the velocity v, which expresses the speed of the 
water through the valve opening, is also evident. 

The above theory cannot be considered as complete. In many cases we 
should take into account the acceleration of the valve. The height to which 
the valve can rise is frequently limited. 

It is also quite certain that in many cases (other than piston pumps) v, is 
not constant, but is greatly influenced by the value of h. Nevertheless, it is 
plain that if we merely consider the motion of the valve just before its closure, 
we can assume that 7/, is constant; and can thus determine the magnitude of 
the shock produced by closure of the valve, with a very fair degree of accuracy. 

It will be seen that some shock must occur, and that the limit at which the 
shock becomes detrimental is somewhat a matter of opinion. 

Lindner {Ztschr. D.I.V. , Aug. 29, 1908) states that c s , should not exceed 
o - 33 foot per second. Berg {Ztschr. D.I.V. , Aug. 6, 1904), states that there is 

no “ audible shock,” provided that h 0 , does not exceed in a circular valve, 

the diameter of the valve cover being d. or-in the case of an annular valve, 

250 ’ 

where B , is the radial breadth of the valve cover. 

This mathematical investigation may at first sight appear to be somewhat 
artificial. Berg {ut supra ) gives several graphic comparisons between the path 
of a valve cover as actually observed, and as calculated by this theory. The 
agreement is satisfactory, more especially during the interval just before the 
closure of the valve. When applying the theory to practical problems the 
difficulties which arise are mainly caused by the fact that the experiments were 
not well adapted to discover what are the conditions under which the shock at 
closure proves detrimental. Berg, Bach, and Westphal, all appear to consider 
that the valve works satisfactorily, provided that it does not give rise to an 
audible sound when closing. If a metal valve “ sounds,” it will rapidly become 
leaky, but valve covers made of leather or rubber may work well under circum¬ 
stances which would cause a metal valve to sound. 

Thus the above opinions are only approximations, for the harm done by 
the shock depends upon the total energy of the moving water at the instant 
of closure. At this moment the piston is moving with a velocity equal to C s ; 
and the valve being closed, the water in any passage in communication with 
the piston is moving with a velocity equal to c p , where qpF p =C s F, the area 
of the passage being F,,. If 4, be the length of this passage, the mass of 

water moving with a velocity c p is —5 Fj,/ J ,= M J) , say. 

S 

r 2 Tvr /- 2 

Thus, the total energy is SMp—+ —— = E, say. 


Or E-^-^C i 2 F 2 2^- + MifA ) where M y , is the mass of the valve, and the 

z s r p z 

summation is extended over all the water which is not separated from the 
piston by a closed valve, or by an air chamber. 

Thus, if the pressure valve is considered, we must take into account all 
the water in the cylinder, on the valve side of the piston, and also the water 
in the suction main down to the foot valve, unless there is an air vessel on the 
suction main, in which case we have only to consider the portion of the main 
between the cylinder and the air chamber. 








VALVE RESISTANCE 


805 


The Value of v. —The value of v, has been shown to be of primary im¬ 
portance in this connection, whatever opinion may be adopted as to the precise 
conditions for avoiding detrimental shock. 


Bach {Versuche iiber Ventilbelastigung und Vcntilwiderstand, and other 


papers, a complete list of which is given in Hutte, vol. 1, p. 884) states as follows : 


Let P, be the load on the valve in lbs. including its own weight, and any 


spring, or other mechanically produced loading. 

fi ~ — 1 - is the area of the opening in the seat of the valve (not the valve 


cover), in square feet. 

zq, is the velocity of the water through the area f, i.e. v x f = vlh-\-fc~YC. 



2 



(a) Then, for valves without guiding ribs, i.e. in which l=-nd : 



( b ) If the valve has i guide ribs, of a thickness represented by s , so that 
l~ 7T d — is : 


/ 



The values of X and /z are variable. 

I. For flat valves with no ribs (see Sketch No. 237, Fig. 1): 


Case (a), with : 


b , lying between o’io d u and 0*25^, 
and h , lying between o’iod u and 0*25^. 



(3 = o'i6 to 0*15, 


the first values of /z and /3 occurring when b, is large. 


II. For flat valves with ribs (see Fig. No. 2) : 
Case ( b ): 

X and /z are 10 per cent, less than in Case ( a ), 



a is 1*8 to 2*6 times the value of a in Case (a), and 
/8—170 to 1*75. 

III. For conical edged valves, with b — o’\d^ h-=o'\d\ to 0*15^1 (see Fig. 
No. 3), as in Case ( a ) : 

X= —1*05, n = o' 8 (). 



a = 2 ’ 6 o , 13= - 0 - 8 , 


y = o‘I 4 . 






806 CONTROL OF WATER 


IV. For valves with a conical bottom and with conical seat. With 
A = o'125 d\ to 0*25^ (see Fig. No. 4), as in Case (a) : 

X = o* 38, /* = o'68. 

£=a+l 3 (j\ : a = o’6o, /3 = o'i5. 

V. For valves with a spherical bottom and conical seat. With 
h—o'\d Y to 0*25^ (see Fig. No. 5), as in Case ( a ): 

A = 0*96, H-= VI S- 

f= a +/3('|)+y(x) : 

a = 270, /3 = — 0*80, 7 = 0*14. 

The values given above cannot be considered as universally applicable. 
With one exception they were all obtained from valves of the dimensions 


© 




© 


© 


© 



shown in Sketch No. 237, and apparently not more than one valve of each 
type was experimented on. 

It will also be observed that the equations given refer to cases when the 
valve is fairly wide open. Bach ( Ztschr . D.I.V. , May 15, 1886) has given 

equations for P, and £ for two valves of Type I. which hold from h = ^ to h= ~. 
Berg (ut supra) states for flat valves (Type I.) that: 

and tabulates k as follows, when d— 60 mm. 

ho o'1 o'2 07 o'4 07 o'6 o'8 i'o 1*5 mm. 

k o' 65 071 078 C845 °‘89 0*911 o'9i3 0*902 0*870 0788 

For larger values of h, the equations already given apply. 














































































SPRING LOADING 807 


It is probable that these values apply equally well to all valves except 
perhaps those included in Type II. 

The load P, is usually produced by a spring. Putting P = ze/ + S, where w, 
is the weight in water of the moving portions of the valve, and S, is the spring 
load, S, can be calculated as follows (see Unwin, Machine Design, p. 99) : 

Inch Units are used.—Let r, be the radius in inches of the cylinder on which 
the axis of the wire forming the spiral spring lies. Let d, be the diameter of 
the wire in inches, and n , the number of turns in the spiral spring. 

Then, for steel wire, less than § of an inch in diameter, a load of S pounds 
shortens the spring by S inches, and : 


5 = 

S, must not exceed 


S/zr 3 
1 So^oo *'/ 4 
12,000 d s 
r 


lbs. 


[Inches] 

[Inches] 


The general equations are : 


* 64 r 3 zzS 

IT 


. [Inches] 


where C, is the coefficient of rigidity of the wire, and : 


S, should not exceed 


fgd z 

i 6 r 


lbs. 


[Inches] 


where f is the permissible shearing stress in lbs. per square inch. 

The calculation of v , is now obvious. We calculate the value of 7q, from 

the known value of P, and by substitution arrive at the value of v. Since we 

are mostly concerned with a valve which is very nearly closed, we can, for a 

first approximation, consider P, as the load corresponding to a closed valve 

(i.e. when P, is produced by a spring, the spring is extended as far as the valve 

seating permits). So also, if we think that it is desirable to take into account 

the acceleration of the valve, we can consider that P, is decreased by a 

ati <Ph 
term ML 

These figures are also useful when we are dealing with the valves of a 

v 2 

hydraulic ram. Here P, is given, and also H = £— = /*i, in the original 

2 g 

investigation (see p. 845). Consequently, we can calculate zq, and so 
determine /z, the opening of the valve. In practice, the question is best 

27 2 

investigated by tabulating P, in terms of /z, and /z 1} or in terms of zq, and 
then selecting the correct values. 




CHAPTER XIV.— (Section B) 


WATER HAMMER 

Water Hammer. —Pressure produced by a change in the velocity of water in a pipe— 
Effect of the time occupied in producing the change—Corrections for the elasticity of 
the pipe metal—Practical rules—Comparison with observation. 

Gradual Stoppage of Motion in a Pipe. —Gibson’s investigation—Criticism— 

General Investigation. 

Resonance. —Period of valve closure—Period of the pressure waves in the main— 
Practical Applications —Values of % and 

SYMBOLS 

A, is the area of the pipe, in square feet. 

a, is the area of the vena contracta near the valve (see p. 814). 
a x (see p. 814). 

C=— j=, is the coefficient of skin friction for the pipe. 
s'rs 

d, is used for the sign of differentiation. 

E (see p. 811). 

f, is the diameter of the pipe, in feet. 

PI, is the total head, in feet, producing motion through the pipe and valve. 
h, is the head producing motion through the valve. 

K (see p. 811). 

/, is the length of the pipe, in feet. 

4 (see p. 815). 

p x , is the pressure near the valve when the motion of the water is uniform, and its 
velocity is v v feet per second. 
pi, is the maximum impulsive pressure. 
pm, is the mean value of the impulsive pressure. 

p a , is the statical pressure, i.e. the head H, expressed in pounds per square inch. 

The p’s, are all measured in pounds per square inch. 
q (see p. 815). 

Q (see p. 815). 

t, is the symbol for time in general. 

4 (see p. 811). 

m 2/ 2/, _ 

T = — or — (see p. 810). 

A 

T 0 (see p. 814). 

u, is the thickness of the pipe walls, in inches. 

v x , is the initial velocity of the water, in feet per second. 

v, z , is the final velocity of the water in the pipe, in feet per second. 

Av (see p. 816). 

77 (see p. 816). 

A, and X e (see p. 811). 

KV-, represents the head lost in the pipe when the velocity is uniform and equal to v, feet 
per second. 


808 



WATER HAMMER 
SUMMARY OF EQUATIONS 

62*5/ 

A»= —ft lbs> P er square inch. 

2 X 62'^/ 

P* = '~ i44gt ( w i~®a) +A~?2 lbs. per square inch. 

Practical Formulae. 

2/ 

(a) t, less than-seconds (see p. 811). 

4700 v 1 ’ 

pi —4(^1 )+A ~ P<i lbs. per square inch maximum value. 

Corrected for alteration in wave velocity produced by pipe thickness 
pi = 60 (vj - v. 2 ) +pi~f>2 for small pipes'l ,, . , 

Pi =* 5 ° ( v i — V P) + Pi ~Pi for large pipes j bs " P er S( l uare in ch. 

0*027 (®i - %) 


809 


[b) pi~o if is greater than 


Pi-Pi 


Water Hammer. —When the motion of water in a pipe is altered in any 
way, the change in the velocity of flow is attended by a certain alteration in the 
momentum of the whole mass of water in the pipe. This can only be effected 
by a definite force. 

Let /, be the length of the pipe in feet, and A be the area of its cross- 
section in square feet. The mass of water in the pipe is expressed by : 

62*5/A 

~g~ 


and if v lt be the velocity of the water, in feet per second, the momentum is : 


62‘$/Av 1 

g 


If the velocity be reduced to 7/ 2 , bi a period of /, seconds, the rate of change 
in momentum is : 


62'5/A 

g* 


(wi-v 2 ) 


and the force required to produce this rate of change is : 

Tr _ 62*5/A 


gt 


{v x -v 2 ) 


Thus p nlf the mean impulsive pressure required to produce the change in 
velocity is given by : 

i44A/ m =F 

62*5/ 


or, p m = 


144 gt 


(p\ — vP) lbs. per square inch. 


Now, let / 1} be the pressure in pounds per square inch, measured at the 
valve, the closure of which produces the alteration in velocity, when the velocity 
is t/j, and is uniform. 

Let / 2 , be the similar pressure when the velocity is t/ 2 , and is uniform. 
Then, approximately p\—p R —kvp, and po=p s ~K 7 ^ 2 2 , where/.,, is the statical 
pressure. 

Sketch No. 238 shows the general course of events during the time that 
elapses while the uniform velocity v u is changed to the uniform velocity 7 ' 2 . 
The diagram indicates that the change in the pressure from p i} to p 2 , does not 
proceed uniformly, but that the value of the pressure oscillates backwards and 











8 io 


CONTROL OF WATER 


forwards, and only attains a steady value equal to ft 2 , after a certain time has 
elapsed. The maximum impulsive pressure generated by the alteration of 
velocity is given by fti-\-ft\~fti, and experiment shows that this is very 
approximately equal to 2ft m . 

We therefore denote this maximum impulsive pressure by fti , and find that: 
ft i = 2 ft m +ft 1 -ft 2 = ?^^\v 1 -v 2 )+ft 1 -ft 2 lbs. per square inch 

represents the maximum pressure tending to rupture or otherwise damage the pipe. 

It will be plain that the equation could be obtained by assuming that the 
relation between pressure and time is of an approximately triangular shape, as 
shown in Sketch No. 238. If the matter is thus regarded, the experimental 
results merely indicate that the minor waves in the time and pressure diagram 
do not materially affect the maximum value of the pressure. 

So far we have implicitly assumed that water is incompressible, so that the 
velocity of the whole volume of /A, cube feet of water is changed from v ly to v 2 , 


Pressure nhen iva/ei • is at res/ 



in the interval t. This is not the case, and the diagram of pressures already 
referred to shows that the pressure jumps up and down much as a weight 
hung on a spring would do. Mathematical investigations, which have been 
confirmed experimentally, show that if /, be less than a certain value, T, 
the pressure does not increase beyond the value given by putting t— T, in 
the above equation. The value of T, can be calculated from the equation 

2 1 ... . 

T = — where X is the velocity with which a w r ave of compression travels in the 
water and the pipe. We thus have two cases to consider : 

. 2/ 

(1) Where /, is less than Put in the equation for/,, and we get i 

, 62’5\ . 

~ T ( v i — 7/ 2) +fti —ft* 

2 1 

(ii) Where /, is greater than : 

A 

fti = 0-027 ^— ( v x - V 2 )+ ft !- ft - 2 . 




















811 


TIME OF VALVE CLOSURE 


The distinction between the two cases is at first sight somewhat artificial. 


Its physical basis is best realised by considering that if /, be less than 2 /- the 

A 

whole change of velocity near the valve is completed before the wave of com¬ 
pression can travel up to and return from the upper end of the pipe. Thus, the 
momentum of the water at and near to the upper end of the pipe cannot be 
transmitted with sufficient rapidity to produce an effect in increasing p and 
what really happens is that the value p^ is attained not for one instant only, as 
is shown in Sketch No. 238, but for a certain space of time as is indicated in the 
inset to the Sketch. The real basis of the theory is the fact that it can be 
experimentally confirmed. 

Considering the first case, we have as follows : 

Theoretically A is equal to the velocity of sound in water, and is equal to 
about 4700 feet per second. Thus : 

- (T- . * . •» 

pi = byMvi—v<P)+p 1 —p 2 lbs. per square inch. 



In actual practice, we must take into account the fact that not only is water 
compressible, but that the metal of which the pipe is composed is extensible. 
This fact somewhat reduces the value of A. 

Let K, be the bulk modulus of water, =300,000 lbs. per square inch. 

Let E, be Young’s modulus for the metal of which the pipe is made, i.e. 
E = 30,000,000 lbs. per square inch for steel, and E = 15,000,000 lbs. per square 
inch for cast iron 

Let R, be the mean radius of the walls of the pipe, and t L , their thickness in 
inches. Then: 

(i) If the pipe is fixed so that it can only expand circumferentially, the 
effective value of A, say X e , is : 



A 



2K ? 
E A 



for steel, 


v 



for cast iron. 
R 


25A 















































8 l2 


CONTROL OF WATER 


(ii) The pipe can expand both longitudinally and circumferentially : 



for steel, 


for cast iron. 


The first case is that which most closely resembles the conditions which are 
usually met with in practice. 

The experimental verification of these formulas has been effected by 
Joukowsky, Gibson, and others. When the value of 63*4(2/! — 2/ 2 ), does not 
greatly exceed 120 to 150 lbs. per square inch, or v x — 2/ 2 , does not greatly 
exceed 2, to 2*5 feet per second, it is found that the calculated values of p^ 
corrected for the difference between X and X f , agree very exactly with the 
observed values. When, however, this value is exceeded it is found that the 
observed pressures are considerably less than those calculated as above. The 
difference is explained by the yielding of the joints in the pipes, and if 
necessary an allowance could be made by taking a smaller value for E, as Pi, 
increases. 

The formula may therefore be regarded as giving good approximate results 
in all cases, and as indicating values which are somewhat higher than the 
truth when the impulsive pressures are large. 

For a given alteration in velocity the shock is usually smaller in the case of 
large pipes than in those of less diameter. For preliminary calculations the 
following formulae may be used: 


pi = 6 o(v 1 — v 2 )+p 1 —p 2 m small pipes.. 
px — 50(2/! — V2)~\~Li ‘ — P2 i n large pipes. 


The following figures show Joukowsky’s observations (Stoss in Wasser- 
leitungsrohren ) on pipes 4 and 6 inches in diameter, with 7=1050 feet, and 

'll. 

1066 feet, and 7=0*03 seconds. Consequently, /, is less than The calcul- 

A e 

ated values are obtained from the formulae : 


pi — 63*72/, corresponding to inextensible pipes ; 
and pi— 56*62/, corresponding to a cast iron pipe, with 

— = 8, and E = 15,000,000 lbs. per square inch, 
n 

where v, now represents the change in velocity, and in this particular case the 
valve being entirely closed : 


v 2 = o, so that v — v x . 

The second case presents but few difficulties, and it is sufficient to observe 
that pi= o, or that there is no shock provided that: 


/, is equal to, or greater than 


o‘oiyl(v l — v 2 ) 
P2-P1 










GRADUAL CLOSURE 813 

FOUR-INCH PIPE. 


• 

v , in Feet 
per Second. 

pi observed 
in Lbs. per 
Square Inch. 

pi calculated. 

A = 6 37 v 

in Lbs. per 
Square Inch. 

From the Formula 
pi =56 - 6 v 
in Lbs. per Square 
Inch. 

°*5 

31 

3 1 

27*9 

1 *9 

"5 

118 

106*0 

2*9 

168 

183 

l62’0 

4 'i 

232 

258 

228*0 

9*2 

5*9 

580 

512*0 

SIX-INCH PIPE. 

0*6 

43 

38 

33*5 

1 ‘9 

106 

118 

106*0 

3 *o 

173 

189 

167*0 

5*6 

369 

353 

312*0 

7*5 

426 

472 

429*0 


Gradual Stoppage of Motion in a Pipe. —This problem is extremely 
complex. The principles of the following investigation are due to Gibsorn 
(.Hydraulics and its Applicatio?is'). The results agree very fairly with experi¬ 
ment, and the theory may therefore be considered as correct, for pipes of 
small diameter at any rate. 

A consideration of the terms which are neglected in the investigation has 
led me to believe that the theory may not hold for large pipes, and I shall 
therefore discuss a more exact theory later on. I have not, however, been able 
to discover any case where Gibson’s theory does not agree very fairly well with 
experiment, and the accurate theory may therefore be regarded merely as a 
subject for investigation in cases where Gibson’s theory does not entirely agree 
with the results which are experimentally obtained. 

Referring to the theory already laid down, we find that the important instant 

O l . 

of time is seconds before the valve closes down on its seat. 

A 

Let z/j, be the velocity of water in the pipe close to the valve at this moment. 

Let (^) ? represent the rate of change of the velocity at this moment. 

Then, since A is the rate at which a wave of compression travels along the 
pipe, the velocity at the upper end of the pipe is : 

. I(dv\ 

Vl+ \\dt)i 

and the mean velocity of the whole body of water in the pipe is : 

/ / dv\ 




































814 


CONTROL OF WATER 


2 1 

This velocity is reduced to o, in a time y and also at the instant considered 

the water is being retarded at a rate represented by ) • Thus, it is neces- 

sary to apply the results of the two cases which have been previously discussed 
and the pressure produced by the closure is : 

, . f , l (dv\ 'j 62*5 l(dv\ , , 

* = 63 n Wi+ i 

where p lt is the pressure corresponding to uniform velocity v lf and p*, is the 
pressure when the valve is shut, and the water is at rest (i.e. p% — fi$). 

The determination of v Xi and is effected by Gibson as follows : 

Let H, be the total head in feet causing motion through the pipe, i.e. the 
head corresponding to the pressure p s — p 2 . 

Then, if f be the diameter of the pipe, and h, be the portion of H, expended 
in forcing the water through the valve, then: 

v 2 4 l 


H 


C 2 / 


■h 


where v — CVVj, is the friction equation of the pipe. Also, if a, be the area 

of the vena contracta of the jet issuing from the valve, and v v , the velocity of 
the jet at this point, then: 

tt / 2 

av v — -^—v = Av, say, 

4 * 


and H = *-*(*)'. 

2 g 2 g \ a / 


Thus, H = A&f + ^a '») = 


kv £ , say. 


At 


Now, Gibson assumes that the valve closes so that a — =-, where is the 

A 0 

time before the complete closure of the valve, and T 0 , is the time before closure 
when a, was equal to A, assuming that the valve was closed uniformly. 

A^/ 

Thus, putting a x — c-qr, so that a u is the area of the vena contracta at a 

A e L 0 

2 1 

time before the complete closure of the valve, we get: 


v x = 


/ 


H 


/ 4 L 
V c 2 y 


4/ , A 2 

V 2gai* 


A 


dv\ 
dt) 1 = 


VH 


lc 2 /^ 


A 2 


2ga x 


y 


A 3 

2ga x 3 T 0 ' 


From these values p x , and pi, can be calculated. 

The theoretical difficulties are obvious, and Gibson has since (see Water 
Hammer in Pipes ) treated the problem by a different method. In particular, 

the value for 5 plainly obtained in a somewhat peculiar manner, and 

the equation : 

might be employed with advantage. 

Nevertheless, the results calculated by Gibson’s method agree very well with 
observation, and the discrepancies which occur when the pressure is large are 












FORM OF PRESSURE El A GRAMS 


815 


probably amply explained by yielding of the lead joints of the pipes, as has 
been previously mentioned. 

The experiments refer to pipes y 6 inches in diameter, and a careful 
examination of the theory leads me to doubt if it will be found equally accurate 
when applied to larger pipes. The general investigation now given renders it 
likely that Gibson’s equation does not lead to results which are less than the 
truth, unless the motion of the valve is purposely adjusted so as to produce 
resonance effects. I therefore believe that Gibson’s method is valuable, for if 
its application shows that the calculated pressures do not exceed values which 
the pipes can sustain, we are entitled to consider that failure by shock is 
improbable. 

General Investigation.—Consider Sketch No. 239. We see that if the 
velocity is altered by an amount represented by dv, waves of compression and 
rarefication are set up in the water, and in the metal of the pipe. The observed 

_ 62*5 


values of the pressure can be represented by q 


144^ 


dv<p(r) lbs. per square 


inch, where r represents the time reckoned from the moment when the valve 
was first moved, i.e. the point A, and q, is measured from the dotted line, which 
shows the value of the pressure when the oscillations have completely died 
out. Now, putting X for the effective velocity of these waves (i.e. their velocity 
when corrected for the elasticity of the pipe), theoretically if /, be the length 
of the pipe, and 4, be the distance of the point considered from the upper end 
of the pipe, we have: 

Where, measuring from the line DG, or 


62*5 

M4^ 


dv <p (r) = — p . 2 +_pi, so long as r is less than 


(p (r) = 

G) = 

(/> (r) = 
cp (r) = 


i, when r lies between 


o, 


5J 


n 


55 


jj 




55 


/-4 

X 

/+4 

^T 

li-h 

x 

3/4-4 


and 


55 




5? 


/-4 

x 

M-4 

X 

3 /-4 

X 

3^+4 

X 

5/— -4 


4/ 


and thereafter the last four values of cp (r) repeat with a period of 

The observed values do not agree with the theoretical ones, as is evident 
from Sketch No. 239, and we get the wavy curves A^C^Ei ... in place of 
the crenellated diagrams ABCDE . . . The difference is possibly largely 
explained by defects in the indicating apparatus, and as the diagrams given 
in Sketch No. 239 were taken from a pipe which was only four inches in 
diameter, where friction has a relatively large influence, it is possible that 
good diagrams from say a 4-foot pipe would resemble the theoretical cui\e far 

more closely. . . , . , . . . , . 

Putting this, aside for the moment, it is plain that the total impulsive 

pressure produced at any time /, by a continuous movement of the valve, is 
given by the equation : 

«- 6 &/•’©, 














816 CONTROL OF WATER 


where /, is reckoned from the commencement of the motion of the valve 

and is the value of when t=t ly and $(/—4) or <£(r) is a 

function of /, l and 4 of the character shown. 

This equation is almost useless. But let us suppose that we have 
experimentally obtained a diagram of the type shown in Sketch No. 239, and 
let this diagram be reduced so as to correspond to dv— 1 foot per second. 
Then if: 


The area of the hump A 1 B 1 C 1 D 1 = ?7 1 . 

The area of the hump D 1 E 1 F 1 G 1 = t 7 2 , where rj 2 is negative. 
The area of the third hump =173, and so on. 


Then theoretically : 

if 4=/, 

7 

= T 


2/ 


*7i = 


X 



If 4 is not equal to /, 



V2— — ~sr 5 an d so on. 


Now, let Av lt represent the change in v, during the interval 

I—O to t= T= 

A 

Let Av 2 , represent the change in v, during the interval 


/=T to t — 2T — 


X' 


Let Av n , represent the change in v , during the interval 

t=(n— i)T to t=nT. 

Then, when t=nT, we have approximately : 

Q = rj 1 Av n +773 A v n _ x +77 z Av n _ 2 + etc. + rj n Av v 

The form lends itself to solution by the method of arithmetical integration. 
Starting at t= T with uniform velocity v ± , we can ascertain Av, by considering 
that the total available head H, is consumed as follows : 

(i) In the friction head required to maintain a velocity equal to v x —bAv x . 

(ii) In the head required to produce a discharge equal to — ^Azq}- 
through the variable opening formed by the valve. 

(iii) In accelerating the velocity from v 1} to v 1 — Av 1 in the time T. This 
of course in the usual case of a closing valve has a negative sign. 

The mathematical aspect of the question is fully treated under the head of 
Water Towers, and in actual practice I have found that it is simplest to use the 
two following equations : 

(a) H — Q = The friction head+The retardation head. 

(&) Q = The head producing discharge through the valve. 

The experimental difficulties are very great. The time and pressure 
diagrams are not easily obtained, and are probably affected by instrumental 
errors in very much the same manner as indicator diagrams erf gas engines. I 
should not therefore have considered that this discussion (which is defective 
in many ways) was worth the space it occupies were it not that it enables the 
principles affecting “ resonance ” to be intelligibly dealt with. 

Resonance.—It will be obvious that while r]^ tj 3 , etc. are positive, rj 2 , 77 4 , etc. 




RESONANCES 817 

are negative. If therefore for any reason (Av) nl , ( Av)„- 3 , etc. are equal 
to o, or are small in comparison with the terms (Av) n , (A7/)„_ 2 , etc. the value of 
Q, may become very large. Thus, any method of valve closure which is likely 
to produce such results is extremely prejudicial. As examples, let us assume 
that T = o ‘5 second, and that the valve is closed by a machine running at 120, 
or 60 revolutions per minute. It is obviously possible for the machine to fall 
into step with the pressure oscillations of the water (which must be carefully 
distinguished from the far slower visible oscillations which the whole mass of 
water in the pipes performs, and which produce surges in the surface of the 
water in any vessel which is in communication with the pipe), and thus pro¬ 
duce abnormal pressures. A similar action may occur if the natural period of 
the governor which regulates the admission of water to a turbine is a small 
multiple of T. The matter cannot be reduced to calculation, as the pres¬ 
sures induced are so great that safety is generally secured by the machinery 
being forcibly put out of step. But for this very reason, the effects (when they 
do occur) are far reaching. Thus, a pumping engine which naturally ran at or 
near to a prejudicial rate would probably be forced to run at a slightly different 
period, although cases have occurred where the pipes were damaged before 
the period was changed. A far smaller machine, however, which worked on 
a balanced valve would not be materially affected by the induced pressures, 
and there is little doubt that a machine thus situated could be designed which 
would infallibly break any long pipe carrying water at sufficient velocity, when 
adjusted so as to close down the valve in the appropriate manner. 

The question has not as yet become acute, although most-hydraulic 
engineers have experienced “inexplicable fractures,” and are well aware that 
a repetition of these fractures is likely unless some small and apparently 
unimportant modification is introduced when the break is repaired. 

Designers of turbine governors are, however, fairly well aware that the 
relation between the period of the governing machinery and the length of the 
main conveying water to the turbines requires consideration ; and in these 
cases the question is likely to become more acute when the deflecting nozzle 
(see p. 929) is abandoned in favour of regulators which do not secure safety 
by wasting water. Indeed, I have been privately informed by several 
engineers that trouble l as already been experienced in certain cases, and 
regret that owing to the difficulties which attend accurate observation none of 
these gentlemen were able to furnish numerical data which would permit the 
matter to be theoretically tested. In one case, however, I am fairly certain 
that resonance was produced by the coincidence of the period of a three-phase 
alternator with that of the pressure main* 

Practical Applications. —At present we are without any definite in¬ 
formation for large pipes, but it may be inferred that the larger the pipe, the 
less rapidly the values of rj decrease. 

It would therefore appear that very fair results will be obtained in small 
pipes by considering only the first term. In the case of larger pipes diagrams 
of a simple alteration, v 0) to zq, say, must be taken and studied. 

When investigating a question of this character, which related to a pipe 12 

'll 

inches in diameter, I was led to take the following as values of the ratio 17: 

for ; t)i = 0-9 V2 = 73 * 07 

rj 4 = -0-6 f/5 = 0*2 and rfQ - t? 7 = o 

S 2 


8i8 


CONTROL OF'WATER 


I do not pretend that these values have any pretensions to accuracy. They 
appeared reasonable when compared with the best procurable diagram, and 
the results obtained permitted me to discover that a small fracture which had 
occurred, was probably not due to resonance, but to an accidental stoppage 
in a branch main. 

Trial being made after the obstruction had been removed, the fracture was 
not repeated. 

The values of r] 2 , rj 3 , etc., depend upon the reflection of the wave at the upper 
end of the pipe. The subject has been investigated by Rayleigh ( Theory of 
Soimd) and by Gibson. 

The following circumstances appear to favour a good reflection : 

(i) The upper end of the pipe opens well below the water surface in the 
forebay, or feeding reservoir. 

(ii) The pipe has neither alterations in section, nor a bellmouth entry. 

Our object is to minimize 772, 773, etc., as far as possible. 

Thus, the upper end of the pipe should be bellmouthed, and should enter 
the reservoir at as high a level as possible (allowance for unavoidable variations 
in water level being made). Also a wall, or other obstruction in front of the 
upper end of the pipe, should be avoided if possible. The best solution, there¬ 
fore, is a bellmouth entrance in a horizontal plane, as little below the lowest 
water level as is possible. 


CHAPTER XIV.— (Section C) 
EJECTORS AND SYPHONS 


Jet Pump, or Water Ejector.—G eneral theory. 

Syphons.— General theory—Preliminary design of a syphon—Syphons carrying air and 
water—Theory—Examples—Practical applications. 


SYMBOLS CONNECTED WITH JET PUMPS 
a, is the area of the orifice of the jet. 

a.j, is the area of the cross-section of the ejector cone at the point where the mixture is 
complete, which is assumed to be the throat, or minimum section of the cone. 
a :i) is the area of the cross-section of the pipe through which the mixture is delivered. 

A = av + cu. Aj =av* + cir (see p. 821). 

B = H + hb + — (see p. 822). 

c, is the area of the orifice through which the substance lifted is delivered previous to 
mixture. 

h, is the gauge pressure, and H 0 = h + /i bt the absolute pressure, in feet of water, of the 
jet or pressure water just before it passes through the orifice a. 
kb, is the height of the water barometer, in feet (see p. 6). 

H, is the geometrical lift, in feet, from the ejector to the reservoir into which the 
mixture is delivered. 

Hj, is the absolute pressure, in feet of water, existing at the point where the pressure 
water and the lifted substance first come into contact. 

H.j, is the absolute pressure, in feet of water, at the point where complete mixture takes 
place, i.e. at the cross-section a 2 . 

H 3 , is the absolute pressure in feet of water at the cross-section a 3 . H 3 = B, 
approximately, or accurately, B +friction terms. 
k, is the gauge pressure, and K 0 = k + k b , the absolute pressure in feet of water, at which 
the lifted substance is delivered just before it passes the orifice c. 

av + cu Total discharge of ejector . „ ox 

q =- = -—-—7— r — 5 — - -(see p. 538). 

1 av Discharge of jet 1 

u , is a velocity such that cu, is the total quantity in cusecs of the substance lifted by the 

ejector. 

v, is a velocity such that av, is the total quantity in cusecs of pressure water passing 

through the jet. 

v 2 = aV + <U -, is the mean velocity in feet per second of the mixed substances just after 
a 2 

mixture is complete. 

v 3 , is the velocity, in feet per second of the mixed substances in the rising main. 

?v, is the weight, in pounds per cube foot of the pressure water. 
w x , is the weight, in pounds per cube foot of the substance lifted, 
i', is a coefficient expressing the frictional losses. 

' 7 2 

Thus, = frictional loss of head in the converging cone of the ejector. Theoretically, 
2 i 

* 819 





CONTROL OF WATER 


8io 


9k(r/ 

£ — where g , is the acceleration of gravity, /, the length of the pipe considered, 


and d, its diameter in feet. Practically this equation does not hold as C, is altered 
from its usual values by turbulence in the flow, and the mixture of air or sand with 
the water. Therefore, f is used to indicate this altered value. 


’ = < see P' 538). 


Jet Pump, or Water Ejector.—T he theory of this'apparatus is in a very 
unsatisfactory state. The results developed below require experimental con¬ 
firmation, and the most that can be said is that this theory is the least open to 
objection of any that have as yet been put forward. 

Let a jet with an orifice of an area denoted by a, deliver a quantity of water 
av, at the point C. 

Let the absolute pressure at which this water reaches the orifice be : 

H 0 — say, where //&, is the height of the water barometer. 



Sketch No. 240.—Jet Pump Diagram. 


Let a quantity of water cu , be delivered at the point C, through an orifice 
the area of which is c, and let this water reach the orifice under an absolute 
pressure K 0 = k+hi, say. 

Let the two bodies of water move along the pipe CD, and arrive at D, in 
a state that can, for practical purposes, be represented by a volume av+ci/, 

moving with a uniform velocity v 2 , so that the area at D, is a., = a : jArCU 

v 2 

The mathematical difficulties of the investigation are entirely due to our 
ignorance of the processes involved in the complete mixture of the two bodies 
of water which is assumed to take place in the pipe or converging cone CD. 
The definition of complete mixture is plain,—the velocities at individual points 
in the area a 2 , must not differ materially from those which prevail in a pipe of 
an area a 2 , carrying a quantity of water equal to a 2 i> 2 , in steady motion. 

So far as can be inferred from the practical details of ejectors (which are, 
however, known to be designed by rule of thumb only), the length CD, is 
usually about five or six times the diameter of a circle of an area a 2 , and the 
best results are certainly obtained when CD, is a converging cone. There are 































JET PUMP 


821 


also certain indications that H 1? as later defined, should be greater than if 
rapid mixture is desired. 

Let the mixed stream pass along the diverging cone, and finally enter a 
pipe with an area represented by <z 3 , with a velocity v 3 = The stream 

a 3 

then flows through this pipe and is delivered into a tank at F, say. 

Let H 1} be the absolute pressure at C, i.e. just beyond the orifices. 

Let H 2 , be the absolute pressure at D, i.e. just after complete mixture has 
occurred, and assume that C, and D, are at the same level. 

The motion between C, and D, may be considered as follows: 

There enters at C : 


(i) A quantity of water av , with an energy proportional to H x + 


2/ 

u- 


(ii) A quantity of water cu , with an energy proportional to Hid-. 

2 g 

During the motion from C, to D, the first quantity changes its velocity from 

( v _ v \2 

v, to ^ 2 ) so that energy proportional to - ~ is lost. Similarly, the second 


quantity loses energy proportional to 


2 g 
{y-v 2 y 
2 g 


In addition, some energy is lost by both quantities of water in frictional and 

v 2 

other resistances to motion, and this is assumed to be proportional to (—. 
Finally, the quantity av+cu , leaves D, with an energy proportional to 




2 g 


In practice, v 2 is always greater than u or v. 


The whole reasoning is a mass of assumptions, and experimental proof is 
difficult. Quite apart from any questions as to the validity of Borda’s equation 
(which Zeuner and other good authorities consider to be inapplicable to the 
conditions prevailing) the value of C almost certainly bears no relation to C, in 
the equation v — C y/rs, which would be the frictional equation for the pipe CD 
under ordinary circumstances. 

Thus, all that can really be stated is that the form of the equation is 
probably correct, and therefore the investigation forms a starting point foi 
comparison between ejectors which do not differ very greatly in size and 
general proportions. 

We thus arrive at the following equation : 

(v-v 2 y 


(«!+-.) +^(h 1 +^.) = (^+^){h 2 +^(i+C)} + 

(u—v 2 y 


av 




+cit- 


2 g 


Simplifying, and putting A = av+cu. A 1 = < 27/ 2 +^ 2 

AiV 2 


or, 


A(H 1 -H 2 )=A^ r (2+f)- ; g 

h 1 -h 2 =^W)-| 1 | 


If in place of water lifting water, a fluid with a weight equal to w, lbs. per 











822 


CONTROL OR WATER 


cube foot lifts a fluid of a weight equal to w x , lbs. per cube foot, the equation 
is of precisely the same form, but: 

A = wav + w x cu, and A x = wav 2 -f- w x cu 2 ; 

and the heads H 1} and H 2 , are expressed as feet of a fluid of a weight equal to : 

wav+ ei x cu cube foot, i.e. the weight of the mixed fluid that flows in 

av+cu r 

the rising main. 

The mixture has now to be lifted to F, at a height H, above the point D. 
Thus, for the motion from D, to F, we have: 


H 2 +^-= H+/; s - 


'7/_2 




gr(i + C 2 ) = B + C 2 ^r=H 3 say; 

ns ns 


*27 * 

where £ 2 — represents the head lost by friction in the rising main, so that if 

8 o-l 

this be of a length equal to /, and of a diameter d, then approximately. 

Adding these equations, we get: 

h.-b+£{. 

= B+^{i+f+f 3 }- Al7 ' 2 

where, = • 


A g 


' a :i ■ 


The corrections for friction and other losses in the diverging cone are 
obvious, but do not alter the form of the equation, and in view of the un¬ 
certainties existing as to the correct values of { and £ 3 it hardly seems necessary 
to express them by special symbols. 

Solving this equation, we have: 


v 2 = 


A i 


A(i +C+C3) 


+ —B) 


\A(l 


A 1 V 


+ C+C 3 )-' 

The negative sign alone is significant, and v 2i attains its maximum value 


A x 


A(i i-C+£ 3 ) 


when the terms under the radical sign vanish. Thus, we have: 


^ 2 


-■A 


Ax 


av 2 -\-cu 2 


or. 


v 2 = 


24B-H1) = ___ 

+ £+£3 A(i + t+Cs) (av+cu)( i+C+fs)’ 
wav 2 + w x cu 2 


; when the jet and lifted fluid differ in 


(wav+WiCuXi+C+Cs) 

density. 

This equation for v 2 is arrived at by all investigators, but as it represents a 
maximum value of v 2 , only, this fact is no proof that their methods are all 
equally correct. 

We can now determine H 1} in feet head of the mixture, for a given value of 
v 2 , and thence we calculate v, and zz, from the ordinary formulae : 

v—c\l 2 < g r (H 0 — u = C\ \^ 2 < ^"(K 0 H x ) 

where c , and c x , are coefficients of velocity, with an allowance for pipe friction 
if required, and where H 1} in each equation must be calculated in feet head of 





















SYPHON 


823 


the fluid considered if the weight per cube foot of the fluids differ. The propor¬ 
tions of a practical ejector are plainly best obtained by trial and error. 

The value of £ is not well known, but certain measurements of my own 
suggest that it varies from twice to three times the value calculated from the 
values for C, found by experiment in cases where the mixture does not occur. 
Jet pumps, however, usually lift a mixture of water and air, or water and earth. 
The first case has been investigated by Gibson, and rules for the value of 
C+Cs are given on page 833. In the second case the experiments of Hazen 
and Blatch (see p. 540) determine C+C3 with all necessary accuracy. 


SYMBOLS CONNECTED WITH SYPHONS 


C= —7=,i s the skin friction equation for the syphon. 
s'rs 

d , is the diaYneter of the syphon pipe, in feet. 

h is the height, in feet, of the water surface in the upper reservoir above a fixed plane. 
/z.„ is the height, in feet, of water surface in the lower reservoir above the fixed plane, 
/zo, is the height, in feet, of the crest of syphon above the fixed plane. 


/z,= 


'i 3 


Tf _ 4 4 - 
Kl_ CV 


Ko = 


44 

C 2 d' 


l is the length, in feet, between the upper reservoir and the crest of the-syphon. 

/ is the length, in feet, between the lower reservoir and the crest of the syphon. 

q\ is the total volume of air carried by the syphon, in cube feet per second. 

q, is the volume of q , measured at atmospheric pressure. 

v, is the velocity of the water, in feet, per second. 

z/j, and v 2 , are velocities in the lengths 4, and 4, if these differ. 

w = 33 - x. 

X } is the absolute pressure existing at the crest, in feet of water. 

/x, is the number of cube feet of air carried per cube foot of water (see p. 826). 


SUMMARY OF EQUATIONS 


Syphon carrying water: 

tv T h x — h 3 


v 2 = 


4A.+ I-5 


2 ~ h 

vd = - 


w 


2 Y 


Limit of 


C*d 

+ h 3 _ 

4 k. 3 -h 2 - w l 


44 

C *d 


a, say. 


Svphon carrying air and water : 

33-^-/z 4 = zz 2 ( k i + ^|) 

v 2 ir 

5 (i -n)+x-33={iN]i) 2 * 
'=>(lT w - 5'5 VS) 


K( 


q=q 


33 - 
33 


x 


Syphons.— In its simplest form a syphon consists of an inverted U tube, 
both legs being full of water. 

In Sketch No. 241, Fig. 1, let 4 be the length of tube from C, at entry in 
the upper reservoir, to the crest D ; and 4 , the length of tube from D to E, the 

exit in the lower reservoir. 









824 


CONTROL OF WATER 


Let the friction equation for water moving in the pipe CDE be, v—C < 0 rs. 
Then, we have the usual equation for motion through the whole length of 
the tube. 

/, _/ ? 2 / 4 ( 4 + 40 + 1*51 j 

/Ji H,_-v ; • • • '• 

I * tl 7 /^ 

where — 5 — } represents the loss at entry by shock and generation of velocity. 


O CT 
~«b 


Now, consider motion through the length CD. We have atmospheric 
pressure at C, of absolute value say 33 feet of water {i.e. the height of the water 
barometer); at D we have an absolute pressure of x, feet say {i.e. a vacuum of 
W = 33 -■**> f eet). 


We thus get : 


2. 


/q + 33- Oh +x) = V 2 { 

For the flow from D to E, since there is atmospheric pressure at E, 

h+* - On + 33 )= v *^r d = - On + w). . .. 3 - 

Now, these two equations permit us to determine w, and for a first approxi- 

. I ‘Cty 2 

mation we may neglect —-—, and get; 

2 g 


w 


j i 2 hx±JOn 
l \+4 


which shows w, is equal to DG, the height the crest of the syphon lies above 
the line joining the water surfaces above its ends. 

But plainly, w cannot exceed a certain value, which is theoretically, 33 to 34 
feet, and practically depends on the amount of air entrained in the water, and 
the temperature of the water, since this determines its vapour pressure. 

Take ?eq, as this maximum value (roughly about 28 feet), then the corres¬ 
ponding values of zq, the velocity in the inlet leg, and v 2 , the velocity in the 
outlet leg, are given by : 

h z — ?n — 

u n n v/rt~ =: *- 


o W x -\-h x — /z 3 
V x - = 


4*1 + r 5 


and 




C 2 d 2 g 


44 

C V 


and plainly, the syphon will not run full if v 2} is greater than ?q. This gives us 
an equation for the ratio which is, neglecting * ^ : 

1 9 


l\ W lV \ -\-h x —h$ 


4 1 i z —h 2 — w x 


a, say, 


4 


and plainly if ~ exceeds this value the vacuum necessary to raise water to the 
*2 

crest as fast as it is carried away cannot be attained, and the outlet leg does 
not flow full 

In general, we have /i 3 — /q, and h 3 — lu given, and wish to work with as 
small a vacuum as possible. The minimum possible value, {h z — /q) is given by 
4 = o, i.e. the crest should be as close to the upper reservoir as possible. 

The graphical construction is evident: 

Set up (Fig. 2) above the two reservoirs heights CB, and EA, equal to 
«q = 27 or 28 feet at most. Then join AB. The crest of the syphon should 















POSITION OP CREST 825 

lie below, or on the line AB, where the line CE, is assumed to be the developed 
ongitudinal section of the syphon. For barely possible flow, put ^ = 33 feet 
corresponding to a complete vacuum at the crest of the syphon. 



2l'above DN.L 


Sketch No. 241.—Diagram of Syphon Flow. 


As examples : Take three syphons, whose crests are all at the same 
evel. 

(a) In the syphon CFE, the velocity is given by either of the three equations 



































826 CONTROL OF WATER 

Nos. i o 3, both legs run full, and the maximum vacuum corresponds to 

I • r 

height' FM, or,i great accuracy is desired and the term — v 2 is taken into 

..... v .. -' ... , 2^ , 

account a slightly arger value will be obtained. 

(b) In the syphon CKE, both legs run full, but the vacuum corresponds to 
KH, i.e. is equal to «/ 1} and all three equations still apply. 

(c) In the syphon CLE, the inlet leg only runs full, and equation No. 2 
with the vacuum equal to alone applies, although if the water happens to 
contain but little air, so that a vacuum of more than feet can be attained, 
and CD, lies below the line B'A', where CB' = EA' = 33 feet, it is possible that 
both legs may flow full, and a vacuum corresponding to LN — w\ say, exists at 
the crest. 

We may therefore sum up as follows : 

If CB, and EA, represent the maximum vacuum obtainable : 

(i) Any syphon whose crest is below AB runs full in both legs under a 
vacuum represented in feet of water by the height of the crest above CE, and 
the velocity is given by equations Nos. i to 3. 

(ii) If the crest lies above AB, the inlet leg only is full, and the vacuum is 
represented by CB or EA, and the velocity is given by equation No. 2, 
provided : 

(iii) The crest does not rise above B'J, the horizontal through B', where 
CB' = w' = maximum possible vacuum, in which case no flow occurs. 

This investigation shows the great importance of the horizontal distance of 
the crest from the upper reservoir. 

It is also quite plain that if we alter the size of the pipes in the two legs, 
we can theoretically, at any rate, cause both legs to run full, eg. consider the 
syphon CDE (Fig. 1). 

Set up CB = EA = 'Z£/ 2 , where w 2 is the maximum vacuum desirable. Join 
BD, and look up the size of pipe required to pass the given discharge under a 
hydraulic gradient BD. Next, join DA, and determine the size of the outlet 
pipe for the same discharge and the new gradient DA. 

The above approximate theory is sufficient for preliminary studies. In 
the final work it is necessary to allow for the losses of head at entry, at 
curves, and due to the alteration of the pipe diameters. The question 
whether the syphon will continue to pass water is investigated in the next 
section. 

Syphons carrying Air and Water. —When the vacuum exceeds 20 feet, air 
is disengaged from the water, and may enter by a leak, at a vacuum of less than 
20 feet. 

The worst position for a leak is at the crest. Let us assume that, up to the 
crest, the pipe carries water only, while after the crest there is a mixture of air 
and water, say /x volumes of air per unit volume of water. We have : 

4 = resistance due to curves 

= ^(K,+r|), say; ...4- 

where /z 4 = /^ — // 2 . 

Also since the mixture of air and water has a specific gravity equal to 
(i—/x), and for want of better information, we assume the skin friction and 



EFFECT OF AIR 


827 


other resistances are not altered by the presence of air, except in so far as the 
velocity is altered, we get : 


*«(i-^)+*- 33 = —_K 2 , ... 5. 

where /i 5 = /i 3 -k 2 ; and K 2 = ^. 

Thus, + - Ui-y.)-h t ... 6. 

Now, experimentally it has been found that the air bubbles do not travel 
along the outlet leg with the same velocity as the water, but tend to travel 
upwards with a velocity equal to 5*5 V(see Herzog, A.F.C ., 1904, p. 19), 
where d is the diameter of the outlet pipe in feet. 

Thus, the quantity of air conveyed away is : 


/ TT(P 
q = p 
4 

measured at a mean pressure 33-. 

2 


(,-T-ss") 


Thus, the volume measured at atmospheric pressure is : 


x 

33-J 

? '_^ = f)Say . 


Now, in any given case, we can assume a series of values of \i. Equation 
No. 6 then gives us v, and from Equations Nos. 4 or 5 we can calculate x, and 
then q' and q. We find that q has a maximum which corresponds to a value 

of /x between u = o, and u = 1- -—p- % 

P P 5’5 Jd 

Hence, we calculate what volume of air the syphon can possibly dispose of 
without being sooner or later stopped by the accumulation of air, either from 
leaks, or dissolved air set free from the water by the vacuum existing at and 
near the crest. 

As an example of the above calculations, consider a pipe of 4 feet diameter, 
with h*, = 20 feet, h± = 14 feet. 

Let us assume that the preliminary calculations have shown : 

Ki+^= 0*032 

2^ 

which corresponds to / T = 86 feet, with C = 100, i.e. a very incrusted pipe with 
many bends. K 2 = 0*016, corresponding to / 2 = 160 feet. It must be noted 
that the question of both legs running full has not been gone into, although, 
in any actual calculation, this should be determined before computations of air 
removal are attempted. 

Substituting the numerical values, and putting (1 —/m) 2 = 1, we get the 
following: 

z/ 2 (0*048) = 20(1—/x)—14, or v 2 = 125 — 4167/x 

33-* = i4+o*o32t/ 2 

?' = i2 '5 Mjqr”) 









828 


CONTROL OF WATER 


The tabulation as effected by a slide rule is : 


A* 

I-fl 

©* 

V 

33 -* 

V 

I ~/X 

f 

i7 

q 

0*005 

0*010 

0*015 

0*020 

°'995 

0*990 

0*985 

0*980 

122*92 

120*84 

11875 

116-67 

i ro8 

io * 99 

10*89 

io*8o 

I 7 , 94 

17*86 

17*80 

1773 

11*14 

11*10 

11*05 

11*02 

0*00879 

0*01256 

0*00942 

0*00502 

0*00678 

0*00969 

0*00725 

0*00386 


We thus see that this syphon can clear away about 0*0097 cube foot of air 
at atmospheric pressure per second, or as the volume of water passing is 
138*1 cube feet per second, the percentage is about 0*0070, which, as will be 
seen from the figures, given below, is probably too small for satisfactory 
working. 

Let us now try a 1 foot pipe under similar circumstances. 

K 7 + —^ = 0*074 K 2 = 0*100 approximately, 

or, 2/ 2 (o*i74) = 6 —20/x v 2 = 34’48 — 114*9/* 

33 = 14+0*074^2 q = o*78s/x(^_ -5*5) 

The tabulation is : 


A* 

I-/X 

V 2 

V 

33 -* 

V 

I -A* 

q ' 

q 

0*01 

0*99 

33‘33 

5*77 

3 

16*46 

5'83 

0*00259 

0*00194 

0*02 

0*98 

3 ‘ 2 -iS 

5' 6 7 

16*38 

5*78 

0*00439 

0*00329 

0*03 

0*97 

31*03 

5*57 

16*29 

5*73 

0*00542 

0*00405 

0*04 

0*96 

29*89 

5*47 

16 *2 2 

5*69 

0*00596 

0*00444 

0*05 

o *95 

28*74 

5 ‘ 3 6 

16*13 

5*64 

0*00550 

0*00409 


The smaller pipe is thus able to carry off about 0*0044 cube foot of air 
per second, and is then carrying about 4*3 cube feet of water per second, so 
that the percentage is approximately o*i, or over fifteen times that of the other 
pipe. 

This figure, I believe, is above that required for satisfactory working. 

The above figures for air removal may be considered as minima, since, in 
syphons with short outlet legs, the air bubbles do not become sufficiently large 
to move upwards with the velocity attained in a vertical tube, whereas, the 
outlet legs in the above examples, if straight, are inclined at 1 in 8, to the 
horizontal. On the other hand, in most practical cases, the outlet leg dips 
3 to 4 feet below the surface of the reservoir into which it delivers, and 
this will produce an extra retardation in the equation for z/ 2 , eg. if the submer¬ 
sion is 4 feet, the equation becomes z/ 2 (o*i74) = 6—24/x. 

The relative values are however, probably very fairly correct, and introduce 
the principle of sucking syphons, used in several French ports. 











































REMOVAL OR AIR 829 

Here, the smaller pipe ( c-g . the 1 foot pipe in the above example) is started, 
and allowed to suck air by a small auxiliary tube from the larger. 

The figures in the above examples are roughly comparable with those of 
the Treport syphons, described by Herzog {ut sup?'a), but the general practice 
is to use a small smooth tube (say 2-inch lead pipe), for the starter. In any 
given case, the best diameter is easily obtained by two or three trial 
calculations. 

This device has not often been employed in English speaking countries, 
and the usual practice is to remove air either by pouring water into a reservoir 
at the crest of the syphon, or by a steam jet, or water jet pump. These, as 
requiring attention, or mechanical appliances, seem to me less practical, and 
the sucking syphon device, with the small syphon so calculated as to be amply 
capable of keeping both syphons clear, seems to me preferable. In this con¬ 
nection it must be noted that the above examples are exceedingly unfavourable, 
as the pipes are assumed to be very heavily incrusted. 

Actual figures as to the accumulation of air in syphons ( i.e . the difference 
between the air given off by the water at the crest and the quantity removed as 
above), are very rare. The only one I have been able to find is given by 
Anthony {Trans. Am. Soc. of C.E., vol. 59, p. 64) who states it to be o , oo38 
per. cent, of the volume of the water for a 12-inch pipe, under a vacuum 
ranging from 8 to 13 feet head of water. By scaling his diagrams, I estimate 
(very roughly, as the scale is small) that the syphon could remove 0*021 per 
cent., so that we may estimate the air given out as 0*0248 per cent, and equally 
roughly believe that 0*028 to 0*030 per cent, removal will permit continuous 
working under such a vacuum. 

We may therefore consider that a removal of 0*050 per cent, will be generally 
satisfactory, but in Anthony’s case, the climate (South African) is hot, so that 
in temperate countries less removal might suffice. I estimate that if a smooth 
4-inch pipe had been laid to suck air from his syphons, or those of my example, 
continuous working can be secured. 

In general, we find that a “small steam jet” is considered sufficient. 

The Brusio syphon of 3 meters diameter, under a vacuum of 16 feet is, how¬ 
ever, provided with a small centrifugal pump, for filling with water. As it is 
unprovided with non-return valves, the pump seems absolutely necessary. 

The theory developed above appears to agree fairly well with experience of 
short syphons of large diameter, i.e. say 2 to 4 feet tubes, 120 to 150 feet long ; 
the general principles being that a velocity somewhat exceeding the value 
5*5 Id should be attained under as small a vacuum as possible. 

In smaller pipes the question is complicated by incrustation, but a 2-inch 
lead pipe seems capable of removing air from very large syphons, and of 
keeping them in regular work. 

For the ordinary cast iron pipe, some 6 to 8 inches in diameter, accidental 
leaks are not only more likely, in view of the greater number of joints, but of 
relatively greater importance, owing to the smaller cross-section of the pipes ; 
hence, air leakage, or accumulations of dissolved air sooner or later stop the 
working. All such syphons, therefore, should be provided with some arrange¬ 
ment for refilling with water. 


CHAPTER XIV.— (Section D) 

AIR LIFT AND HYDRAULIC COMPRESSOR 


Air Lift Pumps. —Theory — Correction for friction and velocity head — Rules for friction 
—Approximate rule for ratio of volume of air to volume of water—Example— 
Efficiency—Cyclic flow—Minimum value of velocity of entry—Influence of size, of 
the pipe—Values of efficiency—Pipes with cross-section increasing as the air 
expands. 

The Hydraulic Air Compressor. —Theory—Extra losses not occurring in the air 
lift—Effect of size on efficiency—Isothermal compression of the air—Practical 
details—References—Injection of air into water—Orifice area—Velocity of the water 
and air bubbles—Efficiency—Summary—Webber’s experiments. 

SYMBOLS—AIR LIFT AND HYDRAULIC COMPRESSOR 

a, is the area of the cross-section of the pipe conveying the mixture of air and water, 
in square feet. 
v * 

C= -7=, is the skin friction constant. 

sirs 

d, is the diameter in feet of the pipe, the area of which is a square feet. 

5 , is the distance in feet below the level from which H is measured at which air is 
delivered into (air lift), or leaves the water (compressor). 
rj, is the observed mechanical efficiency of the process. 

H, is the height in feet through which the water is lifted (air lift), or falls (compressor). 
/if, is the head lost by skin friction, curves, etc. (see p. 832). 
h v , is the head lost by exit velocity (see p. 832). 

K vf+>£ (seep - S32) - 

. ,, Volume of air delivered 

n, is the ratio y olume of water delivered* 

p a , is the pressure of the atmosphere. 

Pi, is the absolute pressure ( i . e . the pressure as measured by a pressure gauge +p a ) of the 
air when delivered into (air lift), or set free from (compressor) the water. 

p, is the pressure at any point. 

q, is the volume of w'ater passing through the machine, in cusecs. 

Va, is the velocity in feet per second with which the mixture of air and water quits the 
rising main (air lift), or the down shaft (compressor). 
v e , is the velocity with which the mixture enters the rising main (air lift), or the dowm 
shaft (compressor). 
v, is the velocity at any point. 

x, is the volume occupied at pressure p, by the mass of air which occupies q cube feet 
at a pressure p a . 


Air Lift. 


SUMMARY OF FORMUL/E 

H + 5 

5 - -^r= = hf-\- h v , in feet of water 

1 + JV 

K 5 = H + hf + hv, in feet of mixture. 

n £i 2 

v a = - (i + n) h v = —~(1 + K) feet of mixture. 

a 2 g 

. 24(5 + 11) y 2 / u\“ r . 

«/= o 2 \ I "^2/ f eet °* mixture (see p. 833) 

830 





Hydraulic Compressor. 


AIR LIFT 



H + 5 
i+K 


8 = hf + ku, in feet of water. 


_ v u 

kv ~V<r + F^ I+a '> ( see P- 424 ) 


2 ^ 


2<b 


/if—as air lift + friction loss for pure water in the rising shaft. 

. * s a ^ so an additional uncalculable loss of head owing to the energy expended 

in mixing the air with the water (see p. 839). 


TABLE OF VALUES OF -=- l a l og A 

* Pi-Pa &e Pa 


Absolute Pressure of the 
Air in Atmospheres, when 
'{delivered at the Bottom of 

the Lift Tube^^l, 

Pa 

Approximate Gauge 
Pressure in Pounds per 
Square Inch. 

(1 Atmosphere = 15 Lbs. 
per Square Inch.) 

K 

n 

2 

15 

0*69 

3 

30 

°*55 

4 

45 

0*46 

5 

60 

0*40 

6 

75 

0-36 

7 

90 

0*32 

8 

T °5 

0*29 

9 

120 

0*27 

10 

135 

0*26 

13 

l8o 

0*2 I 

!5 

210 

0*19 


Air Lift Pumps. —Air lift pumps form the simplest means of lifting water 
from wells, or other narrow reservoirs. 

A pipe is placed in the well, and air under pressure is blown into it. The 
air bubbles up, and when the lift works properly forms an emulsion, or intimate 
mixture, with the water, lifting it to the top of the well (see also p. 834). 

Let H, be the height the water is lifted. Let the air enter the pipe at a 
depth d, hereafter termed the “ dip,” below the water surface in the well. 

Let the mixture of air and water that is lifted in one second consist of q, 
cube feet of water, and a quantity of air the volume of which measured at 
atmospheric pressure is qn , cube feet {p a —34 feet of water approximately). 
Further, assume (as is probably very nearly the case) that the proportion of 
air and water is the same throughout the tube. Let fa, be the absolute pressure 
of the air at the bottom of the tube. Then /,, corresponds to the pressure 
produced by a column of water S+34 feet high. For, if/,, be less than this, 
the air cannot leave the pipe, and if fa, be much greater than this, air will 
bubble out from the bottom of the pipe. Now, as the air rises, it expands, and 
the air being in intimate mixture with the water, the expansion must be 
isothermal (z\e. no heating or cooling occurs). 















§3 2 


CONTROL OF WATER 


Thus, if Xj be the volume of air used per second, measured at an absolute 


pressure p , we have : 


x- 


qnpg 

P 


since the volume when measured at atmospheric pressure is equal to qu, cube 
feet per second. Therefore the mean volume of a cube foot of the air during 
its passage through the tube is given by : 


po 


log, 


Pi 


P\~Pa pa 

The mean specific gravity of the mixture of air and water in the rising main 
is therefore given by : 

q i 1 

—-- 7 +K- say - 

n i+ A^'° s TJ ."" 


1+ -jp.. lot r.,P\ 


, , l0 ge J 

P 1 Pa Pa 


Thus, the head producing flow is given by the difference of the pressures 

produced by a column of water 8 feet 
high, and a column (H + S) feet high 

of mixture of a specific gravity 



i + K 


Thus, 


^ H T 8 / ./ 

8 — ——— — hf-{-h v 
i + lx 


Where : 

hf , is the friction head lost in 
the pipes, etc. 

h v , is the velocity head of the 
water escaping from the 
pipes. 

At present, these quantities are 
expressed in feet of water, but it is 
convenient to express everything in 
feet of mixture. 

We get: 

kS — H = ///+//„ . . . (i). 

where h/, and h Vf arc now expressed as 
feet head of the mixture. 

Now, let a, be the area of the 
pipe carrying the mixture, and d, its 
diameter. 

The velocity of the mixture at entry into the pipe is : 


V e 


H 

a\ 


i+- 


approx. 


Pi / a\ 34 + ^ y 

The velocity of exit from the pipe 5 s v a = -h+n) and in feet of water 

// 




*?/ * 
2 o* 


or: 


h v ~ (i T K)--7-2(1 +;/) 2 feet of mixture. 


2ga 






























EFFICIENCY OF Aik LIFT 833 


///, is less easy to calculate. Gibson (Hydraulics and its Applications ), 
states that ///=6x^~' ^7, (1 + ~) feet °f mixture ; 

where C, is the coefficient in the ordinary equation, v — C^rs, a value corres¬ 
ponding to the motion of water with velocity 1 + ^, in a pipe of diameter d i 


being selected. 

This equation leads to results which agree fairly well with experiment, and 
in default of better information, it must be used in calculations. 

The calculations in any given case are now obvious. We must assume a 
value of «, calculate K, hf, and h v , and see whether equation No. (i) is satisfied. 
If not, another value of n , must be tried. 

In actual practice, we find that: 


When . . H = io 20 30 50 100 feet 

n , is approximately 1*0 1*5 2*0 2*5 3*0 

and these values can be used in preliminary work. 

It will be found that hf, and h v , are appreciable fractions of H. Thus, take 
Kelly’s experiment No. 1, Table V. ( P.I.C.E ., vol. 163, p. 372). 

Here, we have, ^ = 074 cusec, n = 6*4, <2=0*136 square feet, d—0‘^2 feet, 
§=1767 feet, H = 132-8 feet, 7^ = (73+ 15) lbs. per square inch. 

Thus, K = 6*4 x o '2 o 6 log c 5*87 == 273. 

v e z= 11*3 feet per second. v a ~407 feet per second. 


We have, h c — * — = 257 feet of water = 847 feet of mixture ; 
04*4 


hf —6 x 


4X 3°9'5 


x 22*9- = 


Z'929*5 feet of mixture, 


IOOOO XO'42 

•Thus, the efficiency of the air lift is about : 

H 132-8 


^278*9 feet of water. 


H +h v + h f 132*8 + 25*3 + 278*9 


0*305. 


Experimentally, we find that the efficiency calculated from : 

H.P. of water raised 

______—--;--- =0 293 , 

I.H.P. of air in compression cylinder 

so that the efficiency as above defined, which is : 

H.P. of water raised ________ 

H.P. of air as delivered at bottom of lift pipe 

is probably about 0*33. 

The important point, however, is that h f , is but slightly less than twice H, 
even if we assume the efficiency of the air lift to be as great as 0*40 (which, in 
view of the experimental result, would require the air compressor to be in very 
bad order), and calculate h f , from this suppositious value. Consequently, if 
good efficiency is desired, the losses by friction, and exit velocity, must as far 
as possible be minimised. Thus v„ and v a , must be kept as small as possible, 
and in order to minimise friction the air pipe should be separated from the 
rising main, and should not (as is frequently the case) be placed centrally inside 
this pipe, which produces extra skin friction in the rising main. 

53 









CONTROL OF WATER 


834 

In actual practice, if v e , be less than a certain value, the air and water do 
not thoroughly mix (as is assumed in the above theory), and the flow becomes 
variable, the air accumulating in large masses, filling the whole bore of the 
tube, and driving blocks of water before it, very much as was the case with 
the pistons of the old fashioned chain pump. The action is illustrated by 
Kelly’s experiments (ut supra). Here, we find that : 

If v e , be less than 12 feet, per second, the flow in a 5-inch pipe is distinctly 
cyclic. 

The results are as follows : 



Period of the 
Cycle. 

Time per Cycle 
during which Water 

n 

.1 

Efficiency. 

H.P. Water raised 


was lifted. 

f T 


I.H.P. in Air Cylinder 

Ft. per Sec. 

576 

2 mins. 20 secs. 

50 secs. 

8- 9 8 

1 4 V 

o , i4i 

7*60 

2 mins. 

1 min. 15 secs. 

6-88 

0*176 

9-30 

x min. 15 secs. 

1 min. 

6-36 

°' l 91 

I2*8o 

Flow is continuous, but the 

4’95 

0*275 

I 4 ‘ 4 ° 

volume delivered varies mo¬ 
mentarily 

5*47 

0*249 


Thus, in the first four (certainly in the first three) experiments, the air 
acted like a series of pistons. In the fifth, the air and water issued thoroughly 
mixed. 

The maximum efficiency occurs at, or near, the velocity at which the 
mixture first becomes complete. Thus, the determination of the value of v# 
at which piston action ceases, and emulsion delivery begins, is very important, 
and the size of the pipe should be determined so that the desired delivery is 
then obtained. 

So far as our present knowledge extends, the value of 7 / c , at which the 
change occurs depends only upon the size of the rising main. 

The following figures are obtained from : 

Josse’s experiments with H + S=i20 feet (approx.) : 

Piston action ceases when v e , Is less than 5*60 feet per second, in a pipe of 
2f inches diameter. 

Piston action ceases when v ei is less than 7*30 feet per second, in a pipe of 
3 inches diameter. 

Kelly’s experiments with H + 6 = 310 feet (approx.) give : 

' Piston action ceases when v e , is less than ir8 feet per second, in a pipe 
of 4 inches diameter. 

Piston action ceases when v e , is less than 127 feet per second, in a pipe 
of 5 inches diameter. 

Further details cannot be given, but these values are believed not to be 
greatly in excess of the velocities at which the change from piston to emulsion 
motion occurs. 

The above figures show that if high efficiency is desired, the volume of 
water delivered by an air lift pump is not very great. 























MOST EFFICIENT VELOCITY 


835 


For example, take a 5-inch pipe, and assume that : 

H = ioo feet, or ^1 = 3 atmospheres gauge, or 60 lbs. per square inch 
absolute, is about 3. Thus, the mixture which enters the pipe is composed 
of equal volumes of air and water, and v e , should be about 12 to 13 feet 
per second. Thus, the volume of water delivered per second is about: 

I2-C 

—2-xarea of a 5-inch pipe=o*875 cube foot = 5'5 gallons. 

This method of proportioning with accurately obtained values of n , will be 
found to produce a very efficient pump. In practice, however, air lift pumps 
are usually employed in deep wells, where space is limited, and the pump is 
expected to lift all the water which the well can safely yield. Thus, the 
efficiencies recorded are usually smaller than could be obtained if more space 
were available. 

In actual work the recorded efficiency is usually calculated from : 


Water Horse Power 

^ I.H.P. of the cylinder of the air compressor 

which is probably about 0*90, of the true efficiency of the air lift alone. 

Josse found when S + H = 1197 feet, with a pipe 2f inches in diameter, 

that : 


When ^ = 3 

When ™ = - 
H 3 

When 4 = 1 


77 = 0*329 to 0*256 
77 = 0-445 to 0*279 
77 = 0*423 to 0*272 


^ = 2*45 to 3*48. 
n — 2*49 to 3*78. 
n = 3*30 to 4*67. 


With a pipe 3 inches in diameter ; 


8 4 

When 77 = - >7 = 0*397 to 0*307 

3 

When 77=1 77 = 0*372 to 0*311 


^ = 2*58 to 3*20. 
;z = 3*66 to 2*17. 


Kelly, with S + H = 433 feet, and a pipe 4 inches in diameter, found that: 

When 4 = 1*77 >7 = 0*193 to 0*099 ^=10*35 to 17*95. 
rl 

With 8+H = 335 feet, and a pipe 4 inches in diameter : 

When —=1*63 77 = 0*243 to 0*218 n = yS to 8*i. 

H 

When 4 = 1*51 77 = 0*139 to 0*123 «= ii* 8 to 13*0. 

H 

When 4 = i *39 77 = 0*242100*175 ^ = 8*2 to 10*5. 

H 

With S-f H = 309*5 feet, and a pipe 5 inches in diameter ; 

When h = i ‘33 V = °' 2 9 3 ^ = 6*4. 

When —=1*06 77 = 0*300100*198 « = 7*3 to io*o. 





CONTROL OF WATER 




With §+H = 347 feet, and a pipe 4 inches in diameter: 



o 


With S+H = 3i3 feet: 

8 

When — = 1*40 77 = 0*309 to o’175 72 = 5*80 to 12*60. 

The whole of the available results indicate that n, should be kept as small 


as possible for high efficiency. In any given case, the best value of the dip 8 


is that which makes n, least. This condition can be obtained by trial and 
error from the equations already given. 

The above theory makes it evident that when v e , is determined by the 


emulsion flow condition, both h v , and /«/, can be considerably diminished by 


decreasing v a . 

If we increase the cross-section of the pipe from the bottom upwards so 



constant where /, is the pressure at 


Area of pipe 


the level considered, we plainly secure that the velocity at every point is equal 


to v e . Thus, without diminishing v e , below the minimum value already referred 


to, we can considerably diminish hf , and h v , and so increase the efficiency. As 
an example, take the conditions already calculated on page 833. 




9 inches (accurately 0*74 foot) in diameter. 

The principle is understood to be the subject of patents, and considerable 
increases in efficiency have been reported. It is doubtful whether the increase 
is as large as is indicated by theory, since the practical difficulties attending an 
exact fulfilment of the conditions are obvious. 

The Hydraulic Air Compressor.— From a mathematical standpoint, 
the Hydraulic Air Compressor may be regarded as a reversed air lift. Having 
a head H, available, we sink a shaft to a depth 8 measured below tail water 
level. The head H, is employed in keeping in motion a downward moving 
column of a mixture of water and air, of a length equal to H + S, and an 
upward moving column of water of a length 8. At the bottom of the shaft the 
water enters a large chamber, where the air bubbles rise, and are collected 
under a pressure of 0-4338 lb. per square inch (above atmospheric pressure). 







HYDRAULIC COMPRESSOR 837 

The relation between H, and $ is therefore given by the equation 
(see p. 832) : 


H+fi 
i + K 


5 — hf+h v 


where ///, is the head lost by friction ; and h v , is the head lost by change of 
velocities, and the velocity of exit ; both hf and h v being measured in feet 

of water. 


K, is equal to 

o 


log e 


34 + S 

34 


where n, is the volume of air carried down per cube foot of water entering the 
compressor, measured in cube feet at atmospheric pressure. 

This equation can be treated as indicated on page 833, and is best solved 
by trial. The expressions for hf, and h v , however, differ slightly from those 
given for the case of an air lift, since we have now to consider not only the 
downward flow of the water, but also the losses of head that occur during its 
upward motion in the upcast, or rising shaft. 

Thus, hf, consists of two parts, as follows : 

(i) The friction head for the downward motion of the mixed air and water. 
This can be calculated from the formulae given for an Air Lift Pump. 

(ii) The friction head for the upward motion of the water after it has been 
freed from air. This is calculated by the ordinary rules, and is a loss which 
does not occur in the air lift. 

So also, h v , is made up of two portions, as follows : 

(i) The mixture of air and water reaches the bottom of the shaft with a 
velocity v c , and (putting aside such bell mouth, or draft tube arrangements as 

<y% 

are shown in Sketch No. 243) a head equal to —, is consequently lost. 


*y ^ 2 

(ii) The usual methods show that a head equal to (where v w , is the 

velocity of exit at the top of the upper shaft) is lost. Also, that a certain 
v 2 

fraction of —, is expended in setting the water in motion at the bottom of this 


shaft. These last two losses do not occur in the air lift. 

The expressions for hf, and h v , are complicated ; and besides friction in the 
pipes, curve resistances, and generation of velocity, the sucking of the air 
bubbles into the water column consumes a certain amount of head. 

Regarded merely as a hydraulic machine, the compressor has more sources 
of loss to strive against than the air lift. For, on entering the air chamber, the 
velocity of the water and air must be reduced to a low value, in order to secure 
the liberation of the entrained air, and thereafter the velocity must again be 
speeded up when the air-free water enters the up-shaft. 

On the other hand, all existing hydraulic compressors are large pieces of 
machinery, an 18-inch column of air and water being a small compressor. 
Whereas, an air lift with a 6-inch column of air and water is a comparatively 
large air lift. Thus, the efficiencies actually obtained are larger than those 
usually observed in air lifts. 

Also, if we consider the two cycles—from free air, back to free air, in each 
process—the overall efficiency of the compressor is as a whole by far the 
greater of the two. For in the air lift, the compression of the air in the air 







CONTROL OF WATER 


838 

pump is not an efficient process, as owing to mechanical difficulties the ideal 
isothermal compression can never be attained. In the hydraulic air com¬ 
pressor, the air is very intimately mixed with a large volume of water, and is 
consequently compressed isothermally. The efficiency obtained in the process 
of compression is probably as near to unity as is ever attained in practice. 
The utilisation of the compressed air is no doubt subject to the practical 
difficulties arising from possible freezing which compressed air machinery 
(except the air lift) always labours under, but these are easily obviated by the 
use of preheaters. 

Details of practical application of the process are not obtainable. It 



i . . V.i 

appears that many of the methods in use are at present covered by patents. 
Sketch No. 243 shows the diagrammatic scheme usually made public, but this, 
must merely be regarded as a diagram. 

Literature containing complete numerical data is rare. I believe that the 
papers by Frizell (Journal of the Franklin Institution , 1880), and Webber 
(Trans. Am. Soc. of Mech. Eng., vol. 22 p. 599), contain all that is of scientific 
value. Tests showing larger efficiencies than Webber’s results have been 
partially published by various patentees. So far as the results of these tests 
can be checked, they appear to be reliable ; and the improvement obtained 
would justify the use of the patent, or more accurately, of obtaining the 
assistance of the patentees’ special knowledge by use of their patent. Never- 



















































ENTRAINMENT OF THE AIR S39 

theless, an engineer who advises his clients to pay a royalty will be justified in 
obtaining guarantees of efficiency with penalties for non-success. 

Let us now consider the process more in detail. 

The sucking of the air into mixture with the water requires a certain 
amount of pressure difference. Frizell {tit supra) merely allowed the water 
to fall freely through a certain height, and states that one foot head was lost 
thereby. His method was crude, and the figures given by Webber {ut supra) 
show that the head required to force the air through the orifices varied from 
0*58 foot to 1*03 foot of water. So far as can be gathered, this head is obtained 
by providing the entry tube with a constriction near its upper end, thus obtain¬ 
ing a pressure slightly below atmospheric ; the arrangement being similar in 
principle to a Venturi meter, or a jet pump (see p. 80). 

The area of the constriction appears to be about o‘6o, to 075 of the entry 
area ; but, in any actual case, calculations by the rules given under Jet Pumps 
are indicated, and allowance must be made for the volume of the air sucked in. 

When the vacuum produced by the constriction is determined, the gross 
area of the air orifices is easily calculated by the ordinary rules. 

The design of the orifices is likely to cause trouble. It is plainly important 
that the air should be sucked in in bubbles, of not too large a size. Thus, 
there is a size which each individual orifice must not exceed. As will be shown 
later, Webber uses 34 holes, 2 inches in diameter, and it may be inferred that 
this is about as large a hole as is advisable. 

It is, however, evident from Webber’s values that ?z, the proportion of air 
sucked in, greatly influences the efficiency ; and it would appear that the 
greater the area of the air orifice, the less the volume of water which produces 
the best efficiency. 

The best efficiency in Webber’s experiments was attained when n=%, or 
was slightly in excess of j. Judging from the indications thus obtained, I am 
inclined to believe that the head required for the injection of air was obtained 
by an arrangement resembling a Venturi cone, with a throat area about 070, 
to 073 times the entrance area. It is also evident that the total area of the air 
orifices must be capable of adjustment, so as to provide for variations in the 
water supply, if good efficiency is desired. 

The mixed air and water travels down a pipe with a velocity reckoned on 
the water alone of 6 to 9 feet per second in Webber’s case ; and the mean 
velocity of the mixture when the best efficiency was obtained appears to have 
been about 7 feet per second. Frizell’s best results were obtained when the 
velocity was about 4 feet per second, and although it is perfectly evident that he 
never got enough air entrained to secure the best efficiency, the difference from 
' Webber’s best velocity is very great, and it is probable that the dimensions of 
the shaft largely influence the value of the velocity required in order to obtain 
the best results. Frizell states that the air bubbles rise against the water 
current at a velocity of about 075 foot per second, and that this should be 
allowed for in calculation. The friction losses in the downward pipe are un¬ 
known. As already stated, Gibson believes that (when expressed in feet head 
of the mixture) they are about six times the feet head of water lost in a pipe 
of the same size conveying pure water with a velocity equal to that of the 
mixture. Frizell’s results agree fairly well with this rule. His apparatus, how¬ 
ever, had bends and constrictions that might equally well account for the extra loss. 
The bottom of the down shaft is coned out, after the manner of a draft tube, in 


840 


CONTROL OF WATER 


order to minimise the loss of head due to this velocity of 6 or 7 feet per second 
as far as possible. The water-way through the air chamber must of course be 
large, in order to reduce the velocity sufficiently to allow of the bubbles rising 
up from the water. The cone at the bottom is evidently intended to assist this 
disengagement of the air from the water. 

Webber’s apparatus is 16 feet in diameter, so that the velocity is only 
reduced to 3 or 4 feet per second. It would therefore appear that a reduction 
to Frizell’s value of 075 foot per second is not required, probably owing to the 
agitation produced by the cone. 

I tabulate the results of Webber’s experiments, and the dimensions shown 
in Sketch No. 243 are those given in his paper. If we take these results as 
reliable (and the work appears to have been quite as good as is likely to be 
attained in experiments of this magnitude) we may roughly state that for about 
60 cusecs the best efficiency is attained with an air inlet area of 120 square inches. 
For 70 cusecs the best inlet is 113 square inches, and for 80 cusecs an area ot 
106 square inches would probably give a better result than that obtained with 
larger areas. Now, if the area of the air orifice be kept constant, zz, the 
quantity of air sucked in per cube foot of water is also constant. Consequently, 
we may infer that the greater the volume of water used, the less n , should be. 
This, of course, is merely an indication that the terms hf and h v (which depend 
on n)j increase as the volume of water used increases, and that, just as in the 
case of air lifts, the best efficiency is obtained when the velocity of the water is 
just sufficient to produce an intimate mixture of air and water and carry the air 
down to the bottom of the shaft. We may also suspect that somewhat better 
results could have been obtained with a more perfect method of injecting air 
into the water. I should consequently be inclined to design the quasi-Venturi 
meter with a constriction of 0*40, rather than 0*50, as it appears to have been 
made. In default of fuller details, this criticism must be regarded as a 
bold one. 

Frizell’s results are less illuminating, as we are aware that the arrangements 
for the supply of air were bad. They are also irregular, and it can only be 
said that had he been able to inject air in ratios equal to Webber’s ( i.e . 1 cube 
foot of free air per 4 cube feet of water) it is likely that his efficiencies would 
have been as large, or possibly larger, than those obtained by Webber. As it 
was, the best efficiency obtained was 0*52, for 1 cube foot of free air per 8*8 
cube feet of water. Frizell’s other good results cluster around 0*52 to 0*45, for 
1 cube foot of free air, per 9 to 10 cube feet of water, and descend as low as 
0*40, when 1 cube foot of air per 20 to 25 cube feet of water is compressed. 

The practical aspect of the process seems to be as follows : 

It affords a very excellent method of obtaining power from large volumes of 
water, under a low head ; and in such cases the efficiency of the power plant 
is probably higher than that which could be obtained with the low speed 
turbines that are alone permissible, since these cannot be employed for driving 
the machinery direct. On the other hand, compressed air is not a practical 
method of distributing large quantities of power over any large area, the 
theoretical efficiencies being good, but the leakage losses increasing rapidly 
as the mains grow old. The practical application of the method therefore 
appears to be limited to cases where the demand for power is concentrated over 
a small area such as a factory, or a pumping station. The shaft is deep {eg. 
230 feet, for 100 lbs. per square inch pressure), and the first cost is probably 


EFFICIENCY OF COMPRESSOR 841 

equal to that of a turbine installation, but the maintenance of the shaft and 
pipes should be almost negligible. 

I am inclined to believe that the method is not as frequently applied as it 
might be. The reasons are obvious. The process is not greatly studied, and 
the power is obtained in a form which is very little employed. It may really 
be said that the installation would require a specialist to design it and the 
utilisation of the power also requires somewhat special, and rare experience. 

Webber’s installation was as follows : 

The head available varied from 187 to 20-5 feet, the shaft was 150 feet deep 
below the normal head water, so that the air pressure varied from 52, to 54 lbs. 
per square inch gauge. 

We have: 


I. Experiments with Thirty-four 2-inch Pipes as Air Orifice, 
. i . e . 106*8 Square Inches. 


Head in feet ....... 

20*54 

2 °*35 

I 9’93 

Volume of water in cusecs .... 

62*9 

67*8 

73*5 

Cube feet of water per cube foot of free air 

4 - 37 

4*20 

4*04 

Air pressure, lbs. per square inch . 

5 r 9 

53'2 

537 

^rr • . Air HP. 

Efficiency, i.e. —-—— .... 

Water HP. 

56*8 

60*3 

64*5 


II. Orifice as above, with Fifteen |-inch Pipes in addition, 

i . e . 113*4 Square Inches. 


Head in feet ..... 

20*12 

I 9‘5 1 

I9*3I 

18-75 

Volume of water in cusecs 

58-5 

7i*5 

783 

84*3 

Cube feet of water per cube foot of) 
free air J 

00 

LO 

V 

374 

4*26 

4*34 

Air pressure, lbs. per square inch 

51*9 

53*3 

5 2*9 

53*3 

Efficiency ..... 

55*5 

707 

62*2 

63*3 


HI. Orifice as No. I., with Thirty £-inch Pipes in addition, 

i . e . 120 Square Inches. 


Head in feet ..... 

20*0 


19*41 

I 9 ‘ 3 I 

Volume of water in cusecs 

60*5 

71*8 

76-7 

89*1 

Cube feet of water per cube foot of) 
free air J 

4*03 

4 ‘ 3 2 

4*30 

4*79 

Air pressure lbs. per square inch . 

53'7 

537 

53 * 6 

52*7 

Efficiency ...••• 

64*4 

61 *3 

62*0 

55*4 


















1..U 


' <r . ■ 





>ai m ; i 








CHAPTER XIV.— (Section E) 
HYDRAULIC RAM 




:'j i ■ 


Hydraulic Ram. —Description. 

Theoretical Treatment. —Cycle of operation—Period of escape—Closure of escape 
valve — Period of delivery—Shock loss—“Indicator diagram” — Observations — 
Approximate indicator diagram—Efficiency—Loading of the escape valve. 
Practical Rules. —Diameter of ram and delivery pipes—Air vessel—Observed values 
of the efficiency. 

SYMBOLS 


A, is the area in square feet of the cross-section of the ram pipe. 

a 0 , is the area in square feet of the opening of the escape valve. 

a v , is the area in square feet of the cover of the escape valve. 

a = £ - D (see p. 848). 
b=e + D (see p. 848). 

c ( i , is the coefficient of discharge of the area a 0 . 

cv + mv' 2 , is the resistance of the ram pipe and delivery valve (see p. S46). For c, and m 
see p. 846. 


C = ~r=> is the coefficient of frictional resistance of the ram pipe. 
s/rs 

d, is the diameter in feet of the ram pipe. 

ev + itv*, is the alternative value of c'v + m'v 1 (see p. 846). 

D (see p. 848). D' (see p. 848). 

H, is the difference of level in feet between the surface of the water in the working 
reservoir, and the escape valve. 

h, the geometrical difference in level between the water level in the reservoir into which 
the water is lifted and the water level in the working reservoir plus an allowance 
for skin friction and other resistances in the rising main. 

h x (see p. 845). 

its! biYi , q.-\ 

J = ——-— (see p. 845). 


J x (see p. 846). 

Kz; 2 , is the loss of head in the ram pipe by friction, bends and entry head (see p. 845). 
/, is the length of ram pipe in feet. 

mv 2 y is the total loss of head in the ram pipe and escape valve (see p. 845). 


2nv' + b 
2 nv' + a 


(see p. 848). 


nv 2 , is the value of mv 2 , when the delivery valve is opened, and the escape valve is shut 
(see p. 847). 
p (see p. 848). 

Q, is the total quantity of water used in cube feet, per cycle of the ram. 

Qi , is the total quantity of water lifted by the ram per cycle. 

Q e , is the total quantity of water escaping through the escape valve per cycle. 
r, is the hydraulic mean radius of the ram pipe. 

s v , is the maximum height in feet which the escape valve cover rises above its seat. 






hydraulic ram 


843 


S c , and S 0 (see p. 850). 

To, T„ T<{, To (see p. 845). 

t, is the general symbol for time, in seconds. 

XI the velocity of water in the ram pipe, in feet per second. 

V, is a velocity defined by wV 2 =H (see p. 846). 

vx, is the value of v, when the escape valve begins to close, i.e. at a time T„. 

m, 1S the value of v, just before the escape valve closes, i.e. at a time T 0 + T s . 
V* Is . e value of v, just after the closure of the escape valve (see p. 846). 

' max, is the maximum value of v (see Sketch No. 245). 

W, is the weight of moving portion of the escape valve’in pounds, 

a and p (see p. 848). ' 1 

V, is the mechanical efficiency of the ram (see p. 849). 

T] V , is the volumetric efficiency of the ram (see p. 849). 

A (see p. 846). 

SUMMARY OF FORMUL/E 

(i) Escape valve full open : 

0 =yOH -"zz' 2 ) Thus, v=^/^- tanh P- 
} _ A 2 v 2 T 2gsJmH 

1 7 • 

(ii) Closure of escape valve : 


T s — 2 .\J^ v approximately, 


(iii) Delivery valve open : 

X 

_ . ^ V fti It 

v'= -c -> approximately, v' 

la-/ F y 146+^ 


Thus, (a) v- 


- -j [/1 + ev + nv 2 ) 


I aMeV 1 - b 


and T ( { = —loge-, 

2 n 1 - Mev* p B a M 


or, (i) 5 ~ tan ^_ --1, 


or, (<r) t = 


2 n I + a tan 2.71 ~ p 

l 


1 rp X . 2 717 .) 

and l a — — tan ——. 

D' + e 


us/nh 


(tan-Vy /\ *}. 



e 1 


M 



Hydraulic Rams.— This form of pumping machine is old. The following 
may seem to be unduly lengthy if the present practical importance of the ram 
is alone considered, but since the principles laid down permit an approximately 
exact and highly efficient design to be obtained with but little trouble, the 
discussion is not without value. 

;; Sketch No. 244 shows the essential portions of a hydraulic ram diagram- 
matically. The power is obtained by water falling from the reservoir R, 
through the ram pipe RE, and escaping by the escape valve E. Putting aside 
for future consideration the conditions requisite to obtain proper working, it is 
assumed that the escape valve opens suddenly. The water starts to flow down 
the ram pipe, and its velocity rapidly increases until the escape valve suddenly 
closes. This sudden closure produces water hammer, or shock, and the rise 
of pressure thus induced opens the delivery valve D, and forces a certain volume 










'8 4 4 CONTROL OF WATER 

of water through this valve. This volume accumulates in the air chambei A, 
and the pressure existing in the air chamber forces this water up through the 
delivery pipe, or rising main AM, into the reservoir M. The delivery valve 
closes after a certain interval, and the escape valve K, again opens. The 
cycle is automatically repeated indefinitely. 

Using the symbols which are explained later, a quantity of water le- 

presented by : 

Q * Qe+Ql 

leaves the reservoir R, during each working cycle. A fraction Q e , escapes 
through the escape valve, and energy equivalent to 62*5 QeH foot lbs. is thus 
expended. The remaining fraction Qi is lifted through the height h, and 
energy equivalent to 62*5 Qf foot lbs. is stored up in the reservoir M. The 
levels between which H, and h, are measured should be carefully noted. It is 
hoped that the discussion which follows will clear up any uncertainties regard- 


/ 



Sketch No. 244. — Hydraulic Ram, Escape Valve, and Snifter. 


ing the conditions required to produce this somewhat mysterious cycle of 
operations. 

Hydraulic rams are at present the monopoly of three or four firms of 
specialists, who work by “ practical experience,” and by the rule of thumb. 
It is hoped that the following discussion will enable practical engineers to adapt 
commercial rams to varying circumstances. My own experience on the subject 
is that a few careful experiments and a set of spiral springs of graduated 
strength (see p. 807) are all that are necessary. 

Theoretical Treatment. —The exact theory of the Hydraulic Ram 
is unknown, and is probably so complicated as to be useless for any practical 
purposes. 

The following approximate theory has been experimentally investigated 
with great care by Harza {Bull, of Univ. of Wisconsin, March 1908). His 
results show that it is sufficiently close to the actual working of the machine 
to form a useful guide when discussing modifications of an existing 
ram. 





























































WORKING CYCLE 


845 


The working cycle of a ram may be divided into four portions : 


1. The escape valve opens,'water flows down the ram tube, and gradually 

attains a maximum velocity at a time T 0 , from the commence¬ 
ment of the cycle. 

2. The valve continues to close, and is completely shut at a time T 0 +T s . 

3. The delivery valve opens, and water is forced up the rising main for 

a time T<j, the delivery valve closing at T 0 +T s +Td, after the 
commencement of the cycle. 

4. The escape valve opens at a time T e , after the delivery valve closes. 

The whole period of the cycle is therefore T 0 +T s +Td + T e . 


The important portions are (1), and (3), and it is as well to note that both T s , 
and T e , are very small if the ram works well. 

Period 1.—Let H, be the total difference of level between the surface of the 
water in the reservoir, and the escape valve. Let v, be the velocity of water 
in the ram pipe, the area of which is A. Let a 0 , be the area of the discharge 
orifice of the escape valve, and Ca, its coefficient of discharge, which may be 
considered as constant during the time T 0 , but varies during T s . 

Then we have : 

k l7 the head required to force the water through the escape valve is 

given by : _ 

CcKZo J 2gh x = Av 

and the head available to accelerate the velocity of the water is : 

H-ki-Kv 2 

where Kv 2 , represents the head lost in the ram pipe by friction, curves, bends, 
and the velocity of entry ; so that : 

Kv 2 = v 2 ~- r 4- — z/ 2 + Head lost at curves and elbows, 

C l d 2 g 

where /, is the length, d , the diameter, and v = C Jrs, the friction equation of 
the ram pipe. 

Hence, we have as the equation of motion : 

^ = (H —mv 2 )‘~ ..... (i) 

Clt / 

S. 2cy2 

where, mv 2 = /q + Kz/ 2 = Kv 2 + 2 - — s 

a 0 


Now, this can be integrated as : 

, i , n /h+v’Jw 

t = -loge -AW- 7 —” 

s/mH JH-vJm 


or: 

where 


v 




J = 


H e Jt -i 
in e Jt + i 

2g JmH 
l 




Now this curve of v , in terms of t , can be plotted either from the first form, 








8 4 6 CONTROL OF WATER 


or more easily with the help of a table of hyperbolic tangents. We can also 
plot a curve showing : 

A 2 w 2 

R =- 5—at each instant of time. 

2 ga 0 2 cF 


As an aid in studying the general problem, it may be noted that if J, is 
varied, the form of the curve is not varied. For example, if we design a ram 


with J 1} in place of J, the value of V \J^ at the time t lt is the same as that in 

the original at the time t — ; so that one curve permits of a study of 

several rams by properly adjusting the time and velocity scales. So also, if 

A 

is not changed, the curve for h Xi is unaltered. 


C(iCl 0 


civ 


Now, in theory, this motion continues until -^=o, or H = 7/zV 2 , say. 


Actually, however, the escape valve is caused to begin to close when v, has 
a certain value, v x , which is best obtained experimentally. 

We can thus obtain the time at which closure occurs, T 0 + T s , and if we 
assume (as is very nearly the case), that the valve closes instantaneously, we 
can measure T 0 , on the time scale with a fair degree of accuracy. Let V m , 
represent the value of v, just before the valve closes, which is not necessarily 
the maximum value of v, unless the closure of the valve is instantaneous. 

Period 2.—We neglect, as a first approximation. 

Period 3.—A shock occurs, and the delivery valve is forced open. The 
water in the ram pipe now has a velocity v\ less than V m . 

Let X be the velocity of a wave of compression in the water in the ram 
pipe, i.e. X is approximately the velocity of sound in water (equal to 4700 feet 
per second), and can be calculated more accurately from the rules given 
on page 811. 


Then 


-(V m — v) = h+c'v'+m'v ' 2 
g 

— i 4 6(V m — v) approximately, 


where is the head pumped against, including friction, and curve and other 
losses in the rising main ; and fV+wV 2 are the frictional and other losses 
up to the beginning of the rising main, including those in the delivery valve. 

The resistance of the delivery valve now takes the place of that of the 
escape valve. In addition, the resistance of the small length of pipe and 
bends between the escape valve and the air chamber also contributes to the 
term ^V+?«V 2 . 

Now, according to Harza’s experiments, it would appear that m = z/z, and 
that the term c'v', is sufficiently large to require consideration. Harza 
apparently experimented on one form of valve only, and I am inclined to 
believe that in consequence his results apply solely to a rather special case. 
So far as can be judged from other experiments on valves (see p. 805), while 
the condition in = m\ is likely (and can certainly be secured by good 
design), it is not very probable that c'v is at all large in a well constructed 
valve. The delivery valve used by Harza is shown in Fig. 6, Sketch No. 237. 

Nevertheless, as a general rule, it is best to follow Flarza’s investigation, 





delivery of water 



since it is quite easy to put c' = o, when applying his formuke to any 
given case. 

We have as a first approximation for the initial velocity after the shock : 


v = 


X 

g 


V m —h 


O' 


>■ | / 

+c 


and as a second approximation : 


1 46V m --/l 
I4^~\~r 


v' = 1 4 6 Vm — h_ 111 ( 146 V m - /if 

146 + ^ (146 + c') 3 * 

which permits us to set off the height Z'W = v\ as the initial point for the 
curve representing the period (3), and it will be plain that the shock has 
diminished the velocity in the ram pipe by a quantity represented graphicallv 
by ZW ■= V m -V. 

The difficulties attending an experimental determination of this loss of 
velocity by shock are very great. The theoretical equations neglect the 
pressure required to open the delivery valve. No rules can be given for 
calculating this pressure ; but it is evident that the delivery valve should be 
designed so as to open easily. Thus, this valve should be light, and the 

J _ J 

breadth of its seat (denoted by - 1 on p. 805) should be small, and the load 

necessary to secure its closure during the period when the escape valve is 
open should be produced by a spring. In actual practice, the loading of the 
delivery valve appears to have little effect on the efficiency, and losses are 
mainly attributable to the seat being too wide. It is, however, quite possible 
that the apparently excessive values of d—d u found in practice are required 
in order to secure that the valve does not leak when it is old and worn. 

The most important practical condition is that the delivery valve shoul 
be fully exposed to the pressure produced by the alteration of velocity. 

Consequently, a proper design of the approach passages is probably far 
more important than the actual load on the valve. 

The equation of motion thereafter is plainly : 

« . ^ = — &(h+ e v+nv 2 ) .... (iii) 

' dt l 

where Harza takes e — c\ and n = in' — in , which is probably not absolutely 
correct, since the resistance between the delivery valve and the air chamber 
should be included in these coefficients. Harza’s notation has therefore been 
abandoned. 

The fact that h, expresses not only the geometrical height through which 
the water is lifted, but the frictional and other resistances in the rising main, 
should be borne in mind. These resistances, if required, can be estimated on 
the basis that the velocity in the rising main is uniform and has such a value 

O 

that Qi cube feet are delivered per cycle, t.e. at the rate T?-f T e * 

The solution of this equation has two forms, according as ^ 2 , is greater, 
or less than 411/1. 








CONTROL OF WATER 


(a) Corresponding 
than 4 nil. 

Put D = 


to relatively small delivery heads : i.e. e 2 , 

pD 

jA-47ih, a = e-D, b = e+D, p = -p 


greater 


m = 2 «C±* 

271V -j -a 


Since v = v\ when t = o, we get: 

i aM.e pt —b , P _ D » i-M^ bt 
V ~ 2nT=UJ»‘ ’ np gc "1 - M 2 n 

and v — o, i.e. the curve cuts the time axis when : 


. . (iv) 


/ =1 log ,-4 = T ri , approximately. 
p 

This curve can be set off, just as the curve of v, and /, was set off for the 
first period. 

(b) For relatively high heads, when e 2 is less than 471/1 , 


put D' = J 471/1 —e: 2 ^ and 


g D' . 2 7iv'-\-e 

P = NT ’ an d a = ~jy~> 


1 27 iv cos / 3 /—(D'-fag) sin ft / 
2« cos ft/+a sin ft/ 



and s = — log, (cos ft/+a sin ft/) — —. 

Tig 271 


. I 2#t/ 

t — Trtan 1 Va* . " 
ft D +a<? 


This curve cuts the time axis when : 

r » ,• 

= T f { approximately. 

(f) The most useful form is that obtained when £ = o. We get : 

t~ —-—/tan -1 ?/, tan" 1 ?;, /^. . . 

gLnh\ v // v Al 


(vi) 


In any particular case we can draw the various curves obtained by the 
above theory, and obtain a diagram such as OXYZWO' (see Sketch No. 245, 
Fig. 1). In this diagram the abscissae represent time intervals, and the 
ordinates the values of v, where Av, represents the volume of water in cube 
feet per second passing through the ram pipe RE. Thus, if we consider the 
area B'BCC', we see that the total volume of water that enters the ram pipe 
in the interval B'C', is given by Ax area B'BCC', cube feet. 

The diagram can thus be considered as a species of indicator diagram for 
one cycle of the ram. Hence we have as follows : 

OX' = T 0 , XX '— v x =velocity in the ram pipe when the escape valve begins 
to close. Similarly YY / = V ma x = maximum value of v, attained during the 
valve closure. X'Z' = T S and ZZ'=V m =value of v, at the closure of valve; 
and Ax area OXYZZ' = Q e . During the lifting portion of the cycle we have : 

WZ=V m — v = shock loss. Z'W =7/ = value of 7/, when delivery valve 
opens, and Z' 0 ' = T (J ; so that Ax area Z'WO' = Q t . 










EFFICIENCY DIAGRAM 


849 


Thus, if the “indicator” diagram be completely determined, we can 
calculate : 

The volumetric efficiency, n v — Q = ^ rea ^ WQ,..; 

Q e AreaOXYZZ' 


and the mechanical efficiency, rj = SltL= K ^. 

OeH H 


This last definition is that known as Rankine’s, and d’Aubuisson considers 

the mechanical efficiency, r; A = Q -- ^ 

(Qei-Qi)K 

The question is purely a matter of point of view, and is mentioned solely to 
indicate the necessity of a definite specification. 



Sketch No. 245.—“ Indicator” Diagrams of a Ram. 


Returning to Harza’s indicator diagram. The curve OBCX, is set out from 
equation No. (ii), and the curve WO', from the appropriate form of the three 
equations No. (iv), Nos. (v) and (vi). In Harza’s experiments the escape 
valve was mechanically opened and closed by cams on a rotating shaft. 
Hence, the time intervals T 0 , T s and T (Z were definitely known, and the only 
indefinite portion of the boundary of the diagram was the curve XYZ, which, 
since v x , V ma x, and V TO , are all nearly equal, cannot differ much from a 
horizontal straight line. Under these circumstances Harza’s experiments 
show that if the various constants c d , m, c, e , ?i , are determined and their 
average values used to calculate the curves OX, and WO', the calculated 
values of the volumetric and mechanical efficiencies agree very fairly with 
the values obtained by measuring Q e and Q t . 

The theory can therefore be practically applied to such cases as Pearsall’s 

54 





































CONTROL OR WATER 


850 

ram, where the valves are opened and closed by cams, worked by a heavy 
pendulum which receives an impulse at each swing by the escape of a small 
quantity of air from the air reservoir. In many other cases the escape valve 
is controlled by a swinging weight, and while the times T 0 , T. s , and T d, may 
not be accurately determined, T 0 + T s , and T f { + T e , can be calculated. 



In general, however, the valves are controlled by springs, and the theory is 
more complicated. I have investigated the matter experimentally, and find 
that the following process permits a trial value for the loading of the valve to 
be obtained. 

Calculate S c , the spring load on the escape valve in pounds, when it is 
















































































































SPRING LOADED VALVES 851 


closed. So, the spring load on the escape valve in pounds when it is open to 
its fullest extent. W, the weight of the valve in pounds. 

Then, taking the case shown in Sketch No. 246, where the escape valve 
opens upwards, we see that, 


S c —W = 62 , 5 <z 0 H : 


gives a minimum value of S c , as if S c , be less than this value the escape valve 
never opens. 

Again, S 0 -W=62‘5 a v h x and^,= 

2ga 0 2 c<f 


gives the value of v x . Thus, we can determine XX', and so fix X. If the 
valve is of one of the types discussed on page 805 a more accurate value for v x , 
could of course be obtained by using the figures there given. 

No experiments exist which enable us to calculate T s , but it is plain that T s , 
should be small, and thus W, should be decreased. In my experiments I 
assumed that: 



where s V) was the maximum lift of the valve cover. 

The formula has no pretensions to accuracy, but the results obtained did 
not conflict with observations of the quantity Q e , which will plainly depend 
greatly on the value of T s , if T s , is a large fraction of T 0 . The shock loss ZW, 
can now be determined, and the curve WO', set off. 

In practice, we can determine w, and J, by observing the steady discharge 
through the ram pipe when the escape valve is held open, and similarly n, by 
observing the discharge from the reservoir M, when the delivery valve is open, 
the escape valve closed, and the ram pipe removed. 

The process is obviously not as accurate as Harza’s, but the practical results 
are good, and after three or four trials an increase of 10 to 15 per cent, in 
efficiency can usually be obtained. 

Also, if Q e , be observed, a check on the value of T 0 +T s , is obtained, and 
similarly if Qi be observed, a check on the value of T c i, is obtained. 

The valve shown in Sketch No. 244 is probably too heavy, but excellently 
illustrates the principles of good design, since the rubber beats produce a 
certain increase in S c , without any increase in S 0 > and the form of the valve 


cover secures a large value of the ratio Similarly, in the valve shown in 

tto 

Sketch No. 246, S c , can be increased as necessary by lifting the starting lever, 
while So does not depend upon S c . So far as my experiments go good efficiencies 
are usually obtained with S c , only a little greater than the minimum value, and 

So-W, about 75 per cent, of S c -W, but the ratio ^ is more important. The 

delivery valve load should be as small as is consistent with preventing water 
from leaking back through it. 

In preliminary calculations we may take the values given by Eytelwein. 

T 0 = o* 65 period of complete cycle. 

T s =o-io „ „ 

Ta~o’2o -• „ > • • „ 

T e = 0’05 ,, ,, 




CONTROL OF WATER 


852 


Fig. 2, Sketch No. 245, shows a diagram calculated for a case of spring 
loaded valves, by the methods detailed above ; the only assumption made was 
that v x — V raax = V m , and the calculated and experimental results agreed within 
2 per cent. The average error was found to be about 8 per cent., but the 
efficiency could usually be predicted within 5 per cent, after the first 
experiment. 

Practical Rules. —The function of the air chamber is merely to absorb 
shocks, and to keep the water moving steadily forward in the rising main 
Since the ram is in essence a shock producing machine, the air chamber is a 
most important factor in producing smooth working; and great care must be 
taken to keep it well charged with air. See Snifter in Sketch No. 244. 

The size of the ram pipe is usually calculated so as to pass at least three 
times the available quantity of water under the working head H. 

The length of the ram pipe is often taken as : 

Length of ram pipe = Total vertical height between the escape valve and the 
reservoir M = 

If we modify this by including an allowance for friction in the vertical 
height, the rule agrees very fairly with successful practice. 

For small values of H, however, this rule gives somewhat shorter ram pipes 
than are found necessary. 

Clarke suggests as follows (.Hydraulic Rams, p. 54): 


H . 

. 2 ft. 

3 ft. 

4 ft. 

5 ft. 

6 ft. 

7 ft- 

8 ft. 

9 ft. 

10 ft. 

II 

X 

• 

• 3 

2*8 

2*65 

2 ’45 

2*25 

2'0 

1*85 

1-65 

i *5 

if h , exceeds 100 feet; 








• 

X 

II 

• 3*5 

3*25 

3 *o 

2-8 

2*6 

2*5 

2-25 

2*1 

2*0 


and states that while shorter lengths work successfully, trouble is experienced 
in adjusting the valves. 

The delivery pipe, or rising main, should be proportioned according to the 
ordinary rules. A rule of thumb is : 

For long distances : 

. Diameter of ram pipe 

Diameter=- £LJ — 


For short distances : 


Diameter= 


3 x diameter of ram pipe 

8 ~ 


The air chamber is usually proportioned by the rule : 

Volume = 2 xarea of delivery pipe x length of rising main. 

It is plain that if the air chamber can be proportioned so that its period of 
oscillation is a fraction of the period of the ram cycle, so much the better. 

It seems needless to enter into such details as the precautions necessary 
when impure water is used to lift the pure article for human consumption. So 
far as I can ascertain, no appreciable loss of efficiency occurs in such cases. 

The theoretical investigation has, I think, made it obvious that the escape 
and delivery valves should be as light as possible, and that the easier the 
delivery valve opens, the better. I append a very excellent design (Sketch 
No. 246). 




EFFICIENC V OF RAMS 


853 

The efficiency of a well designed ram is high, e.g. the Bollee ram at 
St. Julien le Vaublanc, where ^ = 45*9 feet, H = ii*5 feet, ^=16*1 per cent. 
The mechanical efficiency is 80*5; or, if friction in the rising main is allowed 
for, 817 per cent. 

At Vernon, ^ = 47*5 feet, H = 39*4 feet. The mechanical efficiency = 66’9 
per cent, when allowance is made for friction. 

Harza’s results show that a ram with a ram pipe two inches in diameter 
can be adjusted so as to have an efficiency exceeding 60 per cent, over a very 
wide range of head. Considering the size of the machine, it may be inferred 
that a carefully adjusted ram is probably one of the most efficient hydraulic 
machines in existence. 


• r, 


\ :)'// 




* ) 1 , • , r.. . . • 

• K’ ?; 

/ • r • ■ ki v / • 


1 m 


i 


* r * 



ini 




m 





1 


rrt 







JO 






ill.. 


*• •'J ' J - A' < '• il 


:>*» ? >t wi ■ ii j- - - i>r • -* '• ' 

i' ' 11 . • ' 

CHAPTER XIV.— (Section F) 

RESISTANCE TO MOTION OF SOLID BODIES IN WATER 

Resistance to Bodies Moving in Water. —Friction of a flat body moving in 
water—Froude’s experiments. 

Resistance to a Body Moving in a Pipe. 

Friction of Rotating Discs. —Unwin’s experiments at low velocities—Table—Gibson 
and Ryan’s experiments at high velocities—Table—Influence of temperature 
Average values. 


SUMMARY OF FORMULA 

Board moving in water : 

F = B( —j pounds per square foot (see p. 855). 


Body moving in a pipe : 

F = ^ pounds (see p. 856). 
4 2 g 


Friction of a rotating disc (both sides)!: 

M = ^ 7rfa> /R n+3 foot pounds (see p. 859). 
n + 3 

Horse power = ^ 7rt ° -/R n+3 horse power. 

55o(« + 3) 


Friction of a Body moving in Water.— The laws of friction between a body 
moving through, or past still water seem to be very similar to those between a 
body at rest and water moving past it. 

When a long, straight board is towed in still water, it is found that the 
first three or four feet experience a greater resistance per square foot than the 
remainder of the length. This is obviously due to the friction of the first three 
or four feet having set the particles of water near the board in motion, so that 
the velocity of the remainder of the board relative to the water surrounding it 
is diminished. This effect is not likely to occur if the water is moving 
sufficiently fast to have a turbulent motion, unless the surface of the board is 
abnormally rough. 


854 






RESISTANCE OF BOARDS 


S 55 

The following figures are given by Froude (.Report on Frictional Resistance 
of Water on a Surface, see also Encyc. Brit., article “Hydromechanics”), for 
boards with sharp ends, towed in water : 

The resistance in pounds per square foot of area is : 

( V \ n 

—J where B is the value of F, when v— 10 feet per second. 


1 

Character of Surface. 

Length of Surface, or Distance from Cutwater 

, 

in Feet. 

Two Feet. 

Eight Feet. 

J «C • ) l 5 

n 

B 

C 

n 

B 

C 

Varnish 

2 'OO 

0*41 

0-39 

1-85 

°' 3 2 5 

0*264 

Paraffin 


0 38 

°’37 

1 '94 

°‘ 3 I 4 

0*260 

Tinfoil 

2*16 

o‘ 3 ° 

0-295 

r 99 

0-278 

0*263 

Calico 

I‘ 9-3 

0*87 

0-725 

1-92 

0*626 

0-504 

Fine sand . 

2*00 

0 ’81 

0*690 

2*00 

<>'583 

0-450 

Medium sand . 

2*00 

0*90 

0730 

2 - 00 

0-625 

0*488 

Coarse sand 

2 "OO 

1*10 

o-88o 

2*00 

) 

o' 7 i 4 

j 1 1 • 

0-520 

• 

Twenty Feet. 

Fifty Feet. 


n 

B 

C 

n 

B 

c 

Varnish 

1-85 

0-278 

0-240 

183 

°' 2 5 ° 

0/226 

Paraffin 

1 '99 

0-271 

0-237 

• . . 

... 

• f • • 

Tinfoil 

1 '90 

O '262 

0-244 

i-8 3 

0*246 

0*232 

Calico . 

1*89 

°' 53 1 

0-447 

I *87 

0-474 

0-423 

Fine sand . 

2 '00 

0-480 

0-384 

2 *o6 

0-405 

°‘337 

Medium sand . 

2 ‘00 

°’534 

0-465 

2*00 

0-488 

0-456 

Coarse sand 

2 ’00 

0-588 

0*490 

• 

* * * 

• • • 

• • • 


The values of B, give the average resistance over the whole area of 
the board of the given length, in pounds per square foot, at 10 feet per 
second. 

The values of C, give the resistance under the same circumstances of one 
square foot at a distance from the cutwater equal to the length given at the 

head of the column for any length of board. 

Resistance of a Body moving in a Pipe. —Our knowledge of the motion 
of bodies the cross-section of which is of a size comparable to that of the pipe 
through a pipe filled with water, is limited. 









































CONTROL OF WATER 


856 

Sorge (Gluckauf December 14, 1907) gives as follows : 

The force required to move a cylinder of diameter and 0*3 m. (say 
10 inches) long, with a velocity v feet per second, through a pipe of diameter 
^=o - o 26 m. (say 1 inch) is given by the equation : 


F = ~<f 1 2 £— pounds, 
4 1 -if 

where is as follows : 


cs 

tc 

1 

£ 

c 

m- - 

* 

c 

0-25 

1-07 

°‘93 

074 

45 ’ 6 

0-56 

o '45 

377 

0-83 

076 

5 2 ’ 1 

0-56 

0*64 

157 

0*67 

... 

• • • 

... 


Sorge also states that these figures are very fairly represented by 


£+ 1 — 


(I-V ) 2 * 8 

The theoretical value would be : 


where 




+ I= _L_ 

where c, is the coefficient of contraction for the orifice formed by the cylinder, 
and the walls of the pipe ; and the values of c , thus obtained, are tabulated 
above. 

No experiments exist which would enable us to test these values of c, but 
we may expect that: 

(a) In larger pipes, with cylinders the area of which bears the same ratio to 
that of the pipe, the values of £ will be somewhat increased, at any rate for the 
larger values of 77. 

(1 b ) For a thin disc, or a sphere, the values of £ will be somewhat less 
than those for a cylinder of the same relative cross-section. 

Friction of Rotating Discs.—For circular discs rotating about an axis we 
have : 

If afv n , be the friction on a small area of a> square feet, moving with a 
velocity of v , feet per second, the frictional moment for both sides of the disc 
is plainly : 

M = 4 ™! /R n+3 foot lbs. 

n + 3 y 

where &> is the angular velocity of the disc about its axis, and R, is its radius 
in feet. 

Unwin ( P.I.C.E. , vol. 80, p. 221) gives the following figures for a disc with 
a radius of 0*85 foot rotating in a cylindrical chamber. 































RESISTANCE OF DISCS 


8 57 


Character of Surface. 

Value 
of n. 

Value of f x io n when the distance 
between the Sides of the Disc and 
the Ends of the Chamber is 

' 


1 \ in. 

3 ins - 

6 ins. 

3*5 ins- 

Clean polished brass 

Clean polished brass, chamber\ 

i-8 5 

0*202 

0*209 

0*230 


coated with coarse sand . j 

*'95 

• • • 

0*244 

• • • 


Painted cast iron 

i*86 

0*218 

0*232 

0*247 


Painted and varnished cast iron 

1 ‘94 

• • • 

0*220 

0*233 


Tallowed brass 

2*06 

• • • 

0*2 18 



Cast iron .... 

2*00 

0*213 

0*227 

0*243 


Cast iron covered with fine sand 
Cast iron covered with coarse\ 

2*05 


0*340 



sand. J 

Cast iron covered with coarsen 

1 *91 

°' 5 8 7 

0*638 

°‘ 7 I 5 


sand, chamber coated with - 
coarse sand . 

2*17 

• • • 

• • • 


0*799 


Apparently f is independent of the radius, but its value increases as the 
distance between the edges of the disc and the sides of the chamber is 
increased. 

These values may be employed in the calculation of the effect of dead water 
friction on the wheels of centrifugal pumps and turbines ; and it should be 
remembered that in most cases the distance between the wheel and the fixed 
casing being less than inch, they may be considered as high. 

While Unwin’s experiments cover the greatest variety of surface, they were 
made at speeds ranging from 67, to 350 revolutions per minute (i.e. about 10 
feet per second mean velocity). Those of Gibson and Ryan ( P.I.CE ., vol. 179, 
p. 3 I 3 ) being made at speeds of 450 to 2200 R.P.M., agree better with the 
conditions usually found in modern centrifugal pumps. 

Messrs. Gibson and Ryan use the formula given above, except that the 
thickness of the outer end of the disc is held to influence the friction ; which, 
although correct for the particular experiments under consideration, does not 
usually apply in practical examples. 

A tabulation of Messrs. Gibson and Ryan’s results is shown in table on 
page 858, the term “ clearance ’’being used to indicate the distance between the 
sides of the disc, and the sides of the casing. 

Messrs. Gibson and Ryan also investigated the influence of the temperature 
of the water on the frictional resistance. 

Let P*, denote the quantity known as Poiseuille’s ratio (see p. 19) where : 

p __^_ 

1 +o-o337T+o'ooo22iT 2 
if T, be expressed in degrees Centigrade, 

or P« = 


0*474+o*o 144^+ o * ooo 682/ 2 
if /, be expressed in degrees Fahr. 






























8 5 8 


CONTROL OF WATER 


Character of 


Disc. 

Casing. 

n 

Polished brass. 

Rough cast iron. 

1*8 

12 inches in 

to 

diameter. 


i*8i 

f ' 

Painted ,, 

179 



to 

• - 1 \ 


i *8o 

1 . 0 

Smooth ,, 

177 



to 

* * ' 


1*82 

Do., 9 inches 

Painted ,, 

1-83 

in diameter. 

; 

Rough cast 

Rough 

1'91 

iron, 12 inches 

Do., with 2 an- 

r88 

in diameter. 

nular baffles 
£ inch deep. 



Painted cast iron. 

i*8o 

to 

. 


i-8i 

Do., 9 inches 
in diameter. 

j> >) 

1-85 

Painted and 

Rough „ 

1-85 

varnished, 12 

Painted ,, 

i*8o 

inches in dia- 



meter, cast 



iron. 



Painted and 
varnished cast 
iron, 9 inches 
in diameter. 


1*83 

Brass, 12 inches 

Painted cast iron, 

T *91 

in diameter, 

vanes ^ inch 

with 4 radial 

deep 



vanes in each 
face. 


Value of/x io 2 when the Clearance is 


B in. 

1 in* 

is in. 

l§ in. 

2| ins. 

0*409 

0*422 

0*414 

0*432 

0*474 

0*360 

°'359 

0 * 35 ^ 

; >\ I 

o *359 

» * j • 

... 

0*346 

°'373 

0*438 

0*421 

iO*I 

°* 47 I 


0*342 

• • • 

• • 

♦ 

1j 

• • • 

• • • 

0*300 

o* 3 01 

0*297 

0*302 

• • • 

o '337 

0-337 

. . . 

- 

< • • • 

• • • 

0*428 

0*426 

0*424 

0*414 

• • • 

0*372 

• « 

• • • 

• • • 

• • • 

• • • 

o *353 

• • • 

• • • 

• • • 

• • • 

0*361 

0 

• • • 

• • • 

■ 

... 

0*340 


■ *• 

• • • 

0*903 

1 *067 



• • • 

Clearance measured over the Vanes. 

/w inch. f inch. 

0*668 0*687 


Do. 

Vanes, \ inch 
deep. 


Let Wt, denote the weight of a cube foot of water at a temperature t. 

Then putting R< for the resistance at a temperature equal to t degrees and 
R 05 for the resistance at 65 degree Fahr. : 

P* \ 2-n / wt 







































GENERAL FORMULAE 859 

and the figures tabulated above are those appropriate to a temperature of 
65 degrees Fahr. 

The increase in resistance per degree Fahrenheit at a temperature near to 
65 degrees Fahr. is about ^ per cent, when n — i # 8o, and is inappreciable when 
n — 2'00. 

In none of Gibson and Ryan’s experiments does this increase amount to 
2*5 per cent. It is therefore not proved that the correction will hold accurately 
for such temperatures as 120 or 150 degrees Fahr. 

A study of their own results, and those obtained by Unwin, has led Gibson 
and Ryan to propose the following table of average values of #, and f: 


1 < ♦ ' • * ? 1 

I hi lil 4 <f» 

CJ 4 I .* 

Casing. 

. • 1 ■. V 1 * j t . j /< ( 

Mean 
Velocity 
of Disc 
in Feet 
Per.; 
Second. 

f i . \ ■ 

Disc. 

Polished Brass. 

t 

Disc. 

Painted or 
Varnished Metal. 

Disc. 

Rough Cast Iron. 

n 

/x IO 2 

n 

/x IO 2 

n 

/x IO 2 

Smooth, i.e. 

10 

1'85 

0-31 

^94 

0*26 

2*00 

0-23 

machined or 

20 

1-84 

°‘33 

1*91 

0’29 

1-96 

0*27 

‘ painted 

30 

r8 3 

°*35 

r88 

0-32 

1*91 

0*32 

metal. 

40 

1*82 

°'37 

1*84 

°*35 

i*86 

o *37 


5 ° 

r8o 

o *39 

1*80 

o *37 

1 *81 

0*42 

- t > 

Rough cast 

10 

■»;} - r .1 1 

1*92 

0*29 

i *97 

0*27 

2 ’00 

0’26 

iron. 

< 

20 

1*89 

°‘33 

1-94 

0*29 

1*98 

0*27 


30 

1-86 

o *37 

1*91 

0*31 

1-96 

0 ' 2 S 


40 

1-83 

0*41 

i-88 

0*33 

i *93 

0*29 

, 1 !T( >' ' <r. * 

5 ° 

I '80 

= . wt ti • 

0-44 

1*85 

: • ■ • ' 1 

°'35 

1*91 

0-30 

: 


These results cover all practical cases, and serve to show the extreme 
importance of keeping the clearances small. 

I believe that the suggestions made by the authors for design ( vide ut supra) 
are erroneous, since their sketches seem likely to permit more leakage to take 
place than is really permissible. Their principles, however, are quite sound, and 
are decidedly neglected in many modern designs. 

• ' “ ‘ r ‘ • . . j * » •**"*'' 

.* h '*> -»: r ; .• . , • : . J i .** 


v/. 


h.». : 



u 



t * 
./ 


• j * 


C> ^ •*) ; 


' 


























I 


Vv> 


A 


\ 


" H ” ' ■ f" ■ n ' ' b . 3i ■ J ■ 

CHAPTER XIV.— (Section G) 

IMPACT OF WATER ON MOVING BODIES 

General Equation of the Motion of Water in a Tube that is Moving in 
a given Manner.—G eneral equation—Equation for pressure at a point in the 
tube—Application to turbine wheel—General equation of turbines—Practical rules 
for selection of points of entry and exit. 

Impact of a Stream of Water on a Moving Body.—T heoretical equations— 
Deflection angles—Loss of head by shock—Practical rules—Pelton wheels—Loss 
by friction on the surface of the body—Francis turbine—Loss by change of velocity. 

SYMBOLS 

a, is the area of the jet of water before it strikes the vane. 

A, is the area of the wetted surface of the vane (see p. 867). 

at, is the area in square feet of the closed channel at the point of complete entry 
(see p. 862). 

hi (see p. 862). hi (see p. 862). h s (see p. 862). 

H, is the total head in feet under which the turbine works. 

A suffix notation, is employed in connection with the following symbols: 

Suffix a , refers to any point intermediate between i, and e. 

Suffix e, refers to the point of exit from the vane, or moving channel. 

Suffix i, refers to the inlet or point of entry into the vane or moving channel. 

p, is the pressure in feet of water. 

Q, is the quantity of water delivered in cubic feet per second. 

u, is the absolute velocity of any point in the moving body in feet per second. 

v, is the velocity of the water relative to a point moving with velocity u. 

w, is the absolute velocity of the water. 

V j, is the observed velocity of the water immediately after the impact is complete, relative 
to a point moving with velocity zq. 

v s , u' e , w' e (see p. 865). v'i — Q (see p. 865). 

Qi 

Vo _Vi + Ve ( see 867). 

2 if 

is the angle between the positive directions of u, and v. 

5 , is the angle between the positive directions of u, and w. 

e, is the hydraulic efficiency of the turbine. 

di, is the angle between the direction of vi as geometrically obtained, and the observed 
direction of V 1} i.e. the shock angle. 

K h is the angle between PD, and PE, the actual direction of V,. 

\j, is the space angle between vi and Vj. 

SUMMARY OF FORMULAE 

Energy imparted to the vane or pipe: 

62 ’ ■, 

-—^ ( u,Wi cos di~u e w cos 50 foot lbs. per cusec. 

g 

Relative velocities: 

v^ — ui 2 + wi 2 - 2 UiWi cos 8 i 

Wj _ Vi 

sin / 3 i ~ sin 5 ,- 


860 





GENERAL EQUATION 


861 


Pressure equation: 

Pi ~ Pa ~ h\ — 

General equation of a turbine : 


Ui 2 - u 
2 g 


2 


a 


Vj~ - Vg 2 
2 S 


£*H = w 2 u 2 cos d 2 - w 4 u 4 cos 5 4 


eH 


W - 70* | Up~ - U * 


Loss by impact at entry 


2 g 


Theoretical, 


2 g 


vpmx -dj 
2 g 


or, 


2 g 

vi 2 sin 2 X* 

‘ 


(see p. 88o). 


Practical, 0’5 to 07 Vi s * n2 or 

2 g 


7 p 

♦Observational, — 

-V 

or, 

Vi 2 - V? 

• 



2 S 


2 § 



Loss during motion over the vane : 






V, 

Observational, — 

2 -zV> 

or, 

V a ~ V? 

v'i 2 

- Q 


2 § 


2 ? 


ai 

nj .2 _ rfj 2 

Farmer s rule for all losses • 1 e 

with 


^ e — n *n?66 

A 

I 

2 g 

v ( 

) 

a 

V 

V 0 


General Equation of the Motion of Water in a Tube that is 
MOVING IN A GIVEN Manner. —The motion of a fluid in a space the bound¬ 
aries of which are themselves in motion is a somewhat complex problem. 

Since the surfaces bounding the fluid are themselves in motion, the pressure 
may be a discontinuous function of the co-ordinates, and the general hydro- 
dynamical equations given by Euler require modification. No very good 
investigation exists in English, although Mise’s Theorie der Wasserrdder gives 
a comparatively simple presentation in German of the practical case of a turbine 
wheel in which the space considered is rotating round a fixed axis. 

At best, the proofs are long, and require greater mathematical equipment 
than engineers usually possess. 

The following method of investigation is simple, and is subject only to the 
same uncertainties as affect the use of Bernouilli’s equation in ordinary 
hydraulic problems. In the only practical application that has yet been made 
the results are known to be quite as accurate as are those of any hydraulic 
calculations, and they are believed to be applicable to all possible cases. 

Consider first the simplest case of motion in one plane, and measure all 
velocities in feet per second. 

Let Q, cusecs of water enter the pipe or moving space, with an absolute 
velocity Wi, at a point the velocity of which is Ui. Then, Q, cusecs of water 
must leave the pipe with a certain absolute velocity, say w e , at a point the 
absolute velocity of which is u e . 

Then, assuming that there are no losses by shock at entry, or exit, the 
energy imparted to the pipe is : 

■ ~ (UiWi cos bi—u e Tv e cos b e ) foot lbs, per second ; 


where bi and b e are the angles between the directions of u iy and w { , and u e 
and w e . 

This equation can be easily verified for such simple cases as a pipe moving 


















862 


CONTROL OF WATER 


with uniform velocity (i.e., z/» = u e ), by actually calculating the pressures on the 
pipe. A general proof for three dimensional motion is given by Thomson and 
Tait (.Natural Philosophy, Part i, p. 208). Thus, the water loses the same 
amount of energy, and : 


pi+ 


w i 2 

2*r 


— pe~\~ 


W e 2 , Willi COS hi — W e Ue COS 

Zg g 


The equation can also be transformed by considering the relative velocities 
Vi, and v e . We have, see Sketch No. 247 : 

Vi 2 = Ui 2 j rWi 2 — 2UiWi cos Si, 
and V e 2 = U e 2 +W e 2 — 2U e W e cos S e . 


Thus, pi—pe = 


Ui 


■u e 


Vi 2 — Ve 2 


2 g 


2 g 


This equation must of course be corrected for frictional and other losses 
in the pipe, and also for any difference in elevation between the points 
represented by i and e (see below). The results of such experiments as exist - 
(which, for practical reasons, are mainly confined to pipes moving uniformly 
or rotating round a fixed axis) confirm the equation, and do not indicate that 
the laws of friction are in any way altered, provided that the velocity of the 
water, relative to the pipe, is used when calculating the frictional losses. 

The questions concerning losses by shock at entry or exit are discussed 
in detail later. For the present it suffices to state that if hi, represent the 
total loss of head by friction, curvature, and shock, reduced to feet of water by 
the usual rules, then : 


P% pe h\ 


Up—U? V? — V? 
2 g 2 g 


) 


So also, if it be desired to ascertain the motion at any point a, intermediate 
between z, and e , we have : 


p\—pa — 


u 


.2. 


Ur 


2 g 


Vi 2 —Vq 2 
2 g 


and if h\, represent the friction and other losses, and h s , the height of the 
point represented by a, above the point represented by z, then : 


pi pa h 1 hs — 


u 


.2. 


■Un 


V, 


.2 _ 


Vn 


2 g 


2g 


In applying these equations to practical problems, two cases occur, which 
should be distinguished before the frictional and other losses are calculated. 

(i) Open Vane.—The water while on the vane has a free surface exposed 
to constant pressure. Then pi=p e = p a , so that v e , or v a , can be calculated. 
This is the case of a Pelton wheel, or free deviation turbine. We have at once : 

Ui 2 — U a 2 — (Vi 2 — V a 2 ) = - 2 g{h'i + h s ) 

As a particular case, we frequently have Ui = u a = u e . 

Then, if we assume h’i, and hi = o, 

Vi 2 —v a 2 = 2 ghs, and if h s = o, v t = v a = v* 

(ii) Closed Pipe.—The water moves in a closed passage : 


Then, v t = 2 , v e =S f 

&i <Xe 


and v a 



Thus, p t , or p a , can be calculated. 












EQUATION OF FRANCIS TURBINE 


863 


These general equations can be applied to any problem. In practice, 
however, the fundamental equation of a turbine is more easily arrived at by 
the following process. For distinction’s sake (see p. 907) use suffixes 2, and 4, 
01 t e entiy and exit sections (see p. 877) of a turbine. Then, the change 



4 


u? 

Veloci ty Diagram 
for loss on 


fanettel? 


Velocity Dia a ram at Exit 
No Vane losses, ori> e = u t 


Jet Velocity or, 



Vane Velocity iq 



Velocit y Qia g ram at Entr y 
Shochless Impact on Open Urns: 


^ 4 k ^4 \v 

; e V\ 1t\ \ 


o e = iq cos 0L ^- lesslhanu{ 
Veloci ty Oiag ramsat Exit 

Jet Velocity ufj 

Vane VelfixJ 




Velocit y Diag ram at Exit 
corrected for Vane losses 
u e less than or qcosfli 

0 ; 


V 


Velocity Ota?' 
a ramatUit/ 

/ 



Velocity Diag ram at Entr y when Q-equj, 



_-Vi' "O-v 

Change of Relative Velocit y 
When Q is greater than cq iq Q = a; v q 
If Q is less than cqiq jet does not veil the lube 
Shockless Entry into h Closed Tube 


t 



- 




ft o 

vj, 



i.&i 

% 

y>T 

*/sJ 



/ vjr 


Velocity Diao ramat Entr y n 
-Shock, occurs but /j 

~et Velocity = gq - 



R y'fU'QS* Chang e of Relative Vclofi Iv after 

Shock,since Q is not erjualto ayqcos<k 

Entry into Closed Tube with Shoc k 


Veloci ty Diag ram at Entr y showin g Shock Losses 
Impact on Open I /one vuth Shock 
Sketch No. 247.—Diagrams for Motion on Vanes and Pipes, 
in the moment of momentum of the water round the axis of the turbine is 

62* C 

—- ( w 2 r 2 COS b 2 — w 4 r 4 cos 84) foot pounds per cusec. 

CT 

<b 

Thus, if co be the angular velocity of the wheel, work is done at a rate of: 

cos 8 2 — w 4 r 4 cos b 4 ) = -E 3 {iv 2 u 2 cos 8 2 — iv 4 Ua cos S 4 ) 

g ' g 

ft. lbs. per cusec. 


g 



















































864 


CONTROL OF WATER 


The work done by one cusec of water is : 

62‘5eH foot lbs. 

where e (see p. 880) is the hydraulic efficiency of the turbine. 

== W 2 U 2 COS § 2 “ ^4^4 COS S 4 , 

and, iH = 

2 ? 2 g 


We thus get: 
. • . (0 
. . . (ii) 


The practical applications of the above equation present but little difficulty 
so long as the cross-section of the pipe is so small that the velocities and u , 
can be considered as uniform. Judging by practical experience, no appreciable 
error is introduced provided the mean values of w, and u, are used in the 
equation, and the value of z/ 2 , or zz 4 , does not vary more than 5 per cent, 
over the whole area of the cross-section at entry or exit. Thus, the partial 
turbines considered later should not have a radial breadth greatly in excess of 
one-tenth of the mean distance of these areas from the axis of the turbine. 
The selection of the precise points or sections of entry and exit is more difficult. 
The method given on page 907 leads to correct results in every case which I have 
been able to test thoroughly, but observations on turbines are hardly sufficiently 
precise to enable a definite statement to be made ; and if shock at entry or 
exit occurs, the figures obtained by any process are only comparative. As 
a rule, we are justified in stating that any difference between the results of 
theory and experiment is to be attributed rather to an erroneous selection 
of the sections of entry and exit, or to neglect of shock, than to any defect in 
the theory. 

The matter is very excellently discussed by Gelpke ( Turbinenu?id Turbinen- 
anlagen , p. 57), who states as follows : 

(i) When the water entirely fills the space between two consecutive guide 
vanes, take the points O, and a , as corresponding to complete entry, and 
complete exit (see Fig. 3A, Sketch No. 261, p. 926). 

(ii) Where, however, as in Fig. 3B, the water does not entirely fill the space 
between the vanes, the points of complete entry and complete exit are those 
corresponding to and a. 

The reasoning is obvious, and, so far as experiment can inform us, it 
is correct. 

Subject to these remarks, equations No. (i) and No. (ii) may be considered 
to be rigidly proved, and as only subject to errors produced by the non-uniform 
distribution of velocity over the cross-sections of the water stream, such as 
have already been discussed when considering Bernouilli’s equation. 

The general equation for a Pelton wheel can be obtained in precisely 
the same manner. The only difference which needs to be considered is that 
since the jet is under atmospheric pressure throughout its whole motion : 

pi — pi = atmospheric pressure 

Consequently : 

v? = —(up — up) —2 g{hi +As); 

which permits us to calculate v e when hi has been obtained. 

Shock or Impact Losses. —-In the above discussion we have assumed 
that no shock or impact losses occur at entry. The geometrical condition for 
this is plainly that the direction of Vi shall be the same as the direction of the 
tangent to the vane or pipe at entrance. 





IMPACT LOSSES 


865 

Let us now assume that Vi as determined by the velocity triangle makes an 
angle Bi with this direction. As will later appear, Bi may be a space angle, i.e. 
determinable by three dimensional geometry only. 

The best method of ascertaining v (i.e. Vi, v a or v e ) is the ordinary diagram 
of velocities, and is best expressed by stating that the line representing w is the 
diagonal of the parallelogram formed by u and v. Or in vector notation, 

Vector w — Vector u-\- Vector v. 

The circumstances which occur during the motion of water over an open 
vane (eg. a Pelton wheel bucket) are shown on the left hand of Sketch No. 247. 
The full line diagrams, with undashed symbols for velocities, show how exit 
occurs when u e = Ui. Theoretically, we then have : 

With no shock at entry, v e = v^ 

With shock at entry, v e — Vi cos Bi = V 1} say in practice. 

The dotted line diagrams, with dashed symbols for velocities, refer to a case 
where u e , differs from Ui- According to the theory we then have : 

With no shock at entry, v e 2 = Vi 2 +(u e 2 —Ui 2 ). 

With shock at entry, v e 2 = v? cos 2 0 i+(« e 2 — ui 1 ) 

or, in practice, = V 1 2 + (« e 2 — up). 

In practice, these equations require correction for friction and other losses 
occurring during the motion on the vane. Thus, v e , will generally be less than 
the theoretical value. Observation, however, shows that when shock at entry 
occurs, V 1} the observed relative velocity just after entry, is usually greater than 
Vi cos 6 i ; hence the effect of the vane losses may be masked by a decrease 
in the shock loss. The right hand side of the Sketch shows similar diagrams 
for motion through a closed tube. The circumstances at exit are less compli- 

cated, since the ratio — e , is determined by the cross-sections of the tube at entry 

Vi 

and exit. The entry conditions, however, are more complex. Neglecting for 
the present the difficulties introduced by three dimensional motion, let us con¬ 
sider geometrically shockless entry. 

Put v\ = — and let Vi, denote the geometrically obtained value of the 
ai , f 

relative velocity at entry. If v iy be greater than v the tube is not filled, and 
if Vi, be less than v'i, splashing occurs. In practice, however (eg. Francis 
turbines), the tube (or wheel cell) is not isolated, and the jet is bounded by rigid 
surfaces (guide vanes and crowns). Thus usually, the tube is filled at entry, 

and an increase or decrease of pressure equivalent to 

7 /.2_ 7 ,.2 

V-— feet occurs. 

2£- 

Thus, in reality, the entry, although geometrically shockless, is probably 
attended by a certain loss of head (compare p. 798) caused by incomplete con¬ 
version of velocity into pressure, or vice versa. A similar loss is possible when 
shock at entry occurs ; the equations are as above, except that Vi cos Bi or V,, 
must be substituted for Vi. 

It should also be realised that while the above discussion makes a distinction 
between an open vane and a tube, a large jet impinging on an open vane may 
produce a very fair imitation of the geometrical (as distinct from the pressure) con¬ 
ditions of impact into a tube, by the interference of individual portions of the jet. 

55 



866 


CONTROL OF WATER 


Sketch No. 248 is intended to illustrate this case, which is of importance 
when Pelton wheels with large jets (say over two inches in diameter) are con¬ 
sidered. Let a jet moving with absolute velocity Wi, along AP, strike a body 
which is moving with absolute velocity Ui , along PB', at P. Then (see Fig. 3) 
AB = is the relative velocity, and is in the direction CP. But (see Fig. 1) 
the surface of the body being represented by the plane ETr'E-r, shock occurs, 
and the water will move off along DP, the projection of CP on this plane, with 
a relative velocity which is theoretically equal to Vi cos X*, where X* is the angle 
CPD. Now, assume that either due to mutual interference of the various 
portions of the jet, or due to the body being really a closed tube, the water is 



Sketch No. 248. — Three Dimensional Impact. 

(1) Perspective Sketch. (2) Spherical Diagram. (3) Velocity Diagram. 

constrained to move off along the direction EP, a further shock occurs, and 
theoretically the final relative velocity is Vi cos 6 i, where 

cos 6i — cos Xf cos Ki ; 

the angle DPE being denoted by m ; so that A is the space angle CE. The 
spherical .diagram (see Fig. 2, which has been turned through 90 degrees 
around the normal NP, relative to Fig. 1) shows that if DPE = ki, we have : 

Vi COS 6i = Vi COS X; COS <i 


and the shock loss is, 


Vi 2 sin 2 Oi 

2? ‘ 


I have endeavoured to test the above theories experimentally. The difficul¬ 
ties are very great, and the results were by no means concordant. In every 
case, however, I was able to assure myself that a loss of the order of magni¬ 
tude indicated by the theory occurred. Thus, while I believe that the 
numerical rules now given are extremely unreliable, I have no hesitation in 
stating that the theory forms a good basis for design, and that the various 
methods of producing loss by shock which are here indicated should be 
avoided whenever possible. Considering the losses in detail : 

(z) Loss by shock. The usual theory states that: 


Loss = 


v^ sin 2 6 i 


2 g 









VALUES OF SHOCK LOSSES 


867 


Observational results suggest that this value is not attained until S t is at 
least 40 to 50 degrees. 

For smaller values of Si it appears that some water adheres to the vane 
near the point of impact, and this (probably eddying) mass of water forms a 
curved excrescence, so that “ shock ” probably does not occur, the observed loss 
being more of the nature of curve loss. 

The tests carried out on Francis turbines suggest that an average value is ; 

t IT, , Vi 2 sin 2 6 i 

Loss by shock = 0*5 to 07-- 

2 £ 

and it is probable that the coefficient the average value of which is 0*5 to 07 
is really a function of Si, which increases from o, when Si = o, to 1 when 
Si = 45 degrees approximately. 

Tests of Pelton wheels and Francis turbines which receive water over a 
portion of their circumference only indicate that the full value of the theoretical 
loss may occur, but I have never found a case where more than the full value 
was obtained. 

Thus, generally speaking, we can assume that Vi, the observed velocity just 
after entry, is greater than Vi cos Si, but is less than V{. 

(zV) Loss by impact of water on water. 

This is peculiar to closed tubes, and is caused by Vi, not being equal to v\. 

Theoretically, if v\, is greater than Vi, and splashing is prevented, there is 

rjj \2 __ r U^ > 

no loss, but merely a drop of pressure equal to —- 

Similarly, if v'i , is less than Vi, Andres’ experiments lead us to expect that a 
rise of pressure will occur, but that the observed rise will be about 70 to 90 


per cent, of the theoretical value 


2 £- 


I have observed both the rise and fall, but in no case did the observed 
values come within 20 per cent, of the theoretical. 

(zzz) Losses in the vane or tube. 

These are analogous to skin friction and curve losses in fixed pipes. 

Reference is made to Finkle’s (see p. 933), and Eckhart’s (see p. 937) experi¬ 
ments, also to page 888 for Lang’s rules. 

Farmer {Trans, of Canadian Soc. of C.Es. 1897, p. 275) found experiment¬ 
ally that 

J .~ — 0*0266 — 


Vo -Vo 0 * 3 

where A, is the area of the wetted surface of the vane, a is the area of the cross- 

r , Tr Vi-\-V e 
section of the jet, and V 0 = —-—• 

The form of the equation has a certain rather insecure theoretical basis. 
Details are not given, but it is known that the jet used did not greatly exceed 
three-quarters of an inch in diameter, and also that the velocity of the jet did 

not greatly exceed 120 ft. per second. The values thus obtained when - = 6*6, 

range from 0*955 t0 °‘947, and compare so favourably with the experiments of 
Eckart and Finkle that I am inclined to believe that there can have been no loss 
by shock at entry {i.e. the plane was adjusted until Si — o), and that the stream 
cannot have traversed a curved path during its motion on the vane. 








CHAPTER XV 

TURBINES AND CENTRIFUGAL PUMPS 

) 

Turbines. —“Francis Turbines”—“ Pelton Wheels ”—Method of developing the 
theory—Partial turbines—Mathematical methods employed. 

Description of a Francis Turbine. —Guide vanes and crowns—Wheel vanes and 
crowns—Motion of the water—“Flow lines,” or boundaries of partial turbines— 
Arrangement of turbines relative to the turbine house—References—Horizontal and 
vertical turbines—Multiple turbines with two, three, or more wheels on one shaft. 

Notation. —List of symbols—'“ Space ” angles and lengths. 

Theory of the Ideal Turbine.— Losses in the various portions of the water path — 
Pressure at the various sections of the water path—General equation—Expression 
in absolute velocities only—Hydraulic efficiency—Mechanical efficiency. 

Practical Design of Turbines.— Ordinary equations relating to pipe friction are 
probably inapplicable—Values of the individual losses—Methods of reducing these 
losses—Loss by leakage—Allowance for cyrve losses in the wheel—Draft tube 
losses—Loss due to residual velocity—Relation between rj and e—Table—Estima¬ 
tion of e when the loss due to residual velocity is given—Example. 

Preliminary Sketch Design of a Turbiae. — Experimental basis of the fundamental 
equation—Calculation of the losses due to skin friction. 

Determination of the Necessary Proportions and Size of a Turbine.— 
Relation between the head and the angular speed and horse-power of a turbine— 
Classification of turbines by values of C—Gelpke’s eight types—Table—Comments— 
“Specific speed”—Extension of table—Moody’s values—Examples—Variation of 
the head—Modification of the standard types—R 61 e of turbine designers. 

Tabulation of Velocities and Dimensions in the Various Types. —Quantities 
which mainly depend on the speed of the turbine—Dimensions which mainly depend 
' on the horse-power of the turbine—Comments—Estimation of the hydraulic effi¬ 
ciency. 

Number of Guide Vanes and Wheel Vanes .— Table. 

Preliminary Estimation of the Efficiency of a Turbine. —Influence of the 
quantity of water passing through the turbine—Form of the efficiency curve—In¬ 
fluence of the speed of the turbine—Detailed estimation of the losses in the guide 
vanes—Allowance for curvature losses in the wheel. 

Systematic Estimation of the Various Losses. —Losses in the draft tube—Entry 
into the turbine—Losses in the guide passages—Regulation—Length of guide 
vanes. 

Circumstances in the Wheel. —Leakage losses—Entry into the wheel—Determina¬ 
tion of the shock loss by selection of the point of entry—Comments—Passage 
through the wheel—Partial turbines—Initial and final points on the turbine 
boundaries—Determination of the intermediate portions of the boundaries—Kaplan’s 
method—Criticism—Number of partial turbines—Conditions at exit—“Radial 
exit ”—Definitions—Determination of the exit angles—Summary of the exit losses— 
Approximate estimation of r 3 and r 4 . 

Accurate Method of Gelpke. 

Geometry of Wheel Vanes. 

Application to an Existing Turbine .— Practical rules. 

Mechanical Design of Turbines. —End pressures—Balancing piston—Shafts— 
Vanes and crowns—Calculation of thickness of wheel vane—Wheel crowns—Wheel 
boss—Guide vanes—Clearance space—Bearings—Lubrication. 

868 


BUYING OF TURBINES 869 

Methods of Regulation. —Fink’s method—Cylinder gates—Valve regulation— 
Governor specification. 

The Fall Intensified— Herschell’s theory—Comments. 

Pelton and Spoon W heels.—D escription—Methods of regulation—Sphere of 
utility—Size of jet—Practical rules. 

(i) Typical Pelton Wheels.— Dimensions—Ratio of area of jet to area of 

bucket Number of buckets—Direction of jet relative to buckets—Angle of 
impact—Angle of exit. 

(ii) Spoon Wheels. —Description—Dimensions—Direction of jet relative to 

buckets—Number of buckets—Theoretical advantage over the typical Pelton 
wheel Criticism Probable sphere ofutility—Probable value ofthe efficiency 
of Pelton and Spoon wheels. 

Notation. 

Investigation of the Efficiency of a Pelton Wheel.— Finkle’s method— 
Eckart’s values for the energy of the jet—Deviation of the water at various points of 
the jet Impact losses “ Foam and friction ” losses—Loss due to residual or exit vel¬ 
ocity—Final value of the hydraulic efficiency—Eckart’s values of the various losses. 

Centrifugal Pumps. —Theory—Estimation of hydraulic efficiency—Method of as¬ 
certaining the type and preliminary dimensions of a centrifugal pump—Design of 
housing. 

Tosses by Shock .—Design of guide vanes—Practical corrections—Variation of H as Q 
is altered—Values of efficiency—Preliminary rules—Divergences from turbine design. 

Governing of Turbines. 

Water Tower.—General theory—Solution by the method of arithmetical integration— 
Example—Water tower of variable cross-section—Preliminary approximations— 
Harza’s method—Preliminary determination of the size of the water tower—Larner’s 
method. 

Differential Water Tower.—Theory—Johnson’s investigation. 


The treatment of turbines given in this chapter is almost exclusively regarded 
from the point of view of a buyer. The customs of turbine manufacturers 
are referred to on several occasions, and are almost invariably contrasted with 
the results of calculations. It is therefore advisable, once for all, to state 
that I consider that these customs are logical and practically desirable. 
Attention is drawn to these customs, for the very practical reason that 
ignorance or forgetfulness of such matters on the part of the buyer, leads to 
delay and mutual dissatisfaction. I would strongly advise that every 
engineer when inquiring for turbines should obtain the makers’ values for the 
maximum volume of water that the turbine can pass, and also the horse-power 
then developed. Even if the information is not required, the attention paid 
to the subject in the reply will form a very excellent preliminary means of 
discriminating between the agent whose information is derived from a study 
of catalogues, and the trained engineer who can provide valuable practical 
advice, in addition to turbines delivered F.o.B. 

I must at once acknowledge that my methods of investigation are largely 
founded on those laid down by Gelpke ( Turbinen tmd Turbinenanlagen , lately 
translated as Gelpke and van Cleeve, Turbines and Turbine Installations ). 
Either this book or Mead’s ( Water Power Engineering) gives a more complete 
presentation of the subject than exigencies of space permit me to do. 
Indeed, were the turbine designer’s or maker’s the only possible point of view 
this chapter would be incomplete, and in a certain degree misleading. My 
object, however, is to treat the subject from a civil engineer’s point of view, 
which is solely that of a turbine buyer. 

Thus the treatment of page 888 et seq. is intended to fix the main dimen¬ 
sions, and approximate outlines of the turbines required. The accompanying 



CONTROL OF WATER 


870 

hydraulic works can be then designed, and tenders for the turbines invited. 
When the maker’s drawings are obtained, the methods of page 901 et seq. can be 
used to investigate the designs in detail. The relative values of the divergences 
from the generally accepted theories can then be estimated from the theory 
detailed on page 916 et seq. 

Two defects must be carefully borne in mind. No treatment of the 
mechanical, as distinct from the water tower (see p. 944), methods of turbine 
regulation is attempted. A mathematical theory, very closely resembling 
that employed in connection with alternate currents in electrical design, can 
be developed, and I intend to publish the same shortly. In practical applica¬ 
tions, however, the various constants cannot be estimated from the drawings, 
and the makers have not at present realised their commercial value. Thus 
the investigation would form no check on the maker’s guarantees. 

The sketches of this chapter must be regarded mainly as diagrams. I 
have endeavoured to avoid obviously unpractical design, but in practical work, 
the drawings to be useful should be on a large scale (usually natural size). 
Thus, when illustrating principles, it has frequently been necessary to 
exaggerate defects to a degree that should never occur in modern practice. 

The mechanical details of turbine design are not considered. In practice 
the strength and stiffness of the shafts, and the pressures on the bearings and 
footsteps should be calculated. These are usually correct. The minor details 
of nearly all turbines are far less well designed than is usually the case with 
engines or pumps, but I doubt if a civil engineer can with advantage insist on 
alterations, and in practice the best turbine hydraulically is usually also the 
best designed mechanically. 

Turbines. —It is not proposed to enter into the question of the various 
types of turbine that have been employed. Modern turbines, almost without 
exception, fall into the two following classes : 

The inward flow, central discharge turbine, generally known as Francis’ 
turbine (see Sketches Nos. 249 and 250); and the class in which a free jet 
impinges on an open bucket, usually termed a Pelton wheel (see Sketch 
No. 262). If the history of the development of the machine is alone con¬ 
sidered, these names are somewhat misleading. The type of turbine used by 
Francis was a very special form of the far larger class now termed Francis 
turbines, and was probably invented by Boyden, while the theory of the 
machine (as used by engineers) was first developed by Poncelet. Francis’ 
investigations {Lowell Hydraulic Experiments') were, however, the foundation 
of all really practical rules for design, and his methods might, even after more 
than sixty years have elapsed, be generally imitated in reports on turbine 
tests with great advantage ; thus, the use of his name in connection with 
turbines of this class is a well deserved compliment. The term Pelton wheel 
is less justifiable, as it is doubtful whether Pelton had anything other than a 
commercial connection with the development of the class. The term is none 
the less well understood by engineers, and saves repetition. 

The theory of the design of a turbine can be simply expressed if we 
assume that the cross-sections of all the channels traversed by the water are 
very small. This assumption is not correct in practice, and the variations in 
the velocities, both of the water and of the turbine, that actually exist 
complicate the calculations. In order to apply the results of the theory to 
commercial turbines, we are therefore obliged to consider the turbine as split 


GEOMETRICAL CONDITIONS 871 

up into several “partial” turbines, of such a size that the cross-sections of the 
channels can be considered sufficiently small to permit the theory to be applied 
to each partial turbine. Thus, the practical process for the design of a turbine 
leally consists in designing four or five, or more, partial turbines by theoretical 
mles, and then combining these into a practical machine. So also, the 
mathematical testing of the proportions of an existing turbine is effected by 
splitting it up into several partial turbines, and ascertaining how far these 
partial turbines depart from the theoretical rules. This book being intended 
foi the use of civil engineers, the second process is the more important. I 
therefore, pioceed as follows. The theory of an ideal turbine of small cross- 
section is developed, and the methods of selecting the practical type which 
most closely conforms to local conditions are given. I then assume that the 
first diaft design of such a turbine is selected in accordance with practical 
expei ience, and show how this rough design can be split up into partial 
turbines. These are then designed so as to accurately conform to the special 
requirements of the case, according to theoretical rule. 

We can thus obtain the direction and shape of the edges of the guide 
and wheel vanes of the turbine at any point which may be selected. The 
intermediate portions of the vanes are not in any way defined, and the designer 
must form them so as to produce a smooth, continuous passage for the water, 
avoiding any sudden enlargements, or unduly lengthy passages, in order to 
reduce the losses of head that would thus be produced. 

The final form of the vanes therefore largely depends upon the skill of 
the designer, and it may be necessary to depart to a certain extent from the 
theoretical results in order to obtain a well “formed” vane. 

No rules for effecting this adjustment between the claims of theory and 
practical necessities can be given, and in practical work the final design 
depends very largely upon the skill of the moulders, and upon the methods 
used in constructing the turbine. I therefore prefer to consider at length 
the practical methods for ascertaining the degree to which an existing turbine 
conforms to the theoretical rules, and the amount of discrepancy between 
practice and theory which is usually permissible. 

The hydraulic calculations connected with the design of turbines are 
comparatively simple, although the five- or six-fold repetition necessitated 
by the use of partial turbines is tedious. The fact that the motion of the 
water is in three dimensions, however, introduces many geometrical difficulties, 
since very few of the dimensions required in the calculations can be measured 
direct from drawings such as are usually employed by engineers. 

The selection of the best method for dealing with the geometrical problems 
that thus arise has been very carefully investigated. The ordinary methods 
of plane trigonometry, or geometrical diagrams, are insufficient. After many 
trials, I have decided to employ spherical trigonometry exclusively. The 
selection has been made for the following reason. The method of geometrical 
projection from plan and elevation diagrams, is probably clearer, but actual 
trial shows it to be more tedious. Very few civil engineers employ the 
method in ordinary practice; and, judging by my own experience, they 
would require to re-learn a method which had probably been laid aside on 
leaving the Technical College. On the other hand, most civil engineers are 
accustomed to use spherical trigonometry at intervals when dealing with 
surveying problems, and although they may have to recall the methods, it 


CONTROL OF WATER 


872 

is probable that this will entail less labour than would be required if the 
projection method were employed. A skilled draughtsman accustomed to 
the methods of solid projection will, however, find it advisable to employ 
them, and the additional clearness of conception thus gained is very great. 

I am of the opinion that it forms the only satisfactory method for practically 
laying out the forms of a turbine vane, and I not only employ it myself, 
but believe that it is used by all practical turbine designers. The practice 
in vogue some years ago in Technical Schools of making the students design 
and draw turbines as though they were flat machines is probably largely 
responsible for the depraved designs which were then common in England. 

Description of a Francis Turbine. —A Francis turbine in its simplest 
form consists of two portions, the guide crowns, and the turbine wheel (see 
Sketches No. 252, etc.). The guide crowns are two fixed circular rings, usually 
flat and parallel to each other, and the space thus enclosed is cut up by metal 
sheets which are termed guide vanes. The crowns and vanes form a series 
of passages through which the water passes, and their function is to direct 
and guide the motion of the water so as to cause it to arrive at the wheel 
with a definite velocity in a definite direction. 

The turbine wheel consists of two crowns, connected by correctly shaped 
sheets of metal (termed the wheel vanes), and the crown and vanes rotate 
round a fixed axis. 

A typical turbine in which the axis is vertical is shown in Sketch No. 252, 
and it will be noticed that while the guide crowns and vanes are flat pieces 
of metal, the wheel crowns and vanes are curved in a somewhat complicated 
manner, so that if the vertical projection of the motion is considered the 
water enters the wheel in a horizontal direction, and leaves it in an approxi¬ 
mately vertical direction. Similarly, if the horizontal projection is considered, 
the water leaves the guide passages with a motion of rotation round the axis, 
and enters the wheel with a velocity relative to the wheel, which is more or 
less radial, finally quitting the wheel with a velocity relative to the wheel which 
is nearly the reverse of the velocity with which it left the guide vanes, but 
which, when the absolute velocity in space is considered, is practically radial. 

This somewhat complicated deflection of the water causes the water to 
perform work upon the wheel. It will be evident that while the horizontal 
projection of the motion is important in producing work, the whole of the 
vertical deflection is relatively unimportant, and is merely an unfortunate 
necessity due to the fact that the water must get away from the wheel 
somewhere. 

The motion of the water through the guide crowns and wheel is plainly 
in three dimensions, and is extremely complex. 

The lines a x a 8 , AjAg, a\a 8 , etc. (see Sketch No. 249) show the approximate 
projections of the motion of the water on the vertical section, and the dotted 
lines A 1 A 8 , BjB 5 , similarly indicate the approximate projections of the motion 
of the water relative to the wheel vanes (not the absolute motion in space, 
which is a very different matter, when the motion through the wheel is considered, 
and is shown by the chain dotted lines). These projected relative paths 
will hereafter be referred to as flow lines, or partial turbine boundaries (see 
p. 908), and, unless otherwise stated, the term “flow lines” is reserved for 
the projections on the vertical section. When the projections on the horizontal 
section are referred to, the “horizontal flow lines” will be used. From a 


FRANCIS TURBINES 873 

hydraulic point of view, the subsidiary portions of a turbine are the approach 
passages, or mains, and the egress passages. For reasons which will later 
appear, the egress passages usually take the form of a diverging conical 
tube, which is termed the draft tube. 

The anangements adopted in practice are very various. A selection is 
shown in sketch No. 250. 1 his book, however, is mainly concerned with 

the design rathei than with the arrangement of turbines. The works of Gelpke 
(Turbinen und Turbinenanlagen), Wagenbach (. Neuere Turbinenanlagen), and 
Pfarr ( Tin binen) may be consulted with advantage. Thurso ( Modern Turbine 
Practice') gives a less complete presentment in English, but the three German 



Plan l Section of Wheel Vanes 



A 


& 


\ 

v 

\C5 

% 

X 


Relative Fbth 


Guides Wheel DradTube 

Pe!at e k fibs'-■ Vet5along R,R a 


.<1 

v r 

V / 


& 

.d\J 



Jp\ 



wy -— 



Relative fSth 



GuideVanei Wheel ' Draft Tube 

Relative l Rbs ■ Velhslorig B, & 5 


Sketch No. 249.—Motion of Water through a Turbine Wheel. 


books are so excellently illustrated that a knowledge of German is hardly 
essential if facts and suggestions regarding the arrangement of power houses 
and turbines only are wanted, and it is hoped that the problems of design 
are sufficiently dealt with in this book. 

For present purposes we may state as follows (Sketch No. 250):— 

(i) The axis of the turbine may be horizontal (Figs. Nos. 1 and 4), or 
vertical (Figs. Nos. 2 and 3), and the water may reach the guide vanes by an 
open shaft (see Fig. No. 2), or by a closed shaft (see Figs. Nos. 3 and 4), 
or through a spiral housing (see Fig. No. 1). 

(ii) As many as eight separate wheels (i.e. hydraulically considered, eight 
separate turbines) have been fixed on one shaft, so as to produce a machine 
of eight times the power that one wheel would generate (see Fig. 1, Sketch 















CONTROL OF WATER 



Open Cylinder 
rOoiler Plate 


FPrfia! 

Wheel 

Crows 


Cylinder Gate 


Mom 


874 

No. 261). Double and triple turbines (i.e. two and three wheels on one shaft, 
Figs. Nos. 3 and 4) are common, indeed are probably quite as common as 
the simple turbine consisting of one wheel per shaft. 

(iii) While in theoretical discussions the wheel is assumed to receive water 
all round its circumference, cases exist in which the guide crowns and vanes 
extend only over a portion of the circumference of the wheel, so that the 
water enters along say one-half, or one-quarter, or an even smaller fraction, 
of the wheel. Thus, each cell or wheel passage runs empty for a portion of 
the time during which it rotates round the axis. 


Sketch No. 250.—Typical Arrangements of Francis Turbines. 

1. Single horizontal turbine with plate metal spiral casing. 

2. Single vertical American turbine with cylinder gate regulation and partial wheel 
crowns. 

3. Triple vertical turbine. The wheels A and C are provided with leakage holes and 
covers. The wheel B is solid and uncovered, thus the water pressure on this wheel 
partially balances the weight of the turbine. 

4. Double horizontal turbine with bearings in the dry. 

These sketches are founded on actual installations by the firms of Rieter, Sampson, 
Bell, and Escher Wyss, but do not represent the details accurately. 


Tube 

























































NOTATION 


875 


NOTATION 

The various cross-sections of the path of the water through the turbine are 
defined by a suffix notation (see p. 879). 


Suffix o, refers to entry into the guide vanes. 

Suffix 1, refers to exit from the guide vanes. 

Suffix 2, refers to the beginning of entry into the wheel. 

Suffix e, refers to the definite entry section of the wheel vanes, as selected on page 907. 

Suffix 3, refers to the completion of entry into the wheel vanes. 

Suffix 4, refers to exit from the wheel, or entrance into the draft tube. 

In considering partial turbines these points occasionally need to be 
distinguished. In such cases the prefix m , is used for exit from the 
wheel, and k, for entrance into the draft tube (see p. 912). 

Suffix 5, refers to exit from the draft tube. 

Suffix 6, refers to the loss by residual velocity (see p. 883). That is to say, losses after 
the cross-section 5, has been passed. 


SYMBOLS 

The symbols in alphabetical order are as follows : 


A, denotes the nett area in square feet, available for the passage of water, measured 

normal to the direction of V (for A c , see p. 883). 

a, is the width of A, in feet, measured in a plane perpendicular to the axis of the 

turbine. 

b, is the width of A, in feet, measured in a plane through the axis of the turbine. 

B, is the common value of b 0 , b x , b 2 , when these are all equal (see p. 895). 

C, is the type constant of the turbine (see p. 888). 

D, with a suffix, is the double distance in feet, of any point from the axis of the 

turbine. 

D, without suffix (see p. 895). 
d 0 , d lt d 2 , etc. (see p. 910). 

d 4 , is the diameter between crowns of the wheel at exit (see p. 895). 
di, and D m (see p. 886). 

e, is the suffix referring to the point of entry into the turbine wheel (see p. 9°7)- 
d , is the width of the clearance, in feet, between the wheel and its casing (see p. 905). 
e x , is the length of the edge of the turbine vane, in feet, intercepted between two flow 
lines (see p. 917). 

E* (see p. 918). 

/, is the ratio of the nett area A, to the gross area obtained from geometrical calculations, 
when the thickness of vanes, etc. are neglected. 

g, is the acceleration of gravity = 32'2 feet per second per second, in units now used. 

H, is the total head, in feet, under which the turbine works. 

h, is the depth of any point below head water level in feet. 

K, is the symbol referring to the efficiency of the draft tube (see pp. 797 an< 3 9 02 )- 
k, as a prefix, is used to distinguish the point at which entrance into the draft tube 
occurs from a near point on the area of exit from the wheel (see p. 9 12 )* 
k (see p. 912). 


k 2 = (see p. 897). 

V2o-H 

L is the length of the boss by which the wheel is keyed on to the shaft. 

/,’is the length, in feet, of the exit edge of the wheel vane intercepted between two 
consecutive flow lines. 

vi, is a prefix used in distinction to k (see p. 912). 


n 


vi — 


\/H 


(see p. 888). 


m, is also used on page 912, for b m . 





8;6 CONTROL OF WATER 


n. is the number of revolutions which the turbine wheel makes per minute. For n r> 

n s , n e> see page 899. 

N, is the horse-power generated by the turbine. 

o, is the suffix referring to entry into the guide vanes. 

p = jjTT ( see P- 888 )- 


/, with a suffix, is the pressure at any point, in feet of water. 
p , is the number of partial turbines. 

p-wy is the pressure producing leakage between the wheel and its casing (see p. 883). 
p g (see p. 920). 

Q, is the number of cusecs of water passing through the whole turbine. For Q r , Q s > 
Q e , Q m , see page 898. 

Qz, is the number of cusecs of water doing work in the wheel. 
qi, is the leakage between the wheel and its casing. 


2 = 


(see p. 889). 


Q-Q'+? 


r, is the distance of any point from the axis of the turbine. 

r c (see Sketch No. 253). 

s v is the thickness, in feet, of a guide vane. 

^2, is the thickness, in feet, of a wheel vane. 

/, is the distance, in feet, between corresponding points 


on two consecutive 


vanes. 


2irr 

t= - 

z 

u, is the velocity, in feet per second, of any point moving with the turbine wheel. 

v, is the velocity, in feet per second, of the water relative to a point moving with a 

velocity u. For m V 4 , see page 915. 

V is the symbol used to include v, and w , in formulae which apply to either velocity 
(see p. 888). 

w, is the absolute velocity, in feet per second, of the water in space. For m W 4 , 

see page 915. 

x, is a suffix referring to any point in the wheel. 

y, is the prefix referring to a definite partial turbine. 
y 0 ,y c (see Sketch No. 253). 

s 4 , is the number of guide vanes. . ' 

z 2 , is the number of wheel vanes. 


In order to save continual repetition, whenever an angle or length is referred 
to which can only be obtained by considering the three dimensions in space, 
the word “space” is placed in brackets before the word angle, or length. 
Thus, the statement / 3 , is the (space) angle between u, and v, is merely a 
hint that / 3 , cannot be measured directly from the general drawing of the 
turbine, but must be taken from a special diagram, or must be calculated by 
spherical trigonometry. Whereas, if the statement were 0 3 , is the angle 
between u 3 , and v 3 , the angle can be measured from the general drawing, or 
can be calculated by the ordinary rules of plane trigonometry. 

In all the definitions of direction given below, it is assumed that the shaft 
of the turbine is vertical, as shown in the sketches. 


/ 3 , is the angle between the positive directions of v, and u. 

7, is the angle between the direction of u, and the projection of u on the plane of the 
wheel vane (see p. 917). 

5 , is the angle between the positive directions of w, and u. 

e , is the hydraulic efficiency of the turbine. For e r , see page 900. For e max , see page 898. 

£ x , is the angle between the direction of u , and the intersection of a vertical plane through 
the axis and the vane plane (see p. 919). 

77, is the mechanical efficiency oi the turbine. 

0 X , is the angle between the direction of u , and the intersection of a horizontal plane and 
the vane plane. 





GENERAL THEORY 


877 


d, without suffix is used for the impact angle (see p. 866). 

k, is the angle between the projection of ti , on the vane plane, and the intersection of the 
vane plane and a horizontal plane (see p. 919). 

X, is the angle between the line of flow and the intersection of the vane plane and a 
horizontal plane (see p. 919). 

N, the coefficient of discharge of the space between the wheel and its casing. 

/i x (see p. 918). 

v, is the ratio of the losses in the wheel, as calculated for skin friction only, to the same 
losses as obtained experimentally (see p. 901) 

P= l ^ see P ’ 885 ^* 

<y, is a coefficient expressing the ratio of the head lost by shock to the total available head 
(see pp. 908 and 914)- 

r, is a coefficient expressing the ratio of the losses of head by skin friction, etc., to the 
total available head (see p. 879). 

< p , is the angle between the line of flow and the projection of v , on the vane plane (see 

p. 917). 

<f> (see p. 918). 

\p, is the angle between a vertical plane through the exit edge of the wheel vane, and a 
vertical plane through the radius (see p. 918). 

X (see p. 900). 
w (see Sketch No. 253). 

Theory of the Ideal Turbine.— The following theory refers to a 
turbine in which the velocity of the water is supposed to be completely specified 
at each point. Thus, the dimensions of the cross-sections of the turbine, and 
other channels traversed by the water, must, in theory, be indefinitely small in 
comparison with the diameter of the rotating portion of the turbine. In prac¬ 
tice, the relative size of the actual turbine and the ideal channel for which the 
equations are correct, is best illustrated by a study of the equations, and of the 
“ partial ” turbines used in designing work. For the present it is sufficient to 
state that no very great error is introduced so long as the maximum dimension 
of any moving channel does not exceed one-tenth of its mean distance from the 
axis round which it rotates. 

Let us consider a turbine and all its connected channels (see Sketch 
No. 251), which works under a total head of H feet, i.e. let H be the difference 
between the head and tail water levels, so that H includes all losses by friction 
in the pressure main and generation of the velocity in the tail water channel. 

All velocities are measured in feet per second. 

All lengths and areas are measured in feet and square feet. 

All pressures are measured in feet head of water. 

The expression “ relative velocity 55 means the velocity of the water relative 
to that point of the wheel with which the particle of water considered happens 
to coincide at the moment referred to. 

We divide the path of the water passing through an ideal turbine into six 

sections (Sketch No. 251): 

I. From the point where the water enters the case, or masonry housing, of 
the turbine, to the point where it completely enters the guide vanes with a 
velocity w 0i and a pressure fi 0 ; the depth of this point below the head water 
level being h 0 < 

The expression “complete entry” is ambiguous, but for the present we may 
consider that it defines the first cross-section of the water stream that is com¬ 
pletely surrounded by the guide vanes and their housing, so that the area of 
the stream can be determined by actual measurement. The matter is more 



878 CONTROL OF WATER 

completely discussed on page 907, where complete entry into the turbine wheel is 
defined. 

II. From the point defined as above, to the point where the exit from the 
guide vanes begins, with a velocity and a pressure pi, the depth below 
head water level being k v The beginning of exit is defined in the same way 
as the completion of entry. 

III. From this point to the point where the water reaches the first portion 
of the wheel vanes, with an absolute velocity w 2 , a relative velocity v 2 , a 
pressure p 2 , and at a depth /i 2 , below the head water level. 

IV. From this point, until complete entry (as defined for guide vanes 
under I.) into the wheel vanes at a depth /z 3 , below head water level. The 



pressure is now^ 3 , and the absolute velocity in space is w 3 , and the relative 
velocity is v 3 . 

V. From this point to the point of entry into the draft tube, at a depth /z 4 , 
with a pressure p 4 , an absolute velocity and a relative velocity v±. 

VI. From this point, to the point of exit from the draft tube into the tail 
race, at a depth /z s , below the head water level, with a pressure p 5 , and an 
absolute velocity w 5 . 

Strictly speaking, we should divide Section V. into two portions : 

V. From complete entry into the wheel vanes, to complete exit from the 
wheel vanes. 

Va. From complete exit from the wheel vanes, until the last portion of the 
wheel vanes has been left behind and entry into the draft tube at a depth /z 4 , 
etc. occurs. 























































































IDEAL EQUATIONS 


879 


The real reason for not regarding exit from the wheel vanes as an equally 
complex matter with entry into the wheel vanes, is that the losses that occur in 
Section V a. are by no means as important as those that may occur in Section 
IV. Also, unlike those that occur in Section IV., the losses in Section Va. 
will be found to be equally easily investigated when the whole of Section V. is 
considered as a unit. 

If necessary, the equations can be easily written down, and the investigation 
for a partial turbine given on page 912 will suffice to clear up any difficulties 
that arise. 

We also define : 

u 3 , and u±, as the velocity of the wheel vanes at the points defined under 
Sections IV. and V. 

Now, for all these portions, except IV. and V., Bernouilli’s equation 

7 £/‘- 

P ^ Ttt. = constant, holds theoretically (h being positive when measured 

downwards), and this equation corrected for pipe friction, curves, and irregul¬ 
arities in water motion due to sudden enlargements, and shock, is applicable 
to the actual motion. 

For Sections IV. and V., however, the matter is less simple. The question 
is investigated on page 862, and the equations there proved are assumed to 
hold. Reference is also made to that section and page 907 for a discussion 
of the questions concerning complete entry and complete exit. 

It will be noticed that the suffix notation employed in the first of the above 
sections differs from that now used, suffix i being used for entry and suffix e for 
exit. The object is to firmly impress the principle that the points of complete 
entry into, and exit from the wheel, are not fixed, but must be calculated afresh 
whenever the quantity of water passing through the wheel, or the angular 
velocity, are altered. Were this book intended for teaching purposes, a simpler 
and absolutely concordant notation could have been employed. 

In applying the equations to the general theory, it is convenient to express 
the losses by friction in each portion of the motion, not in terms of the velocities 
iv q, 7 v u . . . etc., but as fractions of the total head H. 

We thus get as follows : 

In the first portion we have : 


A+^=^o-r 0 H 

where r 0 H, represents the loss in friction, etc., in the channels up to the point 
represented by the suffix o. 

In the second portion : 

In the third portion : 

p 2 + - 2 - = pi + — +^2-^i- r 2H 
2 g 11 2 g 


In the fourth portion : 


=a+ 




F h 3 — h 2 — t 3 H 







88 o 


CONTROL OF WATER 


In the fifth portion : 




2 .g 

In the sixth portion : 

Ps 


2 g 


w 5 * W A 


2g + 

Adding the first three equations, we get: 
A + 'ttt — ^2 — ( r 0+ 7 ’ 1 +T , 2 )H 



This permits us to calculate the pressure at exit from the guide vanes, when 
w 2 (which can be obtained by measuring the exit area when the quantity of 
water passing through the turbine is given) is known. 

The fourth and fifth equations : 




u 2 


2 _ 


U 


2 g 


^--(r 3 + r 4 )H 


• • • (ii) 


This equation permits us to determine p±, when v 2 , v 4 , u 2 , and u 4 (which 
are determinable by measurement when the angular speed of the turbine and 
the quantity of water passing through it are given) are known. 

Consider the sixth equation : 

p 5 , is plainly the pressure equivalent to the depth below the tail water level, 

uup 

so that h s —p 6 — H, and ——, can be expressed as a fraction of H, say : 

2 g 

9 


Wt 


Thus, A + ^+ H -^4-(*-5+r6) H =o 

z g 

Adding this equation to the last two, and putting, 

i-(r 0 +iq+r 2 +r 3 +r 4 + r 5 + 7 - 6 )==e, we get : 


2 g 


■«H 


:H = 


up —up 


Wp — Wp 


2 g 


n cr 


Vp-Vp 


2 g 


(iii) 


As already stated, the last equation should be considered as fundamental, 
and if the results do not agree with observational data, the points 2, and 4, may 
be considered to be wrongly selected. In practice, if uncertainties as to the 
value of 7-3 and r 4 do not explain the difference, the turbine is not well designed. 
Such a case has actually been observed, and the error appears to have been 
attributable to the fact that the turbine had too few wheel vanes, so that the 
values of v 2i and v 4 , were probably very inaccurate. 

The equation can now be transformed by substituting for v 2 , and z/ 4 , from 
the equations (Sketch No. 252) : 

vp = up + wp — 2U 2 W 2 cos 8 2 
vp = up + Wp — 2u 4 w 4 cos S 4 

We thus get : 

"•fH=« 2 7 t/ 2 COS s 2 - W 4 W 4 COS§ 4 . . . (iv) 

which is the general equation of turbine motion, and has already been proved. 
The fraction e thus arrived at is termed the Hydraulic efficiency of the 












PRACTICAL DESIGN 


881 


turbine. Its relationship to the somewhat smaller fraction 77, the mechanical 
efficiency of the turbine, is discussed on page 884. 

It should also be noticed that the transformation now arrived at is only 
justifiable when no losses by shock occur at entry into or exit from the wheel. 

In actual practice, the equation is usually assumed to hold good when shock 
occurs, the only difference being that the value of e is somewhat diminished in 
order to allow for shock losses. Under these circumstances, the foundation of 
the equation is experimental only. 

Practical Design of Turbines. —While the above equations strictly 
apply only to ideal or partial turbines such as have already been defined, 
it is plain that an equation which will approximately define the motion of 



water in any turbine can be obtained by inserting mean values of the 
velocities u , v, and w. This method enables a preliminary study to be made 
of the various sources of loss which occur in a turbine. 

The values of the various losses TokI, . . . t^H, are dependent upon the 

design of the turbine. 

Theoretically speaking, each coefficient can be calculated by the usual rules 
for loss of head by : 

(a) Skin friction and divergence (see p. 799 )- 

(b) Change in velocity. 

\c) Shock by sudden changes of velocity. 

(d) Curve loss. 

56 































882 


CONTROL, OF WATER 


In a good design losses similar to those in class (c) should not occur, 
and, except in the wheel, losses of class \d) can usually be neglected. 

Our experimental knowledge of the exact values of the coefficients is very 
vague. Consider skin friction ; the available observations mostly refer to 
circular pipes of cast iron, and the velocities do not greatly exceed 7 to 10 feet 
per second. In a turbine the passages are square, or rectangular in section, 
and are usually of very smooth metal, while the velocities may considerably 
exceed 20 feet per second. Thus the calculated values are likely to differ 
from the truth. The calculations, however, are useful, as they afford the 
only means we possess of comparing different designs of turbines, but the 
calculated values of r 0 , etc. r 5 should be considered as giving comparative 
figures only. 

In actual practice, therefore, we may use the figures for clean, cast-iron 
pipes, provided that we do not assume that the values thus obtained are 
anything but relative. Of course, if one design is for a cast-iron turbine, 
rough as cast, and another one is for a turbine of smooth bronze, or carefully 
machined steel, the losses in the more expensive machine must be calculated 
with the coefficients appropriate to smooth pipes, so as to obtain figures 
which will indicate its relative superiority in construction (see pp. 434 and 888). 

The various losses will now be considered separately. 

r 0 H, can be diminished by keeping the velocity in the approach channel 
small. 

The following is the most usual practice : 

The velocity in the approach channel should be equal to, or less than, 
o’1 V 2g"H, for open channels of rectangular section. 

If the channels are carefully proportioned to the quantity of water which 
is transmitted ( i.e . properly constructed spiral housings are provided as in 
Fig. 1, Sketch No. 250), the velocity in the approach channel may be taken as 
high as o‘2o V 2^H, and the connection between the approach channel and 
the housing should be so arranged as to gradually increase this velocity 

to about -y, and the cross-sections of the housing should be accurately 

calculated so as to keep the velocity in the housing the same at all points 
(see p. 939). But in no case should r 0 (when calculated by the ordinary 
rules for losses by skin friction and changes in velocity) exceed 3 per cent. 
If the approach channel, or main, is very long (say several miles), economical 
considerations may require it to be of such a size that the loss of head by 
friction is a large fraction of the total head. In these cases, the nett head 
available at the lower end of the approach channel should be considered as 
equal to H, and the above rule should be followed in determining the losses 
in the turbine casing. Since the velocity in the approach channel will prob¬ 
ably be large, spiral housings should be provided. 

Similarly, ^H, can be decreased by sharpening the outer ends, and 
smoothing the surfaces of the guide vanes, and shaping them so that the 
change from w 0 , to w 1} occurs gradually, and as far as possible uniformly. 
Their number should be kept as small as is consistent with properly guiding 
the water at entry into the wheel, so as to avoid losses by shock (see p. 907). 

t 1} as calculated by the ordinary rules, should not exceed 2'5 per cent. 

t 2 H, should be treated similarly to 7 -jH. 




LEAKAGE THROUGH THE CASING 883 

•» 

Certain losses occur, due to leakage through the clearances between the 
wheel and its casing. 

In preliminary designs it is usual to assume that this leakage loss qi, is 
about 3 to 5 per cent, of the total volume of water passing through the 
turbine. Sketch No. 259 shows rubbing strips, and Sketch No. 260 labyrinth 
packings (see p. 795), arranged so as to diminish the leakage ; as a rule, 
careful fitting of the wheel and the casing is considered sufficient, but in actual 
designs the leakage pressure (see p. 905) should be calculated. An approximate 
value of qi, can be obtained as follows : 

If fi W) be the pressure producing leakage, which is approximately equal to 
ftt—pi (see P- 880), the leakage is represented by : 

qi = HiA c V 2 gp w cusecs, 

where A r , is the total area of the two clearances, and /xi is the coefficient of 
discharge, which depends upon the width of the clearance space, and upon the 
length of the narrow portion of the passage. For approximate calculations /.h 
can be taken as 0*5. 

t., should not exceed 2 per cent, when the entry is shockless. The losses 
due to shock at entry are discussed in detail on page 906. 

7-3H, and t 4 H, should be treated similarly to r x H. 

The actual value of t 3 H, is largely dependent upon the design of the 
wheel vanes, and the loss is probably principally caused by the curvature of 
the passages through the wheel. If this be neglected, and the usual rules for 
skin friction are alone used in calculating r 3 H, it will generally be found that 
To is about i*5 to 2 per cent, in a well designed turbine. The observed values 
of the efficiency of well designed turbines indicate that r 3 is probably some¬ 
where near double the value thus obtained. We may therefore believe that 
when the wheel vanes, and the form of the wheel crowns, are carefully designed, 
T o+ r 4 , should not exceed 4 per cent, provided that the entry into and the 
exit from the turbine occur without shock. When, owing to bad design, or 
to the turbine not running at the proper speed, shock occurs, the loss is 
increased, and the approximate value of the shock loss must be calculated. 
The question is obscure, and the available information is discussed on 
pages 907 and 913. 

t 5 H, depends entirely upon the design of the draft tube, and upon the 
efficiency with which it converts velocity into pressure. 

This question is probably one of the most obscure that exist in turbine 
design, and Andres’ experiments (see p. 799 ) merely serve to show how much 
remains to be discovered. The only lesson that can be drawn from them is 
that the condition of “ radial ” exit, as usually laid down in theoretical investi¬ 
gations (although by no means always adopted in practice), is probably less 
important than was believed to be the case. 

The component of velocity along the axis of the draft tube at entry usually 

varies between o’lV^H, and 0-3 V^H, and r 5 , varies from 2 to 6 per cent, 
according to the value of this velocity, and the length and form of the draft 

tube. 

r H. This loss is evidently dependent upon the velocity w h . As a general 
6 2 

rule, with a vertical draft tube r c H = -p If the draft tube is so arranged that 
w is equal to the velocity of the water in the tail channel, and is in the same 






884 


CONTROL OF WATER 


direction, the loss may be only a small fraction of 


This diminution, how¬ 


ever, is obtained by curving the draft tube, and is therefore attended by an 
increase in r 5 . The general result is that may be taken as about 5 

per cent, on the average. As will be seen later, the assumed value of r 5 +r 6 , or 
of w 4 , forms a starting-point for the preliminary design of the turbine. 

Finally, it must be noted that all these figures depend somewhat upon the 
size of the turbine, as is evident once the fact that they principally represent 
losses by pipe friction is realised. 

Summing up the values of r 0 , etc. r 6 , enumerated above, we get 1—6 = 0*165, 
or 6 = 0*835. 

We term 6 , the hydraulic efficiency of the turbine, and it must be remem¬ 
bered that e, is a function of Q, and n ; but that, unless specially stated, it is 
assumed that e, denotes the value of the efficiency when Q, and n , are so 
adjusted that the efficiency has its greatest value. 

The corresponding maximum mechanical efficiency, as obtained by brake 


tests of the turbine, will be denoted by 77 = 


550 N 
62*5 QH’ 


where N, is the horse¬ 


power given out by the turbine shaft. 

Plainly 77 , is slightly less than the corresponding value of 6, as 77, includes the 
losses by friction of the turbine shaft in its bearings, and also the friction of the 
outer sides of the wheel crowns against the surrounding water, and the power 
expended to produce the automatic regulation, and the forced lubrication of 
the turbine in cases where these are used. 

Thus, we may say that: 77 = 6—0 015 in a large turbine, and that 77 = 6—0*03 
in a small turbine, without forced lubrication, etc. If the power expended in 
such devices is also deducted, Gelpke states that: 


77 = 6—0*02, in a large turbine, and 77 = 6 — 0*04, in a small turbine. 


Thus, Gelpke (ut supra , p. 44), gives for well-designed turbines : 



6 

V 

V 

With Forced Lubrication 
and Automatic Regulation. 

30 HP. turbine . 

100 ,,,,.. 

1000 ,,,,.. 

10000 ,,,,.. 

• 

• 

0*78 

o-8i 

0*84 

0*87 

0*750 

0785 

0*820 

°' 8 55 

0*740 

0*777 

0*813 

0*850 


These values may be employed in preliminary calculations, and an even 
closer approximation may be made in certain cases. The above values of 6, 
are obtained on the assumption that the exit loss (r 5 +r e )H, is 0-04 to o*o5H. 
Now, the exit loss can be easily calculated by measuring the size of the draft 

qjj 2 

tube. Thus, if we find that —differs materially from 0*04, or 0*05H, we may 


at once modify 6 accordingly. 
Thus, suppose we take a 


turbine of 100 horse-power and find that 























EFFICIENCY AND EXIT LOSS 


885 


ivS 


00 7H, the appropriate value of 6, is o'Bi + 0*05 —0*07, say 079 or o'78. 


Similatly, if ^ — o*o2H, it would be fair to assume that 6 = 0*83 to 0*84. 

The fii st turbine is evidently small, cheap, and relatively inefficient ; while 
the second is large, costly, and highly efficient,—indeed, the figure given is 
probably better than could be obtained in practice. 


We may also say that if 6=1 — p — then p = o*Jo, in a large turbine 

where no cost is spared to secure high efficiency ; and p = 0*17 in a small turbine, 

wheie the design is good, but cheapness, rather than efficiency, has been 
aimed at. 


Finally, e, may be made as high as o*88, or even 0*90 (though this figure is 
somewhat doubtful), and may descend as low as 0*73=1—0*17—0*10 (exit loss), 
without the design being in the least discreditable to the makers. 

As an example, the 10,000 horse-power turbines of the Canadian Niagara 
Company may be considered, h or this size 6 = 0*87, hut the value of C (see 
p. 889) is high (2600), so that 6 = 0*84 probably represents the maximum attain¬ 
able at the date of the design. The turbines are erected in a deep pit, dug out 
of the rock, and space is limited ; the draft tube is therefore cylindrical, and 
= w 5 = 21 feet per second. Thus : 


tyy & 

— = 6*9 feet, and H = 134*6 feet 

2 g 

Therefore, r G = o*o52. The draft tube is long, and the friction loss in it is 
approximately o*o3H = r 5 H. 

Now, in a turbine of this size, we might expect that: 

r 5+ r r, =: 0‘oij or 0*02. 

Thus, the small size of the draft tube causes a decrease of 6 per cent, in the 
efficiency, and for this particular turbine we find that : 


6 = 0*84 —0*06 = 0*78, say. 

Experimentally, van Cleve ( Trans. Ain. Soc. of C.E., vol. 62, p. 199), found 
that ?; = 0*727, or probably 6 = 0757. 

The difference 0*023 is explained by the fact that the draft tube is curved, 
and the loss actually observed at and near this curve amounted to o*o29H. 

The design is therefore very excellently adapted to the circumstances, and 
although the nett efficiency is low, it is probable that 0*84 could be obtained 
with these turbines if space could be found for a straight and well-proportioned 
draft tube of a size sufficient to reduce tv 5 , to 8 or 10 feet per second. 

Preliminary Sketch Design of a Turbine. —Assume that he 
velocities w x , w 4 , v 2 , v 4 , zz 2 , and zz 4 , are the same for all portions of the 
cross-sections of the turbine passages denoted by the suffixes 1, 2, and 4. 
This amounts to selecting average values of D 2 , D 4 , etc., and calculating 
average values of the angles / 3 2 , / 3 4 , etc. 


Then, w 4 sin S 4 D m 7r^ 4 


— =Q. 
a 4 -\-s 4 


Now, for a first approximation, 


§ 4 = 90 degrees, and 


J*±_ 

# 4 T s 4 


1 

i*r 




886 


CONTROL OF WATER 


Thus, w 4 — ^ where D m , is a mean value of the diameter at exit, say 

7rD m <? 4 

approximately ^4D m =D 4 2 -^ !i (see Sketch No. 252), and, since the exit is 
assumed to be radial, the velocity triangle at exit gives : 


7 T 


13 mil 


tan 0 4 =-*, where u 4 = , 

u 4 60 


and the negative sign indicates that / 3 4 is greater than 90 degrees. 
Also, ^eH = 'W> 2 .U 2 cos h 2 —W 4 U 4 cos §4. 

Since the exit from the wheel is radial, cos 8 A — o. 

So that, geW=w 2 u 2 cos § 2 . 

Also, the velocity triangle at entry gives : 

w 2 _ V2 _ u 2 

sin/ 3 2 sin S 2 sin(# 2 — 6' 2 ) 

/ TT / tan S 2 \ ttD^i 

“* = V **H 9-^) = -go- 


Also, iv0 — ivi — 7 V 2 approximately. 

We can thus determine the mean velocities and the size of the turbine, if 
we assume values for / 3 2 and S 2 , and the ratio 


w 4 

V ig\\ 


The method is logical, since the ratio — — is a fairly accurate measure 

V 2^H 

o 

of the cost and efficiency of the turbine, while the angles / 3 2 and § 2 (or f 3 4 ) 
define the general lay out of the wheel and guide vanes. 

In practice, however, it is easier to determine the type and appropriate 
size of the turbine as shown on page 894, and to use the values of I) 2 , D 4 , and 
of / 3 2 and S 2 , which are there tabulated, in order to sketch out the rough 
design. The above equations can then be employed to discover the effect of 
any slight alterations which may be considered necessary. Having thus 
determined the modified values of the velocities, we can estimate the various 
losses by skin friction, and ascertain whether the small alterations are likely 
to cause the efficiency to differ materially from the desired value. Sketch No. 
252 shows how the velocity diagrams form a check on the vane outlines. These 
are correct near Q, but require modification near R if radial exit is essential. 
The diagrams are drawn with allowance for the varying directions of the 
velocity u produced by the wheel vane not being radial. In practice, errors 
are minimised by taking the direction of u, the same in all diagrams. 

When applied to turbines belonging to Type VIII. to V. (see p. 889), this 
average method produces results which are cjuite sufficiently accurate to form 
a basis for preliminary estimates. 

For turbines belonging to Types IV. to I., however, the results are less 
accurate, and it is usually advisable (even in preliminary work) to consider 
the turbine as made up of two partial turbines, and to apply the above 
equations separately to each turbine, as is done in the Sketch. In practice, 
the mid path method illustrated in Sketch No. 249, is probably preferable to 
considering the extreme outlines of the vanes (PiQ and P 2 R) as is done in 
sketch No. 252. 

Experimental Basis of the Fundamental Equation .— It is evident that we 














CHARACTERISTIC EQC/ATIOJV 887 

can, with a certain degree of accuracy, calculate each of the quantities 
r 0 H . . . t 6 H, in terms of za’s, or Rs. These can be expressed in terms of Q, 
the quantity of water passing through the turbine ; and u 2 , and can be 
expressed in terms of the number of revolutions of the turbine. Hence, 
equation No. (iii) page 880 can be transformed into : 


2^H = AQ2 + B;zQ+C72 2 

where A, B, and C, are expressions depending upon the areas of the turbine 
passages at the various points where the velocities are measured, the angles 
the vanes make with the radii, and the various experimental coefficients for 
pipe friction, curve resistance, and shock losses. 

We can also investigate the matter experimentally by measuring a series 
of simultaneous values of Q, ;z, and H (where it is plain that the turbine must 
not be regulated in any way during the observations, as otherwise the areas 

A 0 , and A l5 where 7e/ 0 = ^-, wi=zr- will be altered). We can then determine, 

A 0 Aj 

by the method of mean squares, an equation : 

2£-H = aQ 2 + bQ;z + c?2 2 

and can ascertain how closely this represents the actual observations. 

The values of a, A ; b, B ; c, C ; can also be compared, and thus the 
agreement between theory and observation can be tested. 

When this work is performed it will usually be found that the experimental 
and theoretical values agree fairly well, although there is a certain amount of 
evidence to indicate that the experimental relation includes a term in n . That 
is to say ; 

2g'H=a. 1 Q 2 +b 1 Qn+c 1 n 2 +d 1 M 

In view of the fact that the losses due to skin friction are probably more 
closely expressed by : 

>&/=kV 2 + lV or, hf— mV 1,8 , than by the formula hf= n^V 2 ; 

this is not very surprising, and it may be very fairly inferred that when 
the experimental coefficients for losses by friction and curvature are better 
known, the agreement between theory and experiment will become even 
closer. 

We may therefore consider ourselves justified in assuming that the 
general equation of turbine motion as given by the equation : 


H = Ill'll) % COS §2“ ^4 W 4 COS ^4 


can always be transformed by the substitution indicated on page 880. 
the equation : 


Thus, 






2 cr 


, W 2 2 — W4 2 , v 4 2 — v 2 2 

-1--I-r 


*g 


2 g 


and the other forms employed on page 880 can be regarded as sufficiently 
accurate for practical calculations even when shock occurs at entry to, or exit 
from the wheel, provided the value of e is modified to allow for these losses. 
The differences between theoretical and experimental results which are some¬ 
times observed may therefore be attributed rather to an improper selection 
of the points represented by 2, and 4, than to any defect in the mathematical 
reasoning. 





888 


CONTROL OF WATER 


Calculation of the Skin Friction Losses .—In calculating the losses by skin 
friction in guide and wheel vane passages of turbines, it is advisable to 
remember that the velocities are large. The only formula founded on experi¬ 
ments which include velocities of the magnitude occurring in turbine passages 
is that given by Lang (see Hiitte, vol. i, p. 271). 

This formula when transformed to English measure gives : 


hf— 



o 0059 
VVd 


r 8* 


where r, is the hydraulic mean radius, and d, is the diameter of the pipe, and 1 
its length in feet. V, is the velocity in feet per second, and in moving passages 
V = z/, while in fixed passages V = w. 

For smooth pipes a = o'oi2. For clean cast iron a = o'02o. 

c IV 2 

For smooth turbine passages, we can take hf=r> -• 

r & J 8 ioooor 


IV 2 

for cast-iron passages, we can take hf= -. 

The figures are approximate, and probably lead to results which are some¬ 
what in excess of the truth. 

The Determination of the Necessary Proportions and Size of 
A Turbine. —The difficulties underlying the design of a satisfactory turbine 
are entirely due to practical necessities. The problem of designing a turbine 
so as to utilise the energy of falling water with a very high degree of efficiency 
is a simple one, provided that the proportions of the turbine are so selected 
that the quantity of water and the speed of rotation are related so as to produce 
a type of machine which favours high efficiency. 

It is plain that such a machine will not, as a general rule, be a good practical 
solution of the problem of the generation of power from falling water. 

The cost of the turbines in a modern power station is but a small fraction 
of the total investment, and it is only, so to say, accidentally that the conditions 
are such as to permit turbines of this favourable type to be installed. 

To state the problem more precisely. 

Let H, be the fall available in feet, and assume that the general conditions 
are such that a turbine of a horse-power represented by N, running at zz, revolu¬ 
tions per minute, is required. 


Put m = 

VH 


and P = 


N 

Hi' 5 ’ 


and C = ?/z 2 P = 


n 2 N 

H 2 ' 5 * 


Then, a Francis, or inward flow turbine, can be designed so that; 

C=ioo to 4900, roughly speaking (the exact limits and the possibility of 
their increase or diminution will be discussed later on), and for the most 
favourable type referred to above, C = qoo to 900. While for Pelton wheels, C, 
should not exceed 60. 

These figures refer to Francis turbines with one wheel, or to Pelton wheels 
with one nozzle only, and it is evident that if two wheels per shaft, or two 
nozzles per wheel, be used, the horse-power (and therefore also C) is doubled. 
So also, if the turbine receives water over only a part of the circumference, C, 
is proportionately modified. 

Nevertheless, the possibilities of turbines are by no means limitless, and at 










GELPKE S STANDARDS 


889 

the present date skill in design is mainly shown by a careful selection of the 
type which is best adapted to the actual conditions. The proportions of the 
various types are now (thanks to the very careful series of designs published by 
Gelpke in his work, Turbine?i und Tiirbinenanlageri) well established. 

The principles underlying the selection of the appropriate type of turbine 
are probably more important to civil engineers than the actual design of a 
turbine. At the present date the design and construction of a turbine are matters 
which concern specialists attached to manufacturing firms, and the work of 
hydraulic engineers is mainly confined to designing the general arrangement 
of the power station, so as to permit the turbines to obtain the best results. 

Confining our attention to Francis turbines, Gelpke (who was Escher Wyss’ 
designer until about 1905), has laid down eight standard types, and the 
information given permits us to determine the following table : 


1 

Type 

1/1D 

<1 

LF 

0^ 

>—• • 

II 

0 

00 

p 

C = ;« 2 P 

Jc 

Approximate 
Maximum 
Value of 77. 

VIII . 

77 

0*222 

0*020 

118 

10*8 

0*83 

VII . 

80 

0*302 

0*027 

173 

1 3 ' 1 

0*84 

VI . 

83 

°‘ 44 I 

0*040 

276 

16*6 

0*845 

V . 

89 

0*685 

0*062 

491 

22*2 

o*86 

IV . 

96 

1*03 

0*094 

866 

29*4 

0*87 

Ill . 

107 

i‘ 5 8 

°* I 44 

1649 

40*6 

0*87 

II . 

121 

2*23 

0*203 

2972 

54*5 

0*83 

I . 

138 

2*87 

0*260 

495 1 

70*4 

0*77 


The symbols are as follows : 
m — ~~- P = tts- k , where H, is measured in feet. 

Vh’ h 1 * 5 ’ 5 

D, is the overall diameter of the turbine wheel, measured in feet, i.c. D = D 2 
approximately. 

Q, is the number of cusecs passing the wheel when N horse-power is 
developed under a head of H feet. 



T1-. sa».j 

The entries in Column 4 are purposely somewhat inaccurate. 

11 Q 

quantities fixed by the design of the turbine are in — ^7^ and q— ^rg- 


The 


The commercial requirements generally determine the values of n, and N, 
the speed and the horse-power of the turbine. Thus, we must assume a relation 
between N, and Q, or between P, and q , i.e. the value of rj must be assumed. 
Column 4 is calculated on the assumption that rj = o*8o. 

Reference to Column 7 will, however, show that better values of rj can be 






























CONTROL OF WATER 


890 

attained for all types except No. VIII. In the final calculations this must be 
allowed for ; and in large turbines under favourable circumstances, the value of 
D, may be reduced by 5, or even by 10 per cent. 

The practical application of the table is obvious. 

Calculate P (and if double or triple turbines are used, P, is the value 
corresponding to one wheel only), and C. 

The value of C, fixes the type of the turbine, and then from the figures in 
Columns II. and IV. the diameter of the turbine can be calculated. As a 
general rule, the two values of D thus obtained do not agree. Thus, a typical 
turbine running at the given speed will develop less, or more, power than is 
required. Hence, the practical requirements must determine whether a 
typical turbine of approximately the required speed and power can be utilised, 
or whether a special non-typical turbine must be designed. The matter will 
be considered in detail later on (see p. 892). 

The values of VC, are tabulated in Column 6, as this quantity is frequently 
used by designers under the somewhat misleading description of “ specific 
speed.” It may be noted that */C, in metric measurement, is equal to 
4*45 x y'C, expressed in English measure. A similar series of types is given by 
Kaplan {Ban Rationeller Francisturbinen Laufrader). 

The classification of turbines by values of C, may be somewhat extended. 
Thus, according to Graf and Thomas (Ztschr. D.I. V., June 29, 1907) : 

Values of C, from o, to 32, indicate that Pelton wheels are advisable, and 
their best mechanical efficiency is about 0*83 to 0*85. 

Between C = 32, and C = 6i, turbines with free deviation are indicated, and 
77 = 0*80. 

From 61 to 5800, typical Francis turbines are used. 

The appropriate values of 77, are those given in the above table, the extreme 
values being : 

C = 61 77 = 0*82 

C = 58 oo 77 = 0*67 

These values do not indicate the extreme possible values of C, as of late 
years such designs as those of Wagenbach, Moody, and Larner have greatly 
extended the possible range. The information is tabulated by Moody {Trans. 
Am. Soc. of C.E. , vol. 66, p. 306, et seq.), and the following shows the present 
possibilities both in American and German work : 


c 

V 

C 

V 

C 

V 

45 

o*88 

2000 

o' 9 i 5 

6100 

o*86 

250 

0*90 

3 r 5 ° 

0*905 

7100 

0*85 

5 °° 

°’ 9 I 5 

3400 

0*90 

8100 

0*83 

1100 

0*92 

4500 

o*88 


... 


These values of 77 are maxima, and are not likely to be attained at present, 
except with very well designed and well constructed turbines under the most 
favourable circumstances. 

Returning to the table (p. 889). In view of the cheapness of the turbine in 























VARIABLE HEAD 891 

compaiison with the rest of the machinery installed, it will usually be found that 
N, and 72 , are fairly well indicated by a consideration of the usual speed of the 
dynamo, or of whatever other machinery it is proposed to drive. The table, 
howevei, at once permits us to determine whether a turbine can be designed to 
drive the dynamo directly, and also what horse-power this turbine can give. 

As an example, consider the following conditions : 

H = 50 feet, 72 = 300 revolutions per minute, and 500 horse-power per wheel 
is required. 


Thus, m — 


300 

Vh 


300 

7-07 


5 


P = 


5oo 5°° 

H 1 ' 5 354 4 


Thus, C-42'5 l 'x 1-41=2550, or a type intermediate between II. and III. is 
indicated. 

If Type II. be selected, it is found that a turbine 2*85 feet in diameter will 
run at 300 revolutions per minute, and will develop 580 horse-power. A turbine 
2*63 feet in diameter will develop 500 horse-power, and will run at 325 revolutions 
per minute. The first solution is probably that which is best adapted to practical 
requirements, and, unless these are very exacting, a stock turbine of this type 
and 2 feet 9 inches in diameter, running at slightly less than its theoretical 
speed, can be utilised. 

Next, consider the same requirements of power and speed, but with 
H =40 feet. 

We get, 7 )i — 47-5 P—1-98 0 = 4480, and it will be found that a 

turbine of Type I. 2*90 feet in diameter, will run at 300 revolutions per minute, 
and will develop nearly 550 horse-power. 

Such a turbine, under a 50-foot head, would normally run at 335 revolutions 
per minute, and would develop : 


o'26o x 2‘9o 2 X 354 = 770 horse-power. 


Thus, if it is desired to develop 500 horse-power continuously, at a speed 
of 300 revolutions, under heads varying from 50 down to 40 feet, the turbine 
described above will satisfy the conditions, and it is plain that the fact that the 
speed is supposed to be kept absolutely constant may entail a certain decrease 
in the efficiency when the head is 50 feet. 

In power plants working under a variable head water usually is least 
abundant when the head is high. Modern turbines are generally so designed 
that the efficiency is greatest when the guide vanes are adjusted so as to pass 
about three-quarters of the quantity of water which the machine could pass 
under the same head when the vanes were fully open. Thus, the turbine 
considered above should be designed in this manner, and would be run as 
follows, so that even when designed as indicated above, the maximum efficiency 
would be slightly less than could be attained by a non-typical turbine. Under 
a 50-foot head, the guide vanes would be opened so as to pass two-thirds of the 
maximum quantity of water (under a 50-foot head), and the shockless entry 
speed would be about 336 revolutions per minute. Under a 40-foot head the 
quantity passed would be about 0-9 of the maximum possible quantity (under a 
40-foot head). These maxima can be calculated from the tabulated figures. 

If the speed is not rigidly fixed at 300 revolutions per minute, a somewhat 




CONTROL OF WATER 


892 


smaller turbine (where D = 275 feet approximately) would develop 500 horse¬ 
power at a 40-foot head, taking its maximum quantity of water. Under a 
50-foot head, the same horse-power would be developed with about 07 of the 
maximum quantity that the turbine could pass, and the shockless entry speed 
would be 350 revolutions per minute. The speed, however, would be about 
318 revolutions per minute under a 40-foot head, and if the turbine were run at 
a slower speed less than 500 horse-power would be generated. 

The losses in efficiency caused by the speed of shockless entry differing from 
the speed at which the turbine is run must not be considered as at all serious. 
The efficiency curve of a well-designed modern turbine is very flat near the 
maximum value, and in the 2'9o-foot turbine the differences would probably be 
well within the errors of observation. In the 275-foot turbine, a diminution of 
2 per cent, in e will probably amply allow for any difference. The diminution 
in power at 40-foot head, however, is serious, and, in cases where the speed is 
of importance, would suffice to cause the rejection of the smaller turbine. 

Summing up, and remembering that for this type e is somewhat less than 
o*8o, it appears that a stock turbine 3 feet in diameter will certainly suffice, and 
that a guarantee from a good firm for a turbine 2 feet 9 inches in diameter 
might be accepted. Also, the starting point for a special design would be found 
by taking the vane angles appropriate to Type I. with a diameter of 2*90 feet, 
and somewhat decreasing the dimension B. Roughly speaking, B, should be 

about o - 9 ^equal to of the value given by the ordinary rules, i.e. 


B=o , 9Xo , 35 x 2'9o = o , 3i5 x 2’9o = o*9i foot. (See Sketch No. 253 and p. 895.) 

The lower boundary will therefore be slightly below the line N n which is 
that adopted for Type II. (in which B = o'3oD); and D 4 , in place of being 


1*23 x 2*90 —3*89 feet, will be about 3*89 sj ^ = 3*61 feet. 


Any further calculations are premature. The leading dimensions are now 
sufficiently closely determined to permit a preliminary value of the efficiency to 
be estimated, and the losses in the draft tube and approach mains must be 
approximately determined before an exact solution can be obtained. It is, 
however, obvious that the final solution cannot differ materially from a turbine 
3 feet in diameter, and approximately 21 inches deep overall, with a draft tube 
about 3 feet 9 inches in diameter at the top. The guide crowns will be about 
8 inches in radial breadth, and the total space occupied need not exceed 
3 feet 9 inches+ 2 x 8 + 2 x 12 inches = 6 feet 4 inches in diameter, although a 
slightly better efficiency can be obtained by increasing the last dimension to 
14, or even 18 inches. 

The circumstances assumed in this example illustrate the usual manner in 
which the problem of the selection of a type arises. They are in one sense 
peculiar. The appropriate type closely resembles Type I. It is practically 
impossible to design a turbine to revolve at a speed greater than that attained 
by this type. Thus, in the design of the special turbine, the angles and other 
quantities dependent on the speed of rotation were those appropriate to Type I. 
If, however, the value of C, were such as to indicate that the special turbine was 
intermediate between say Types III. and IV., it will be plain that the range of 
choice open is somewhat greater. The special design can then be selected from 
among the following alternatives. 



DESIGN OF HYDRAULIC WORKS 893 

(a) The turbine possesses the diameter, angles, and speed characteristics of 
a turbine belonging to Type III, with the required speed, but B, is adjusted so 
that the requisite horse-power is developed. 

(<^) The diameter and dimensions are those of a turbine belonging to 
Type IV. which develops the required horse-power, and the vane angles are 
adjusted to produce the required speed. 

( c ) Neither the dimensions nor the vane angles are typical, but each is 
adjusted so as to pioduce the required speed and horse-power. The latitude 
of choice thus obtained is so great that special designs are but rarely absolutely 
necessary, except under low and variable heads. The circumstances requiring 
special designs are fairly obvious. The average head should be considered, 
and if the lequired speed and horse-power can be attained with a machine 
belonging to any type except Type I. the head must be more variable than is 
usually the case before a special design is required. 

Unfortunately, high head water powers are now not frequently developed, 
as the available sites are already occupied, and the problem is usually of the 
character already discussed. Thus, the design of Type I. and Type II. and 
intermediate machines is really the most important problem. 

The above discussion should suffice to indicate the difficulties which arise, 
and the necessity for the services of designers who are specialists on the subject. 
The hydraulic engineer can, how r ever, greatly assist or hamper their endeavours. 
The following principles may be laid down : 

(a) Large and well-formed draft tubes should be provided. This is not 
usually difficult. A draft tube is a space which is not filled with concrete, or 
masonry, and is consequently not costly. 

(b) The head being small, the pressure main should, if possible, be an open 
shaft. Spiral housings and similar devices are costly, and should be avoided. 

Thus, the hydraulic engineer will be well advised to procure from the 
turbine makers the following machinery only : 

(i) The turbine wheel, shaft and bearings. 

(ii) The guide crowns and vanes. 

(iii) The regulating apparatus. 

If the turbine makers also supply steel casings, pressure mains, or curved 
metal draft tubes, it may usually be inferred (high head developments and 
abnormal conditions being excluded) that the general design of the hydraulic 
works is not that which is best adapted to secure a highly efficient utilisation of 
the water power. 

Tabulation of Dimensions and Velocities in the Various Types. 
—The type of the turbine being selected, and the overall diameter D having- 
been determined, the following tables permit the leading dimensions of Gelpke’s 
types to be stated. So far as my experience goes these dimensions are very 
closely adhered to by all first class designers, and a tenderer who proposes 
relative dimensions (taking D as unit) which materially differ should be prepared 
to justify his figures either by local conditions or reference to independent 
experiments. A value of D, much less than the calculated value is (in Types I. 
to III.) suspicious, a greater value of D, is less material but requires investiga¬ 
tion, though, since it is usually accompanied by a higher price, the case is not 
very important. 

Quantities which depend mainly on the Speed of the Turbine .—The following 
table gives the values of the various velocities and the angles / 3 1 and / 3 2 (so far 


CONTROL OF WATER 


894 

as these are determined by the construction of the wheel and guide vanes) for 
each type as given by Gelpke ( Turbinen und Turbinenanlageri). 

These values should not be considered as in any way rigidly binding. The 
proportions of a turbine are determined by experience. The conditions of no 
shock at entry, combined with “ radial exit,” theoretically permit all the angles 
and velocities to be rigidly determined when any two have been selected (eg. 
u . 2 , and ftP). In practice, we have to consider not only the conditions under full 
load, but also when the machine is over or underloaded. 

The figures tabulated below compare very well with modern German 
practice, and may be considered as applicable to cases where high efficiency 
is desired, when the turbine utilises a quantity of water which is not greatly 
removed from the maximum quantity which the turbine can pass under the 
given head, and where the turbine is frequently required to develop about three- 
quarters of its maximum horse-power. 

In small pioneer installations, where ample water is always available, and 
where the turbines constantly take the maximum quantity of water that they can 
pass (i.e. develop their full horse-power always), the values of j 3 j tabulated in 
the column headed “ Values for full load ” may be selected when the lowest 
possible cost is desired. As a general rule, under such circumstances manu¬ 
facturers are inclined to advise the installation of turbines of which the catalogued 
“ full load ” is about three-quarters of that which would be calculated by the 
figures given in Table on page 889. A high efficiency is consequently secured with 
turbines of comparatively rough construction. Where the cost of transport is 
not high, this practice proves economical. Under modern conditions, however, 
ample water power (compared with the commercial requirements of the district) 
is only likely to be available in isolated localities where the cost of transport is 
high. Thus, when the cost of transport, as well as the manufacturers’ price, 
is considered, a smaller and accurately constructed (and therefore possibly 
more costly) turbine, which is designed to attain its best efficiency at full load, 
appears to provide a cheaper solution of the problem. 


Type Number. 

c* 

a X 

O c? 

> 

ci 

<0 

G 

• 

in 

ci 

s 

H 

D 

c* 

\X CD - 
-a 

> 

a 

& 

/ 

0 

G ^ 

in 

- 5 -. 

- CJ ^ 

^ “» r \ C 3 

QO. 0 O 

•H 

O ° •— 

wC n 

r-+ 

>1 • 

£ ^ 
c 

T 3 
’-i ci 

O O 

Cl 

Mean value of u 4 

X 

be 

> 

<0 

C 

* in 

3 

I 

X | 

* 

I 

II 

III 

IV 

V 

VI 

VII 

VIII 

°*55 

0-58 

0*62 

0*67 

071 

°'75 

078 

o'8o 

0*90 

079 

070 

o' 6 t. 

0-58 

o *545 

072 

°’ 5°5 

°* 3 2 5 

0*295 

0*25 

0-205 

0-17 

0*14 

O'l 2 

O’l 1 

39 ° 3 o' 

0 t 

32 20 
24 0 50' 

18° 3 o' 

. 0 / 

14 IO 

0 f 

II O 

0 t 

9 0 

8° 10' 

36 ° 30 ' 
29° 30' 

O t 

23 40 

O ° f 

IO O 

O _ / 

13 50 

O f 

10 50 
8° 50' 
8° o' 

138° 

13°° 

11 5 ° 

O 

90 

6 o° 

0 

40 

3 °° 

2 5 ° 

0-79 

0’62 

0-50 

0-42 

0-37 

o ’34 

0-32 

0-3! 

°‘ 3 2 5 

0-295 

0-25 
0*205 
0-17 \ 

0-14 
O'l 2 

■ 

O-II 


Dimensions which depend mainly on the Horse-power of the Turbine. —The 
quantity of water passed by a turbine is approximately expressed by the equation : 

TrBD 2 w 2 sin 8 2 = Q, cusecs. 









































TYPE DIMENSION RATIOS 


895 


In a typical turbine all the factors in this expression except B, are dependent 
upon the speed of rotation. Thus, the quantity of water used by, and therefore 
the horse-power, of the turbine, can only be materially changed by altering B. 
The typical turbines are designed on the assumption that : 

w 2 sin d 2 is approximately equal to w 4 sin d 4 , i.e. constant radial velocity 
(see Sketch No. 249). 

Thus, if the alteration of the entrance area 7 tBD 2 , be accompanied by a 
proportional alteration of the exit area NN (see Sketch No. 253), we arrive at 
a modified turbine developing a slightly different horse-power, but running at 
the same speed as the typical turbine. An example has already been given. 

Subject to the above remarks, the following table gives the geometrical pro¬ 
portions of the turbine wheel for Gelpke’s eight types. These figures deserve 
to be even less rigidly adhered (to by the designer than those already given 
concerning the velocities and the vane angles. 

If the proportions are widely departed from in either direction, the design 
becomes more difficult, and an inexperienced designer may find it impossible 


to attain a high efficiency. 


B d 

The ratios —, and may, however, be varied 


proportionately within fairly wide limits, without introducing any great difficulty. 

The notation needs some consideration. 

D, is the overall diameter of the turbine wheel in feet. For all practical 
purposes, so long as shock calculations (see page 907) are not considered, 
D = D 2 . 

d 4 , is the diameter between the crowns of the turbine wheel at exit, and, as 
shown in Sketch No. 251, is very nearly equal to D 4 , the top diameter of the 
draft tube. 

The area NN, is the area measured normal to the lines of flow, just outside 
the wheel vanes. In the sketch the area appropriate to each type is indicated 
by suffixes. 

As a first approximation we may take = w 4 s ’ n ^4 all along the exit 


from the wheel. 

B, is the dimension usually denoted by <£ 2 , and is also approximately equal 
to b lt and 

The other symbols are shown in Sketch No. 253. 


Type 

B 

D 

d 4 

D 

di 

D 

J Vo 

D 

NN 

D' J 

y c 

D 

r c 

D 

I . 

o ‘35 

1*23 

0-27 

0-24 

1-225 

°’ 3 I 

o ‘475 

II . 

0*30 

no 

o '35 

0’2 2 

1-005 

0*26 

0-44 

Ill . 

0*25 

°*97 

o'qi 

0’20 

0755 

0*2 2 

0*42 

IV . 

0*20 

o-86 

0-46 

ot8 

°' 5 6 5 

• • • 


V . 

o'i6 

075 

0-49 

0-15 

O-44O 

; • • 


VI . 

0-125 

0-70 

o* 5 1 

0-125 

°‘345 

... 


VII . 

O-IO 

0-67 

o ’54 

0*10 

0-270 

• • • 

• • • 

VIII . 

o‘o8 

o '66 

0-56 

o’o8 

0*2 IO 

• • • 

... j 









































CONTROL OF WATER 


896 

The cross-sections shown in Sketch No. 253 are known to produce efficient 
turbines, but they are by no means the only possible forms. In fact, they aie 
those which are appropriate to cases where there is ample space for a draft 
tube. Where this space is limited, the diameter d± (especially in Types I. to 

III.) is often increased far above that given by the tabulated ratios In no 

case, however, should the angle o> exceed 45 degrees. 

Many designers also make the curve of the upper crown tar flatter than is 
indicated here, and, so far as can be judged from Larner’s statements (Trans. 
Am. Soc. of C.E., vol. 66, p. 383), there is some experimental evidence to 
justify this view of the matter. At present, however, the whole matter is 
determined by vague opinion. Certain firms of turbine builders are known to 



Sketch No. 253.—Gelpke’s Eight Type Outlines ( Turbinen , p. 79), and Kaplan’s 

Outline for Types near to I. and II. 


have carried out systematic experiments, and the best form of wheel section for 
any particular case can usually be selected from published drawings, provided 
that the circumstances of exit (i.e. length, flare, and curvature of the draft tube) 
are carefully considered. The wide divergences which at first sight exist be¬ 
tween the practice of German and American firms are in reality quite justified 
if it is remembered that the typical American turbine is a cheaply constructed 
machine, and is therefore larger than the better constructed German article of 
the same “catalogued horse-power.” Owing to this cheapness of construction, 
American turbines are usually less efficient than German ones, although there 
is but little to choose between the best productions of either country. The 
term German in this connection may be extended to include Swiss, Swedish, 
and a few French firms. 

Until lately, turbines of British design could be regarded as not worth 

























































































ESTIMATION OF THE EFFICIENCY 


897 


consideration. At present two or three firms are prepared to supply scientific¬ 
ally designed machines, and, judging by their centrifugal pumps, can justify 
their claims. When high efficiency is desired, good workmanship is of great 
importance. I believe, therefore, that these British firms will soon produce 
evidence that they supply the best possible turbines, as very few machines at 
present in existence can be regarded as of first-class workmanship, according to 
the standards of modern machine shop practice. 

The general outlines of the proposed turbine being thus selected, the final 
design requires a knowledge of the hydraulic efficiency of the machine. 

A rule for roughly estimating this under all circumstances is given on 
page 900. 

Usually we know u 2 , and can express it in the form k 2 1 2gV. 

Then, with all the required accuracy, we find that : 


w»— 


g< H 


k.N 2gYi cos 8 2 


and the quantity of water passing the turbine is given by the equation: 

Q=/ 2 7rD 2 ^2 w 2 sin 8 2 , 


where f 2 , is a factor allowing for the obstruction of the area 7rD 2 £ 2 , by the 
wheel vanes. 

The efficiency under the assumed circumstances can now be investigated, 
and if the value thus obtained does not agree with the assumed value, the 
calculations can be repeated. The labour is not great, as (under the usual 
assumptions) all the losses, except the shock losses a 2 , and <r 4 , are proportional 
to Q 2 . Thus, for example, let e be taken as 075, and, when calculated in 
detail, let the losses be found to be as follows: 

r 0 + etc.+r 6 = o*2O 
( t 2 = o ’ o 6 (t 4 = o , o3. 


So that e, is in reality about 071. Q, has plainly been over-estimated by 
some 3 to 5 per cent. Thus, the partially corrected value of 

r 0 + etc.+r 6 is about o’i8 or o’19. 

Unless the alteration in the values of w 2 , and w 4 , greatly alters cr 2 and cr 4 , 
which can easily be estimated from the velocity diagrams, the true value of f, 
is about 072, or 073, and the quantity of water used is about o’97 of that 

assumed, and the nett horse-power is about - —- —-=0*94 of that assumed. 

0 / 5 

The results are quite as close as is practically required, especially when the 
fact that errors amounting to 10 per cent, of the quantity r 0 + etc. + r 6 , and 20 
per cent, of the quantity o- 2 + 04, are not at all improbable unless the calculations 
are founded on special experiments. 

Number of Guide Vanes and Wheel Vanes. —The number of vanes 
is entirely determined by practical experience. The only binding condition is 
that the number of guide vanes must not be equal to the number of wheel 


vanes. 


57 




CONTROL OF WATER 


898 


Gelpke (ut supra) states as follows: 

For a turbine D, feet in diameter, z u and z 2 , are as follows: 


’ 

D 

’ * ■' 1 

Number of Guide Vanes = x 1 

equal to 
or less than 

20 Degrees 

/3 X between 20 
and 33 Degrees 

& over 33 
Degrees 

Less than 2 feet . 

10 

I 2 

16 

2 feet to 3 feet 

T 2 

16 

20 

3 feet to 4 feet 6 inches 

l6 

20 

24 

4 feet 6 inches to 7 feet 

20 

24 

28 

7 feet to 9 feet 

24 

28 

32 

Over 9 feet 6 inches 

• • • 

3 2 

3 6 


D 

Number of Wheel Vanes = z 3 

( 3 2 equal to 
or less than 
40 Degrees 

& 

about 60 
Degrees 

& 

about 90 
Degrees 

& 

about 115 
Degrees 

& 

about 135 
Degrees 

Less than 2 feet . 

15 to 17 

15 

T 3 

11 

9 

2 feet to 3 feet 

19 „ 21 

!9 

!5 

13 

9 

3 feet to 4 feet 6 inches 

23 » 25 

2 1 

1 7 

15 

11 

4 feet 6 inches to 7 feet 

27 „ 29 

25 

J 9 

15 

11 

7 feet to 9 feet 

3 1 » 33 

29 

23 

17 

13 

About 10 feet 

• • • 

• • • 

25 

x 9 

*3 


These values are not very closely adhered to in practice, and my personal 
opinion is that they may be diminished without detriment. I have not, how¬ 
ever, had much experience of regulation problems, and believe that these form 
the real basis for the determination of the required values. 

Preliminary Estimation of the Efficiency of a Turbine. —In 
practice, turbines are generally so regulated that the angular speed of the 
machine round its axis remains constant under all circumstances. 

Consider a turbine running at a constant speed of 11 , revolutions per minute, 
and suppose that the quantity of water passing is gradually increased from o, 
to Q m , cusecs, where Q m , is the maximum quantity of water which the turbine 
can pass under the given head. 

There are three values of Q, which deserve consideration: 

(i) Q r , the value when the exit from the wheel is “radial” and “shockless,” 
as defined on pages 911 and 913. 

(ii) Qs, the value when the entry into the wheel is shockless. 

(iii) Qe, the value when the greatest value of the hydraulic efficiency, say 
tmaxj is observed. 















































VOLUME FOR MAXIMUM EFFICIENCY 899 

The values Q r , and Q s , can be calculated by the methods given on pages 913, 
and 907. Q e , however, must be obtained by observation. 

In a well designed turbine regulated by Fink’s (or other rotating guide vane) 
method, it will be found that the entry is shockless over a fairly wide range of 
values of Q, say from Q sl , to Q s2 , and Q s , may be defined as the value at which 
entry is shockless when the tips of the wheel vanes are selected as defining the 
point of entry, and the guide vanes are open to their fullest extent. 

As a matter of observation, it can be stated that if Qr=Qs, as above defined, 
then Q e , is very nearly equal to Q r , or Q s , and under these circumstances the 
greatest possible value of e max is obtained, but the values of e fall off somewhat 
rapidly as Q, departs from Q e . Thus, in a turbine where high efficiency at 
one load only, say Qi, is desired, it is advisable to make Q r =Qs=Qi . If, how¬ 
ever, a fairly constant value of e over a wide range of Q, say from Qi, to f Qi, be 
desired, it is found best to design so that Q s —Qi , and Q r = |Q;. 

The maximum] efficiency then never attains quite so high a value as in 
the previous case, but does not diminish so rapidly as the values of Q, depart 
from Q e . The exact figures, of course, greatly depend upon the size of the 
turbine and upon its type, but it may be stated that if 

Q r = Q« = Qi, then we might expect to find that, 
e = «toax = o*84 when Q = Q, = Q e , 
and e = o'75 when Q = |Q;. 

Whereas if Q s — Qi and Qr = fQz, 

then, f = o'8i when Q — Qu 

€ = f.nax = o*83 when Q = |Q;, 
e = o‘8o when Q = |Q?. 

The figures are merely illustrative, and refer to favourable cases ; but they 
serve to indicate the necessity for considering the matter in designing or speci¬ 
fying for turbines. The subject could be entered into more in detail, and in 
some very excellent turbines (and even more frequently in centrifugal pumps) 
practically constant values of e are secured over a very wide range of values of 
Q, by making the entry “shockless” for Q = -*Qr, and the exit shockless at say 
Q = Q e , and the exit radial at say Q = §Qe* 

The methods by which a detailed investigation of the efficiency is obtained 

are discussed later on. 

It will also be plain that if the speed n, be supposed to vary, we could 
investigate the speeds n r , n s , n € , at which radial exit, shockless entry, and the 
best efficiency, occur ; when Q, the quantity of water passing, is constant. The 
practical importance of such results rarely justifies the labour, although the 
question becomes of importance when steam-driven centrifugal pumps are 
considered. 

German stock turbines are usually designed so that, 

Qs=Qm and Qr = |Qm. Hence, Q e , is about fQ«. 

American and French stock turbines are usually designed so that 
Q s =Q r =|Q m , and the horse-power corresponding to JQ m , is that given in cata¬ 
logues. Hence, American turbines can take a markedly greater load than that 
at which they are catalogued ; whereas German turbines cannot. 

Subject to the above remarks, let e be the efficiency of the turbine when 
running at a speed 11, and when passing Q, cusecs of watei. 


900 


CONTROL OF WATER 


We have f = I — (tq + Tj + T 2 + r 3 -l-r 4 + r 5 -}-r 6 -l-cr 4 ). 

Calculate tq+t! by the ordinary rules, and put e+r 0 +r 1 + o- 4 = x. 

When the turbine runs at n\ revolutions, and passes Q', cusecs, the regulat¬ 
ing apparatus (whether hand or automatic in design) moves the guide vanes so 
as to alter 8 , the angle of exit from the guide vanes, and a 0) and a ly the distance 
between two consecutive guide vanes at entry and exit. Let a' 0 , and a\ y be the 

Q' Q' 

new values. Hence, the new value of w 0 , is and w\ = r - 

o^o ^1“ i^i 

Thus, t o and r\ can be calculated, and very approximately : 



and r\ = T i 



If the regulation is effected by a cylinder gate (Sketch No. 250, Fig. 1), then 


w , 0 =(^-)w 0 , and w v ~ 


where b\ y is the new value of b ly and in this case there is also a loss of head 
caused by the sudden decrease of velocity from w 4 to w 2 , which should be 
included in r 2 . 

O , 2 7 T r* 11 

Then v « =—-^-7- and u\ = —can be calculated, and the loss by shock 
z 2 a 2 b 2 60 

at entry can be graphically obtained as indicated on page 907. Let this be </ 2 H. 
So also, (o-' 4 — ct 4 )H, the difference in loss due to residual rotational velocity 
and shock at exit, can be calculated. It cannot be assumed that e was obtained 
when the exit was purely radial, since, as a matter of experiment, the best 
efficiency does not usually occur wdien the exit is radial. 

If shock at entry occurs under the original conditions, a' 2 H, is of course the 
difference between the two shock losses. 

The reasoning is not rigorous, and is probably erroneous if n!, differs greatly 
from n. In practice, however, 11, is usually equal to n , and the formula 

i_ e ' = (i- x ) (^2.^ + t 0 + t x — t 0 — ri + <r' 2 + o-' 4 — <r 4 


can then be proved, under the assumption that all losses (other than shock 
losses) are proportional to the square of the velocities. 

When the matter is tested by actual observation, the results given by the 
formula agree quite as accurately with observations as is necessary for practical 
purposes. 

The chief source of error in the above investigation arises from the fact that 
the actual value of (r 3 +r 4 ) is by no means accurately obtainable by calculations 
of skin friction, owing to the neglect of the effect of the curvature in the wheel 
passages. The following method of allowing for this error has been found 
useful in practice, and is therefore put forward. 

Let us assume that 77 has been observed, and that ( has been calculated by 
allowing for bearing friction, friction of the wheel against dead water, and the 
power consumed in lubrication, etc., as already detailed. 

Let us also calculate : 

{ ' ) % , } , I ’ifitoirvf 

1 ~ei = r 0 + ri+T2 + 7-3 + T4 +r 5 + T 6 + d- 2 Tcr4 

In theory e 1 — e. In practice, a slight difference will be found to exist. This 
may arise from an erroneous assumption of the value of the skin friction losses, 





LOSSES IN THE DRAFT TUBE 901 

but these can usually be ascertained for all portions of the machine, except the 
wheel, from pressure gauge observations. 

We may therefore assume that if c r 3 and c r 4 represent the values of r 3 and r 4 
that actually occur ( i.e . the values corrected for curvature), then : 


cT 3 + c r 4 — To — r 4 = e — e 4 


Thus, c t 3 -\- c t4— *'( t 3+ t 4)j where v is a coefficient which in practice is usually 
about 1*5 to 2. 

It is now fairly obvious that the expression 


1 ~ € ' — T 'o + r 1 + t 2 + v ( T 's+ T \) + T 5 + T 'a + & 2 + #4 


where all the coefficients are obtained by calculation, will probably give a more 
accurate value of e' than that obtained by the preceding method. The method 
is merely suggestive. In a case of actual observation, however, this method 
was applied as soon as the three-quarter load value of e had been obtained, and 
seven predicted values of e' over the range o’4Q m , to Q m , agreed within 0*005 °f 
the observed values, and the errors were well within the errors of observation. 

In this case, six pressure gauges were read to obtain values for the skin 
friction. The pressure gauges had been fixed for some days before the brake 
tests were started, and the departures in r () , r 4 , r 2 and r 5 , r ( . from the law 
^/=m 1 V 2 had been accurately ascertained. 

When the method was applied to cases where the skin friction had not been 
determined experimentally, differences of 0*015 occurred, but these are probably 
explicable by erroneous assumptions concerning the skin friction. 

It will be seen that in practice the process mainly enables the number of 
brake tests to be decreased. 

The first method forms a very excellent check on the makers’ guarantees 
of efficiency, and the consultant’s requirements. A reputable firm’s guarantees 
of efficiency under ordinary loads (say three-quarter, and full load) are usually 
extremely accurate, but if they are asked to predict the efficiency at small 
loads, or at variable speeds, the values stated are frequently found either to be 
impossible, or are obtained by installing a far larger turbine than would other¬ 
wise be required. The last result is unsatisfactory, and the consultant deserves 
most blame when it occurs, since he could avoid this eventuality by demanding 
smaller efficiencies under these abnormal circumstances, after calculating the 
values that can possibly be attained with a turbine which is not too large for 
its work. 

Systematic Estimation of the Various Losses. —The order in which 
the losses are estimated may at first sight appear peculiar. It is that which 
is found most convenient in practical work, as large errors, or departures from 
the specified conditions, can be detected early in the calculations. 

Losses in Draft Tube , r 5 and r, ; . —Let Q, be the total quantity of water 
which passes through the turbine, in cubic feet per second. 

Let H, be the gross available head under which the turbine works. 


The gross area of the upper end of the draft tube is given by - D 4 2 , and the 

nett area is A 4 =_/ 4 D 4 2 , where f 4 , is a coefficient expressing the total fraction 

4 

of the gross area that is not obstructed by the shaft and its bearings. 

In preliminary work we can take .A = 0*97, for cases where the bearings of 


902 


CONTROL OF WATER 


the shaft are outside the draft tube, and = in cases where the shaft 
bearing and supports are inside the draft tube. 


Thus, 



Similarly, — ——— 

/ 5 ^V 

4 ‘ • 

where f 5 , is a coefficient similar to_/ 4 , but which refers to the exit area of the 
draft tube. We thus obtain : 


A-^5-A+^4 = 


Wf-Ws 1 

IT 


(i-K) 


where K, is an allowance for the head lost in friction, and divergence losses 
in the draft tube. We can usually assume that, i — K = o‘8o, but the form 
of the draft tube and its curvature must be considered. If Andres 5 results 
(see p. 799) can be assumed to hold good for large tubes, such as are now 
considered, it would appear that divergence losses may be entirely neglected, 
as there is no doubt that the fact that the water has passed through the turbine 
renders the circumstances extremely favourable. 

Now, / 5 , is plainly equal to jy 5 , the depth of the centre of the exit area of the 
draft tube below the tail water level. 

Thus, y 6 , and (h 6 —// 4 ), the vertical height of the draft tube, being 
measurable, we can determine ; and, as a rule, is less than the atmos¬ 
pheric pressure. 

Also, the exit loss can be expressed in the form ; 

2 

—A-=t 6 H, say (see p. 883), 

and the loss in the sixth section of the turbine is given by the equation : 


K (wl~wj) = H 
2 g 


In preliminary designs it is frequently customary to assume that 


(r 5 + r 6 )H 


_ w 4 - 

~~*g' 


The assumption has a practical advantage, for the value of D 4 fixes (for a 
given type of turbine) all the other dimensions of the turbine within very narrow 


• . . . *W A 

limits. Thus, if we decide to make —^-=o'02H, we obtain a relatively large, 

~g 

but efficient turbine. Whereas, if we go to the other extreme, and make 
wL" 

= o*i2H, we obtain a small and less efficient machine. Thus, the 


2 g 


value of — (“ the wheel exit loss ”) forms a short and concise method of 
~g 

specifying the hydraulic qualities of the turbine. For example, if a designer 
is told that the wheel exit loss should have a value of o*o8H, he is practically 
informed that cost and efficiency should both be considered. Whereas, a wheel 
exit loss equal to o'oqH, or to o^H, is a clear indication that a good efficiency 
rather than cheapness is desired. 











LOSSES IN THE GUIDE PASSAGES 


9°3 


Ejitry into the Turbine , r 0 .—We have now to consider the earlier sections 
of the water path. 

The friction in the approach channel, or pressure main, can be calculated 
by the ordinary rules. If the guide crowns are situated at the bottom of an 
open shaft no other losses occur. If, however, the water enters the casing 
of the turbine at one side, the casing must be shaped into a spiral form in plan 
(Sketch No. 250, Fig. 1), otherwise losses due to change in velocity occur 
similar to those investigated for a centrifugal pump on page 939. The subject 
is not considered in detail, as such losses should not occur in a well designed 
turbine. Any consideration of this question will show that badly shaped, or 
roughly constructed metal casings, are undesirable. Modern practice tends 
towards properly shaped casings of reinforced concrete, forming an integral 
portion of the power house. If metal casings are used, these should be of first 
class workmanship, and Goldmark’s specification for pipes (see p. 459) may be 
studied with advantage. It must, however, be realised that the conditions are 
somewhat more exacting than in steel pipes, as any deformation of the casing 
may produce shocks which will destroy all the gain in efficiency that it is 
desired to attain. The rivets should certainly be countersunk on the inside, 
and stiffeners should be placed wherever requisite. German practice appears 
to employ cast-iron casings exclusively. 

Losses in the Guide Passages , t x and r 2 .—By measurement from the 
drawings we can calculate : 



w x = ■ Q - ,~ (Sketch No. 254). 

Z 1 


s'j, represents the number of guide vane passages which receive water, and 
in a turbine which receives water all round its circumference s lf is equal to the 
number of guide vanes (see p. 898). 

a, denotes the breadth of a passage measured between two consecutive 
vanes perpendicular to the velocity w ; and b , denotes the distance between 
the guide crowns ; so that ab , represents the nett area of a single passage 
measured perpendicular to the direction of w. 

Both a 0i and a lf vary when the guide vanes are moved in order to regulate 
the turbine. (See Sketches Nos. 259, 260.) 

Sketch No. 254 shows the conditions occurring. The velocity at the cross- 
section denoted by A, is w 0 > and at the cross-section denoted by C, is w x . 
The guide vane outlines should be constructed so that the change from w 0 , to 
Wl , occurs gradually, and the form of the passage should resemble that of a jet. 
In the left hand sketch, the links for moving the guide vanes occupy so much 
space that the section at B, is smaller than at A, or C. This should be 
avoided. 

The losses are best estimated as follows : 

{a) Up to A, the circumstances resemble a bell mouth orifice, and the head 

1 • u w » 2 

lost is about o‘Q2 or 003 —-. 

^g 

(S) From A, to C, the usual friction laws hold, dhe foimuke given on 
page 888 may be employed. 

(e) On exit from the guide vanes at C, a certain loss of head may occur by 
sudden expansion, dhe right hand ca^se is favouiable, as the guide vanes end 
in a sharp edge. 




904 


CONTROL OF WATER 


In the left hand case the ends of the guide vanes are blunt. Then 
<w\ — - -= Q --—should be calculated, where D 1? is the diameter measured to the 

1 TrDiBiSinOi 

ID, 2 — H) \ ^ 

ends of the guide vanes, and a loss —— -probably occurs. 

In a well designed turbine, in good order, B = b 1 ^=d 2 . 



Sketch No. 254.—Losses in the Guide Vanes. 


D x , varies when the turbine is regulated, owing to the motion of the 
vanes. The shock losses at exit from the guide vanes, can be expressed by : 

{w x ~w N_ t h 

2 g T2 5 

but this is probably greater than the true value. 

<w\, however, should be used in place of in estimating the circumstances 
at entry into the wheel. 

The calculations concerning this loss are unreliable, and are referred to in 
order to illustrate the importance of regularly examining the condition of the 
guide vanes, and repairing them if blunted by wear or erosion (from sand or 
occluded gases). The sketch shows the possibility of other losses caused by 
bad fitting of the vanes and crowns, or tfie crowns and the wheel. 



































LOSS AT ENTRY INTO WHEEL 


905 

The losses typified by r l H, and r 2 H, are least in Type I., and increase 
rapidly as Type VIII. is approached. 

No definite rules for the length of the guide vanes can be given. Theory 
indicates that a length equal to three or four times the width a 0 , or a u should 
suffice. Four or five times a 0 , or a lf seems to be more usual in practice. 

The case where b 0 , b x , and b 2 , are not equal is not discussed. It occurs 
in turbines regulated by cylinder gates, and in cases where the wheel is 
not properly adjusted relatively to guide crowns. The -loss in efficiency is 
obvious, and can be calculated if desired. 

The values of r 0 , r,, and r 2 can thus be estimated. 

A little consideration will show that while r 0 and are easily calculated 
(when Q, is known) from the readings on pressure gauges screwed into the 
guide crowns near the entry and exit sections, r 2 is not very easily observed. 
Certain tests of my own gave very peculiar results, and, in practice, it appears 
advisable to consider r 2 as included in <t 2 . 

Circumstances in the Wheel. —The design of the rotating portion 
of the turbine must now be considered. When Q, cusecs of water pass out 
through the draft tube, the turbine does not utilise the whole of this quantity, 
as a certain leakage takes place through the spaces between the rotating wheel 
and its casing. 

Let this leakage loss be equal to qi cusecs. Then, if ri, be the radius of 
the rubbing strip between the turbine wheel and its casing, and ei, is the “ play ” 
allowed (Sketch No. 253), we have : 

qi—^nriei /xjV 2 g(p 2 —h 2 -^pi+h^) 
since there are two paths for leakage. 

The value of m can be taken as 0*5 to o*6, and p-2 — h 2 —pi + hi can be 
calculated from equation No. (ii), page 880. 

For preliminary calculations, we may assume that 

2 g(p 2 - h 2 —pi + hi) = 2 g{e - r 5 — t 6 )H - wY> 

The value thus obtained is probably somewhat in excess of the truth ; for if 
the turbine fits its casing closely, the water in the space G, is probably set 
rotating, and thus a more or less efficient centrifugal pump is working against 
the pressure. 

It may therefore be assumed that the leakage through the upper rubbing- 
strips takes place under a pressure equivalent to, 

9 9 

7 U 2 ~ 

P‘ 2 , h 2 pi hi -• 

In the turbine which is now being considered (Sketch No. 253), the leakage 
through the lower space can hardly be supposed to be restricted in this manner, 
but two rubbing strips are shown, so that the formula for a labyrinth packing 
(see p. 795) might be applied. 

The value of p 2 —h 2 can be calculated from equation No. (i) on page 880, but 
the independence of e thus obtained is only apparent. hi~h 2 is plainly the 
difference of level between the top of the draft tube and the rubbing strips ; 
and in accurate calculations the value differs for the two paths of leakage. 

Entry into the Wheel, o- 2 .—In the typical Francis turbine this problem is 
one of two dimensional geometry ; in the case of the cone turbine or in an 
axial turbine, three dimensions must be considered. 




CONTROL OF WATER 


906 


Let z lt be the number of guide vanes. 

Let b u be the height between the guide crowns, and a } , the width between 
two consecutive vanes at exit from the guide vane, measured perpendicular to 
the direction in which the velocity of the water at exit is directed. 

In the modern types of turbine which are regulated by moving the guide 
vanes, a 1} is variable, and in the older and cheaper types which were regulated 
by means of a cylinder gate, b 1 is variable. 


Then, 




Q 

Z-yCl[b\ 


and for preliminary designs we can put : 

z 1 a 1 b 1 — b l (nD 1 sin §1 —^i) 

biTr Di sin Si . , 

= —±—- —- approximately; 

where s lt is the thickness of the guide vanes at exit, and 8 1 is the angle which 
their direction at exit makes with the tangent to a circle of diameter D x ; or 
more accurately, which the direction of the velocity 7£q, makes with this 
tangent. 

Now, let z 2 , a 2 , b 2 , s 2 be similar quantities for the entry into the wheel vanes, 
and put Q — <?i = Qi- 




Then v 2 


Qt 

z 2 ci 2 b 2 


Similarly, in preliminary calculations we may put: 

z 2 u 2 b 2 — b 2 (jr L) 2 sin p 2 —z 2 s 2 ). 


Also, 



7rD 2 ?l 

60 ’ 


where n, is the number of revolutions which the turbine makes per minute. 

Now, set off AB 2 = zz 2 , on an Y convenient scale, and in a direction parallel 
to z/ 2 , and in a direction parallel to v 2 , and AD = w h in a direction 

parallel to w x . 

Thus, the angle AB 2 C 2 = 7t~/3 2 , and the angle B 2 AD = S X . 

Now, if the points D, and C 2 , coincide, the entry is without shock. 

The case is then fairly simple. We need not in practice draw any very 
delicate distinction between the points 2, and 3, and no questions regarding 
the loss of head at entry will be found to arise. 

The numerical conditions are obvious : 


— ~ii 2 2 -\-v 2 2 -\-2u 2 v 2 cos / 3 2 , 

1 . „ . . sin So sin / 3 2 

and = where-- —-. 

v 2 w 2 

The fact that / 3 2 is measured between the positive directions of ic 2) and v 2 , must 
be remembered. 

If, however, as shown in Sketch No. 255, the points C 2 , and D, do not 
coincide, the theoretical “ velocity of shock ” is represented by the line DC 2 , and 
some shock.may occur at entry. The determination of the precise point of 
entry into the turbine now becomes uncertain. Visual study of many glass 
models, and mathematical investigations of recorded experiments, lead me to 
believe that the velocities are spontaneously adjusted as far as is possible, so 







SELECTION OF “ ENTRANCE ” 


907 


that the shock may be minimised. The question can be investigated by con¬ 
sidering the form of the wheel vanes between the point 2, and the point 3, where 
the watei is completely surrounded by the wheel vanes and crowns, and 
ascertaining whether an intermediate point e, can be selected which will render 
the shock less than at the points 2, or 3. 

The matter can be investigated more definitely by calculating 


60 60 ’ 3 Z 2 a z b^ 


and setting off AB 3 — u 3 , and B 3 C 3 = z/ 3 , where the angle AB 3 C 3 = 7r — / 3 3 , and 

AB 3 , represents u z . 

In Sketch No. 255, left-hand figure, the circumstances have been purposely 
selected so that is greater than w 2 , or Thus, whatever point intermediate 
between 2, and 3, be selected as the point of entry, some shock occurs, and the 


z, Guide lanes 





Sketch No. 255.—Shock at Wheel Entry. 


minimum shock is represented by DC 2 . These circumstances indicate that the 
design is bad as regards shock at entry. 

Sketch No. 255, right-hand figure, however, shows a more favourable case, 
where D lies between C 2 and C 3 , so that we can select a point <?, say, between 
2, and 3, where the velocities u e , and v e , would compound into a resultant w e , 
which very nearly coincides with AD. The shock velocity DC e , is now far 
smaller than : 

DC 2 , which corresponds to the point 2, as “ point of entry,” or DC 3 , which 
corresponds to the point 3, as “ point of entry.” 

The circumstances at the point e , and the velocity diagram thus determined, 
are believed to most nearly represent the actual occurrences at entry into 
the wheel. 

We may now assume that there is a loss of head represented by 














9 o8 control of water 

The matter is best investigated geometrically, as has already been indicated, 
but if desired, the formula : 

D Ce 2 = W 2 + TV? — 27V l W e COS (/ 3 j — b c ) = TV 2 

may be used, and we find that : 


the head lost by shock = <r 2 H 


TV, 


?g 


If our knowledge of the experimental coefficients determining the values of 
the various loses of head were sufficiently precise, it would now be advisable to 
regard the point denoted by suffix e , as being the point 2, in equation page 880, 
and we should then regard the motion from the guide vanes to the wheel vanes 
as from 1, to e (2 or 3), and then from e, to the point denoted by 4. In practice, 
the refinement is unnecessary ; and, as will be noticed, the distinction drawn 
between the points 2, and 3, is referred to in this connection only. Hereafter, 
the suffix 2, is employed without distinction for all points at entry into the 
wheel. 

The distinction, however, may be advantageously adopted when investi¬ 
gating cases where the turbine is required to run under variable heads, or to 
develop a power which differs greatly from that which was assumed when its 
proportions were calculated. 

The value ofcan then be taken as constant, but a lt and ( 3 1 or will vary 
owing to the different positions assumed by the guide vanes during regulation. 
Thus, varies, and in consequence the point e, which is that selected as 2, 
will also vary. The theoretical loss of head at entry under any circumstances 
can be calculated. 

In view of the uncertainties as to the exact values'of the various coefficients, 
any numerical investigation except for the normal conditions {i.e. the speed n, 
and the volume Q, so adjusted as to secure entry without shock) seems 
unnecessary ; but there is no doubt that when comparing proposed designs we 
may assume that the turbine in which the shock loss is, on the average, least is 
that which is best adapted to secure high efficiency under the various conditions 
of regulation considered. 

The precise commercial value of the properties investigated above is 
doubtful. As an expression of personal opinion only, I am inclined to consider 
that good workmanship and solid construction are far more important. In 
practice, however, good design and workmanship as a rule occur together, so 
that the selection of a turbine is not usually complicated by such considerations. 

Passage through the Wheel , r 3 and r 4 . —The division of the turbine wheel 
into a series of partial turbines has now to be considered. The assumptions 
upon which the process is founded are somewhat flimsy. Such experiments as 
have been made indicate that the velocities of the water in turbine wheels differ 
materially from those obtained by the methods at present adopted. The 
justification for the assumptions therefore lies in the fact that turbines designed 
in this manner are highly efficient. The principles may consequently be 
considered to be correct, and when sufficient experimental data are available 
the details can be modified in the manner indicated on page 910, so as to secure 
additional accuracy. A well-designed turbine is already so efficient that it is 
open to doubt whether any great practical advantage can thus be secured. The 
present method of turbine calculation is probably quite as close to physical 
truth as are any other engineering calculations. Additional experimental data 


PARTIAL TURBINES 909 

rather than more refined mathematical methods form the real needs of the 
designers of turbines. 

The piactical difficulty is that each designer appears to have his own 
particulai method of determining the flow lines which bound the partial 
turbines, and by actual trial I have found that it is consequently possible to 
somewhat under-estimate the qualities of a proposed design by using a method 
which diffeis fiom that employed by its designer. A reference to Sketch No. 
256, which shows partial turbines as laid out by the methods employed by 
Gelpke and Kaplan, will illustrate this point. It is fairly evident that the forms 
of the wheel boundaries AT, and CS, have been materially influenced by the 
diffeience in method, and that if a turbine is scientifically designed, it is not 
very easy to draw by any sound method satisfactory partial turbines which 
materially differ from those obtained if the designer’s own methods were used. 

Gelpke s method is as follows : describe a circle to touch the crown sections 



Sketch No. 256. — Gelpke’s and Kaplan’s Methods of Drawing Partial Turbines. 


at Nj and N'j and sketch in the line N 1 N' 1 which is perpendicular to both 
crowns. Now take P 2 , so that 

r ] N' 1 P 2 = r 2 N 1 P 2 

Then P 2 is a point on the middle flow line P 2 Q 2 . Similarly we can select 
P, and P 3 and determine corresponding points on the lines N 2 N' 2 and N 3 N' 3 . 
Thus 3 or 7 flow lines and 4 or 8 partial turbines can be sketched out. The 
process has no foundation in theoretical hydrodynamics, and plainly amounts 
to making the areas of the partial turbines equal at each level line NN'. Since 
Gelpke distinctly states that his method is a preliminary one, it appears equally 
logical and less laborious to adopt Kaplan’s method, which consists in taking 
AC, the entry to the wheel, as a level line and dividing it into equal parts 
CPu P1P2) and P 5 A. fhe top of the draft tube SQjQ 2 , etc., is also taken as a 
level line and divided at Q j, Q 2 , so that 

l^QlQ2 = 2^Q2Q3 = etC. 

thus producing equal areas at the top of the draft tube. 




















CONTROL OF WATER 


910 

Nearly all designers assume that the velocities of the water are uniform both 
across the wheel entry and across the entry into the draft tube. 

Thus, (Sketch No. 257) divide up the wheel height b 2 , into say four equal 
parts AP l5 P 1 P 2 , etc., and split up the diameter D 4 , into four sections BQ 4 , 
Q1Q2, etc. such that the areas generated by the sections are equal, i.e. : 


L 2 - 


■L 2 


dL - dl 2 = d 3 2 -d 2 * 


dP- 


-dP = 


dP 


■ d? 


where d 0 , is the diameter of the shaft, and in this particular case since there are 
only 4 partial turbines, <^ 4 = D 4 . 

The initial and final points on the boundaries of the partial turbines pass 
through Pj, and Q 1} P 2 , and Q 2 , respectively. 

The determination of the remainder of the boundaries is a matter of judg¬ 
ment. 

The method which I prefer is the one used by Kaplan {Bau rationaller 
Francisturbmcn Lanfrader). Kaplan considers the path of a particle of water 
(or rather its circular projection on a plane through the axis of the turbine) as 
composed of arcs of circles, and straight lines of the form shown in Sketch 
No. 256, right-hand figure. The assumption is bold, and it must at once be 
stated that it is not confirmed by experiment. Actually, the water particles near 
C, refuse to follow such sharp curves, and Gelpke’s method gives a more 
probable course. The only justification for Kaplan’s method is that it is the 
simplest of those yet proposed, and that none other appears to give results 
which are closer to the truth. My own belief is that Kaplan’s assumption is 
quite sufficiently correct for the upper half of the vanes in the case of very wide 
turbines such as are now considered, and that for the three lower partial turbines 
a very fair approximation is obtained. The method might be slightly improved 

Q 

by distributing the water, not equally between the partial turbines {i.e. -L to 

each), but say in the ratio 0*14 Q ( , for the lowest, and 0*15 Q t , o'17 Q t , 0*18 Q/, 
o f i8 Qt, o‘i8 Q;, for the others in order. 

It will be plain that except in the very largest and most carefully constructed 
turbines such refinements would produce variations in the calculated angles, 
which are hardly capable of reproduction in the forms of the vanes as actually 
constructed. Even the most skilled designers are rarely able both to satisfy 
rigidly all the geometrical conditions obtained by calculation, and to produce a 
nicely formed and easily constructed vane. 

The final design of a vane is a compromise between theoretical requirements 
and practical considerations, and many firms of turbine builders have also 
expended considerable sums of money in experimental research. Thus, except 
when working up the results of refined experiments, the assumption that the 
water is equally distributed between the partial turbines appears to be justifiable. 

Each partial turbine thus sketched out is now considered as a separate 

machine passing a quantity of water equal to ^ cusecs, under a head H 

P 

Where p denotes the number of partial turbines. 

We have already determined the pressures at entry into and exit from the 
wheel, so that the assumed efficiency will (theoretically speaking) be obtained. 

Thus, we have merely to satisfy the geometrical conditions at exit. 

The value of p, depends upon the type of turbine adopted. 



“RADIAL” EXIT 


gu 

As a rule, it will be found that : 

For Types I. or II., 1 = 6 or 8. 

For Types III. to V., 1 = 4. or 6. 

For Types VI. to VIII. there appears to be but slight reason for taking 
more than two partial turbines. 

Conditions at Exit , o- 4 .—As a general rule, it is assumed that the absolute 
velocity of the water in space at exit from the wheel is “ radial ” in direction. 
This term is a relic of the old types of turbines where the wheel was so narrow 
in comparison with its diameter at exit, that the problem could be (or rather 
was in practice somewhat unjustifiably) assumed to be one of motion in two 
dimensions. 

Sketch No. 257 shows clearly that this assumption is erroneous in the case 
of modern turbines. The water at exit from the wheel has an axial velocity 
along the flow line, and the condition which is really considered is the value of 
§ 4 , the (space) angle between the directions zz 4 , and w A . 

The exit is termed “radial” when §4 = 90 degrees, and the exit is at 
10 degrees forward when d 4 =ioo degrees. 

There is no very great reason to believe that radial exit has any virtue in 
itself, especially where the turbine is provided with a long, and well formed 
draft tube. 

In modern designs we generally find that if entry into the wheel without 
shock (for the case where the point 2, is selected as the point of entry as on 
p. 907) occurs when Q, cusecs, pass through the turbine, radial exit usually 

takes place when approximately ~ cusecs pass through the turbine. Conse¬ 
quently, when Q, cusecs pass through the turbine, 8 4 is about 100 degrees, and, 
as a rule, Q, is so selected that it is the maximum quantity of water that the 
turbine can pass. 

The process for determining the exit angles of the wheel vanes is as follows. 

Calculate the area available for the passage of water at exit from each 
partial turbine, say „A 4 , where y, is a prefix denoting the number of the partial 
turbine. 

Thus, y v 4 , the relative velocity of exit at the point Y, is given by : 

hr* 


We can also calculate, ^ 4 = the velocity of rotation of the point 

of exit. 

We thus determine the (space) velocity triangle A^B^C^, where A J/ B, / = „zz 4 , 
and B y Cy= v v 4i and the condition which must be satisfied is that the angle 
BA,C y =y& 4 (where A, is written for S 4 in order to show that S 4 may vary from 
point to point along the exit edge of the guide vane) should be either 90 or 
100 degrees, or whatever value has been selected. 

We thus determine the angle = *r- A„B„C W (the exit angle of the vane) 
for as many points on the exit edge of the guide vane as there are partial 
turbines. It must be carefully borne in mind that the angles thus determined 
are the angles between yzq, and ?/ zz 4 , and are therefore (space) angles measured 
in a certain plane which is fixed by the fact that the projection of y v< on the 
vertical projection drawing is the flow line through the point Y, so that the 




912 CONTROL OF WATER 

direction in which the angle is measured varies at every point along the exit 
edge of the wheel vane. 

In practice we must obtain the angle y ft 4 by successive approximation ; since 
any alteration in y 0 4 also alters y A 4 , and therefore y v 4 . 

Consider any one of the partial turbines, say P2Q2 an< ^ P3Q3, and let M, 
denote the middle point of the exit area ( i.e. M is the projection of the mass 
centre of j/A 4 ). Let ur m represent the component of m w 4 or m v 4 , perpendicular 
to m u 4 (i.e. w m — m w 4 sin m S 4 ). Put M 2 MM 3 = «. 

Let K, be a point close to M, just outside the wheel, such that MK, is a flow 
line, and let Wk, be the velocity of the water at K, in a direction parallel to MK. 
Then w ki is calculated by measuring the length K 2 KK 3 =>£, say, for 

Wk= 7 

p2nrkk 



We also know that should not differ materially from w k , in order to 
avoid detrimental shock at exit. 

Thus, construct the triangle ABC, where AB = u m or u k (if these differ materi¬ 
ally) and AC = w k , and BAC is a right angle. Then the angle ABC is approxim¬ 
ately equal to n- 0 m , where / 3 m is the required value of / 3 4 at the point M. 

Set off along BC, the length BD = ?^=4 l say, on any convenient scale. 

Z 2 

Then draw DE perpendicular to BC. 

Then L)E lepiesents u m -\-s m , the width of the passage between two consec¬ 
utive wheel vanes when the exit angle is ABC, and when the wheel vanes have 
no thickness. If s m , be the thickness of a vane, the nett exit area is z 2 b m a m , where 

b m = m= M 2 MM 3 , and v m ~ —-- , is approximately the value of at the 
point M. 







































LOSSES AT EXIT 


9 r 3 


The velocity diagram AB )n C w , can now be drawn with AB JH = u m = 

oo 


and B m C m ==v m , as above obtained. 

A more correct value of the exit angle v ( 3 i = 7r-AB Hl C H „ and the exit velocity 
can thus be calculated, and the condition §4 = 90 or 100 degrees, as the case may 
be, can be taken into account. Eg. in the sketch it is plain that if radial exit be 
required / 3 m must be decreased ; thus a m will be increased and the corrected 
value of v m will therefore be decreased. Thus the final design will make w m 
more nearly equal to w k , and 8 m more nearly 90 degrees, than is shown in the 
sketch. 

The whole of the quantities considered are measurable from the drawings, 
so that m V4 = v m is determined. 

This is of course only a first approximation to v m , but we can now ascertain 
whether w m , differs materially from w k , and can adjust the angle AB w C m , so as 
to cause „w 4 , to have the correct direction (i.e. AC m , should be perpendicular to 
AB m , if “radial exit” is desired). 

The value of a m , can now be corrected for the alteration caused by the 
angle AB m C, n , not being equal to the angle ABC, and a new (and presumably 
sufficiently accurate) value of m v 4 can be calculated. 

The value of the angle fi m =n~AB m C my which a line traced on the vane 
plane in a direction the projection of which on a plane through the axis of the 
turbine is MK, makes with the direction u m or y u 4 , is thus obtained under the 
assumption that the “exit is in a given direction” (eg. radial or at 10 degrees 
forward) when the turbine runs at n, revolutions per minute, and Q*, cusecs of 
water pass through the wheel. 

In this manner we can determine the angle of inclination of lines traced in 
definite directions on the wheel vanes at P, points ; and the complete design of 
the vanes consists in, so to say, stretching a fair formed skin over a skeleton 
thus obtained. 

The actual design of a wheel vane of types such as I. to IV., is a problem 
for the skilled draughtsman, and the forms adopted by most firms have been 
arrived at by some such mathematical method as that sketched above checked 
by careful experimenting (in the case of American types of turbines, I believe, 
almost wholly by experiment). The above process enables us to check the 
dimensions of an existing turbine, and to detect any gross errors. The method, 
mathematically considered, is a weak one, and only leads to accurate results 
when carefully employed. The system of drawing the partial turbines used by 
Gelpke (ut supra) is in some ways more satisfactory from a theoretical point of 
view. In actual practice, however, Gelpke’s system is so complicated that 
unless regularly employed confusion is bound to occur. When tested by high 
efficiency under working conditions, no appreciable difference exists between 
turbines designed by either method. 

The method of testing a given design is obvious : m v 4 , and m u 4y can be 
calculated, and the value and direction of m w 4 , can be geometrically determined. 
This can be compared with w k , as determined by measurement. 

The losses at exit are then as follows : 


, . . , , m 7V 4 2 COS 2 8 4 

(i) Loss by non-radial exit is equal to -— • 

(ii) Loss by shock of water on water at exit is equal to 


( m ?^ 4 sinS 4 - w k ) 2 

2 g 





9 T 4 


CONTROL OF WATER 


The methods of determining these losses are apparent. 

The average of the sum of the above losses when expressed as fractions of 
H, for all the partial turbines is denoted by cr 4 H. 

It is difficult to estimate (r 3 + r 4 )H, the loss during passage through the 
wheel. 

Our present information hardly justifies more than the following process. 

Calculate y v x , the velocity at various points intermediate between entry and 
exit, by measuring 4 ,= X 1 XX 2 , an d calculating a x , by the method illustrated in 
Sketch No. 249 (p. 873). Then any marked difference between y v x , and y v x , 
where X, and X', are points close to one another on the same flow line, is detri¬ 
mental. So also, any marked difference between y v x , and y \V x ^ where XX 3 , is 
a line perpendicular to the flow line, and y, and y u denote two adjacent 
partial turbines, is probably caused by incorrect drawing of the flow lines, and 
should be investigated. The more accurate methods will be discussed later. 

No numerical rules can be given, but an investigation of the efficiencies of 
well-designed turbines (the proportions of badly designed turbines are never 
published) renders it probable that if the above conditions are fulfilled (r 3 + r 4 )H, 
is about one and a half times to twice as large as would be indicated by apply¬ 
ing the usual rules for skin friction. 

Accurate Method of Gelpke.— The above method is probably the best 
when it is desired to investigate the efficiency of an existing turbine. Where, 
however, it is desired to design a turbine of a previously determined efficiency f, 
the following method of Gelpke ( ut supra , pp. 62 and 94) is employed : 

Consider the general equation : 


fH 




2 g 2 g 2 g 

This refers to a case where there is no shock loss at entry, and where the 
exit is “ radial,” and without shock. If losses of these kinds occur, we have, 
considering the partial turbine M : 


7 1 .2 


2 g 


A =eH — (T 2 H 


Wg _u 2 2 — m u 4 2 k wp — w 5 2 


2g 2g 


2 g 


no 

<5 


where, for the sake of clearness, k w 4 is written for the velocity of the water, just 
outside the wheel vanes, and m u 4 represents the velocity of the corresponding 
portion of the vane edge. The first four terms on the right-hand side of the 

equation are the same for all the partial turbines ; and - can ^ eter . 

2 g 

mined by measuring m r 4 , or r m . 

Also > - ggr 3 =( r 5 + 7-c)H approximately, and is given as one of the 

principal conditions of the design of the turbine. 

We thus arrive at the formula : 


where \f/ H, represents, 

fH — cr 2 H 


rr / £ 

2 o' 

o 




wA . t'A 


iiic 


2 g 


n cr 


2 g 2g 


Ug k Xi > 4 




2 g 


all converted into fractions of H. 

We thus calculate m v 4 for each partial turbine. 












GELPKES METHOD 


9 J 5 


Also m w 4 sin m S 4 = 


Qt 

pf^irrjb 


m 


where ^i=M 2 MM 3 (see Sketch No. 257), and f 4 is a coefficient depending on 
the thickness of the wheel vanes, which may be taken as 0*85, to 0-90 for pre¬ 
liminary work. 

We can now correct the preliminary value of m v 4 , by the equation : 

wV4 2 — w 7 h 2 _|_ m^4 2 sin 2 m 8 4 _ — wp ... 

2 g 2 g 2 g Tg 

and a preliminary value of m j3 4 can now be obtained by setting off m w 4 sin ,„8 4 , 
m V 4 and , n z/ 4 , in the proper directions. 

We can now calculate a more accurate value: 


m 


W 4 sin m S 4 = - 


fib 


m 


27 rr m — ZoS- 


P 1 — sin 2 (f) m sin 2 m / 3 4 


sin V iI 3 4 cos </>, 


where (j) m is the angle between M 2 M 3 , and E 2 E 3 , the vane edges (see p. 917). 

A still more accurate value of TO V 4 can now be secured by putting m W 4 , for 
m w 4 in Equation No. (i), and thus the final corrected value of , n / 3 4 can be 
obtained. 

The process is essentially an endeavour to allow for the shock losses o- 2 and 
cr 4 (which is variable as M alters) and to make each partial turbine per se of an 
efficiency equal to e. 

In practice the distribution of the velocities at the exit edge of the vane 
derived by this method differs somewhat from that obtained when the simpler 
method previously given is employed to design the turbine. Neither method 
produces a distribution entirely resembling that which experiments lead us to 
believe occurs, but Gelpke’s method is closest to the results of such experiments 
as have yet been made. It is consequently probable (quite apart from the 
authority which is attached to any statement made by Gelpke) that this method 
will lead to better results than any other. Nevertheless, it does not appear 
advisable to consider a turbine designed on these lines as necessarily more 
efficient than any other carefully designed machine. 

Geometry of Wheel Vanes (see Sketch No. 258).—The formulae 
and geometrical constructions developed on page 912 and in Sketch No. 249, 
afford a means of obtaining the area of the cross-section of the tube formed by 
two consecutive wheel vanes with sufficient accuracy for preliminary designs. 

More accurate methods are, however, desirable when testing the lay out 
of an existing turbine, especially when, as is frequently the case in Types 
I., II., and III., the area occupied by the metal of the wheel vanes forms an 
appreciable portion of the gross cross-section. 

For the sake of clearness let us assume that the axis of the turbine wheel 
is vertical, and that the water is discharged downwards. 

The following is a list of the makers’ drawings ; 

(i) A circular projection of the wheel crowns, and vane edges, on a vertical 
plane through the turbine axis. This will be referred to as the Vertical 
Projection. (Fig. 1.) 

(ii) A plan, or vertical projection of the wheel vane edges on a horizontal 
plane. This we call the Horizontal Plan. (Fig. 2.) 













CONTROL OF WATER 


916 

It is assumed that the flow lines, or partial turbine boundaries, have been 
traced on the vertical projection, and if necessary corrected in accoi dance with 
the results of the preliminary investigations. 

Consider any point X, on a wheel vane. Draw XF, the flow line through X, 
and X,-XX S (where X r X = XX,) perpendicular to XF, in Fig. 1, of any con¬ 
venient length. Through X r , and X s , draw flow lines X r F r , and X S F S . In 



Sketch No. 258. — Determination of the Relative Velocities and Accurate Exit Angle. 


practice X,F r , and X S F S are conveniently taken as partial turbine boundaries. 
Let X'rX's, FVF' S , etc. denote corresponding points on the next wheel vane. 
Denote all quantities referring to X, by the suffix x. 

We wish to ascertain the nett area (allowance being made for the space 
occupied by the metal of the wheel vane) available for the passage of water 
between the two vanes, and the two cylindrical surfaces generated by X r F r , and 




















ACCURATE EXIT AREA 


9 1 7 

XsF s . 1 his area must obviously be measured normal to the direction of v x , the 
relative velocity of the water at X. 

Consider either big. 3, a “perspective” sketch, or Fig. 4, a spherical 
diagram. 

Draw XR, in the direction ?*, X^ vertically downwards, and XU, perpendicular 
to XR and Xz, and therefore in the direction of u x . Let XNVE, be the vane 
plane. In this plane draw XN the projection of XU on the plane, XV the 
direction of v Xi and XE the intersection of the plane with the plane XRiJ. In 
Fig. 1, draw E r XE s parallel to XE, which is at present not accurately determined. 
Now, we know the following quantities approximately : 

P x = angle UXV = arc UV, the angle between u x and v x . 
m x =X r X s , the perpendicular distance between the flow lines X r F r , and 
X S F >S , measured in a vertical plane. 

The following quantities are at present unknown : 

y x = angle UXN = arc UN. 

c x = ErE,s, the length intercepted between two flow lines on the inter¬ 
section of the vane plane and a vertical plane. 

(f > x —angle FXE = arc FE = angle FUE, the angle between XF 
and XE;,-. 


Also XX' = ~ = 2 r x sin —, if — be a large angle ; and XX' lies along XU, 

Z 2 Z‘2 Z 2 

7T 

and therefore makes an angle - y x with the normal to the vane face. 

2 

The gross area available for water passage measured normal to XV, with 
no deductions for the thickness of vanes, is given by 

E,Tb sin VXE.XX' sin UXV = ** sin VXE -—- sin y x . 

*2 

The nett area A*, is obtained by putting -—- sin y x —s x , for -—- sin y x , 

z z 2 

where j*, is the thickness of the vane at X, measured normal to the vane face. 
Now, since VFE, is a right angle, we have : 


sin VXE 


sin VE 


sin 


7r 


sin FE sin 4 > x 
sin FVE sin UVN 


and since UNV, is a right angle, we have : 


7 T 

sin - 


sin UVN = sin UVN = _ 

sin UN sin y* sin UV sin & 

,_ uvr _sin^ s m^ 
Thus, sin VXE- iE ^r— 

Thus, A.-* sin ^ S 4 ^ { 2 p sin y,-s,} 

sin y x z 2 

j f 2 nr x • a „ sin ( 3 X \ 

=e x sin 4 > x \ -- sm& x -s x -v— j 

t z 2 sm 7* 


■mJ 27rr - sin 0 *-.s/ 4 ^—j ; since plainly, E r E, sin ^=X r X s . 
x i z 2 sm y,J 















9 i8 CONTROL OF WATER 


Thus, except for the relatively small correction term in s x , the area A*, is 

expressed in terms of easily measurable quantities. Also -r—— is always 

r sm y x 

greater than i, except when N, ancl V, coincide, and then sin ( 3 x =sm y x , and 


<px=~- Thus, the obstruction produced by the guide vane metal is least when 

the direction of v x , and the projection of u x on the vane plane coincide ; and 
as a general principle the flow lines should be as nearly as possible perpendicular 
to the lines of intersection of the vane plane and the vertical plane through the 
radius. 

Returning to the general problem : 

EUN, is a right angle. Thus, NUV=~- cf> x , and from the right angled 

2 


triangle VNU, we get : 


tan [ 3 X = 


, t T tt tan UN tan y x 

tan UV =- —f- 

cos NUV sm <p x 


Therefore sin y x — 


sin ( 3 X sin <fi x 


sin ft x sin <f) x 


Vcos 2 /Sa+sin 2 ( 3 X sin 2 <p x V j — sin 2 cos 2 <p x 


Substituting, we get : 


A,=;«J 2 -^sin 

v- 2 9. ' sin cf) x 


Thus, once the direction E r E s is laid off the nett area can be determined in 
terms of ( 3 X , which is approximately known, and <p x , which is measurable. 

The most important case is when X, is a point at exit from the wheel vane. 
In the majority of cases (e.g. in Sketch No. 249) the exit edge of the wheel vane 
is a radial plane, thus the wheel vane edge as shown in the vertical projection 
is the direction E r E, s , and the angle ? ,$4 = 0 .r can be measured at once. 

In Sketch No. 252, however, the wheel vane edge is a rather complicated 
curve. The question has been considered by Gelpke (p. 33). The correction 
obviously only affects the term s x , and at the exit edge s x , owing to the vanes 
being sharpened, is usually small. Thus, the following correction seems 
practically unnecessary. 

Put ^ for the measured angle between the flow line and the vane edge in 
the vertical projection. 

yfs x for the measured angle between the vertical and the vane edge in the 
vertical projection. 

/x x for the measured angle between the vane edge and the radius in the 
horizontal plan. 


Then, the measured vane edge length, between two flow lines, is E*, say, 
and, 


Cx ~ Ex \/ 


1 -f sin 2 \/A c tan 2 


1 + 


A r x 


E. r 2 sin 2 \fs x 



and approximately, e x =E x \/ 1 +s in 2 tan 
Now, we have e x sin cp x =m x =E x sin <!>*. 

Thus, the.collection factor is obtained by using the calculated angle (fi x in 
place of the measured angle <£ r . 

I have applied this formula to check the vane shown in Sketch No. 252, in 

















TESTING OF VANES 


9*9 


which the exit edge departs greatly from a radial plane. The differences 
disclosed are relatively large, but the effect on the nett area A*, is so small that 
I consider the extra calculations useless, unless the workmanship of the turbine 
is far more accurate than is usually the case. The sketch shows a very large 
and well designed turbine, and is the only example that I have ever considered 
would repay the labour entailed. 

The area A*, being determined, we have : 

v ,=. . 

pz% A* 

where p, is the number of partial turbines. 

Thus, the whole circumstances of the motion are determinable. 

Practical Testing of Wheel Vanes .—The above process allows us to test the 
drawings of a turbine. 

The determination of similar quantities in an existing turbine is somewhat 
laborious. I have employed the following methods in several cases. Assume 
that flat strips of thin lead about 4, to i inch wide are moulded along horizontal 
lines traced on the vanes, i.e. intersections of the vane plane with horizontal 
planes. These strips can be laid down edgewise on a drawing board, and the 
following angles determined. (See Sketch No. 258, Fig. 4.) 

The angle d^UXA, which the tangent to the trace of the strip on the 
board makes with the perpendicular to the radius. 

The angle-^=^XB, which the line perpendicular to the board in the 

plane of the strip near X, makes with the vertical ; so that £*, is the angle 
between this line and the direction of u x . 


Thus, arc UA = < 9 *, and arc UB = £*. 
Denote the angle NUA by k x . 

Then, tan y*=tan 6 X cos K* = tan £ x sin k x . 
tan 6 X tan ( x 

Thus, tan y x =—. .7. , -— -xy » 

Vtan 2 0*+tan%* 


and cos k x = 


tan y x 
tan 6 X 


Thus, the point N, is determined. 

Also, we know from the drawings, or from the preliminary calculations, ( 3 XJ 
and (f ) x , and can calculate another value of y x , say A *, from : 

tan X'*=tan 0 * sin (p x 


The values of y and X, 
ciliated from: 


can be compared, or the value of <f> X) say <b ' x , cal- 
tan y* = tan ( 3 X sin </>'* 


compared with that obtained from the drawings. 

As already indicated, at points removed from the \aoe edges the best 

condition, if obtainable, is that given by <£*=-, or & = 

r pp0 process is only a rough one, as neithei 0 X , noi can be accuiately 
measured, but it affords a very fair insight into the workmanship and accuracy 
of the vanes. I believe that some turbine designers employ similar methods, 





CONTROL OF WATER 


920 


as in one very efficient low head (Type I.) turbine thus studied it was quite 

plain that the condition </>=—, had been very carefully followed, even when it 

entailed a markedly non-radial exit. A study of this particular turbine has led 
me to consider that if the draft tube is well proportioned, and tapers widely, 
the loss by non-radial exit (see p. 913) is regained by greater draft tube 
efficiency. 

Mechanical Design of Turbines. —( a ) E?id Pressures .—If Sketch No. 
251 is considered, and the hole E, is assumed not to exist, it will be plain that 
the space C, would soon be filled with water at a pressure A- The pressure at 
any point on the underside of the upper crown of the wheel depends upon the 
distance from the axis, but is plainly less than/ 2 , and, as has been shown, may 
be less than atmospheric near the axis. Thus, the wheel would be exposed to 
a very heavy endways pressure, and the load on the footstep bearing F, would 
be far greater than that caused by the weight of the wheel. 

Owing to the existence of the hole E, the pressure on the upper side is but 
small, and if the area of the hole be large in comparison with the leakage area 
27the resultant pressure is probably upwards, and tends to decrease the 
pressure on the bearing F, the weight of the turbine being wholly or partially 
water-borne. 

The question can be mathematically investigated as follows: 

Let fi g , be the difference between the pressure in the space G, and the 
pressure at the top of the draft tube. p 0i can be calculated when / 4 — p 2 — h 4 + h 2 
is known, if the areas and coefficients of discharge of the leakage strip 27 rr^i, 
and the hole E, are determined ; as a first approximation, fi a =o. 

The resultant upward pressure of the water inside the turbine on both 
ttD 4 2 


crowns is equal to 


W 4 

g 


, as this expresses the vertical momentum generated 


in one second (the correction in cases such as cone turbines where the velocity 
at entry into the wheel is not in a horizontal plane, is obvious). 

Thus, if W h be the weight of the wheel, shaft, etc., the resultant force in an 
upward direction is : 


-Di 2 —- 

g 


Wa 


n 


D 2 


A-W 


In turbines of Types I. or II., especially if the shaft is horizontal, so that W<, 
is o, this force may be small, or it may even be advisable to make 
A=A-A-^4+A> i- e - to abolish the hole E. 

In these cases, and in double turbines, the force is not large, and a thrust 
bearing capable of taking a small end pressure suffices. The thrust bearing 
can never be entirely omitted, as the loss in efficiency by the wheel getting even 
slightly out of position with reference to the guide crowns is too great to allow 
any risk to be taken. 

As a rule, however, the resultant force is downwardly directed, and when 
H, is large, the magnitude of the force thus produced is great, and a balancing 
piston and cylinder of the character indicated in Fig. 3, Sketch No. 250, is 
icquiied. An exacu calculation of the size of the piston and of the pressure 
lequired to pioduce balance is impossible, although the formula given permits a 
close approximation to be made. 

1 10m a piactical point of view this is not important, as a very exact adjust- 





TURBINE SHAFTS 


921 


ment of the pressure difference on the two sides of the piston can be secured 
by manipulating the valve which controls the supply of pressure water to the 
underside of the piston. In the sketch, water taken from the supply to the 
turbine is used, and no regulating valve exists, so that adjustment is not possible. 
Large modern turbines are usually provided with a system of lubrication by 
which oil under pressure is pumped through the bearings by means of a small 
pump driven off the shaft of the turbine. In such cases the oil is usually 
pumped under the balancing piston, and is also employed to work the regulating 
machinery. In turbines which only receive water over a portion of the cir¬ 
cumference of the wheel (see p. 864) sideways pressures may obviously occur. 
Such pressures are usually eliminated by supplying water at two places 
symmetrically situated with respect to the turbine axis. 

In view of the losses disclosed by the discussion on page 904, it is necessary, 
especially in high speed turbines, to investigate the balancing of the wheel, its 
shaft, and all rigidly connected bodies around the axis of the wheel shaft. If 
\V, be the total weight of the rotating bodies in lbs., and their mass centre be 
situated at a distance of r, feet from the geometrical axis, the “ centrifugal 


W /2tt;A 2 


lbs. 


force” is given by F = — r j 

and the shaft deflection produced with say r— o'oi' = J" should be investigated. 
Uncertainties as to the exact value of F, are avoided by remembering that if 
n — 60, i.e. 1 revolution per second, F = W lbs., when r—0’817 feet, 

or r= 10 inches approximately. 

Proportions of Turbine Shafts. —The shafts of turbines are unusually favour¬ 
ably situated as regards liability to shock. 

The twisting moment is given by the equation : 

N 

T = 63,000 — inch-lbs. 

?i 


Horizontal turbine shafts are exposed to bending moments produced by 
the weight of the wheel. The shafts of Pelton wheels and other turbines 
which receive water only over a portion of their circumference are also 
exposed to bending moments produced by the sideways pressures of the water 
jet or jets. 

Let M, represent the bending moment thus produced. Put M = /tT. 

The usual theory states that the diameter of the shaft in inches is : 

d = c f n „ 

where Unwin (Theory of Machine Design , vol. 1) gives the following table of 
values for C. 


Material. 

Cast iron ..••••* T 3 2 
Wrought iron . • • • • -3 5 ° 

Mild steel . • • • • • * 3 

Medium steel . • • • • * 2 99 

Steel castings . • • • • • 3 


The figure given for steel castings is probably high, as cast steel has greatly 
improved of late. On the other hand, so far as I understand a matter 




922 


CONTROL OF WATER 


which is still the subject of dispute, the theory which produces the factor 
3 ^k+ s/k 2 + i, is now held to be erroneous and the factor should be altered 
to 3 V i -\-k' z . 

In large turbines (especially where ei, the width of the clearance space, is 
small) it appears advisable to investigate the deflection of the shaft under the 
bending moment M, and to ascertain if any rubbing is likely to occur. 

Vanes and Crowns .—The advantages of thin wheel vanes are obvious. 
The thinnest vanes are obtained by using steel plates, and are j^ths, to | an 
inch in thickness. Their strength only needs to be considered when the 
turbine wheel is both large and wide. Each vane transmits a moment equal 
N 

to 63,000-inch-lbs. to the upper crown. If this is assumed to be produced 

nz% 

by a pressure which is equally distributed over the whole of the projected area 
of the vane, and if the vane is then considered as a cantilever supporting this 
uniform pressure, the calculated stress is plainly somewhat in excess of the 
truth. 

The vanes, however, should not be too thin, as erosion by sand and 
corrosion by entrained gases are likely to occur. Plate vanes are usually 
pressed into expanding grooves in the crowns by hydraulic pressure. In small, 
cheap turbines they are sometimes fixed in the moulds, and the crowns are 
cast round them. The plates should extend at least half an inch, and better 
still three-quarters of an inch, into the metal of the crowns. 

In Types I. to V., however, the form of the vanes is so complex that a 
steel plate cannot be shaped so as to make a satisfactory vane. In these 
cases, the whole wheel (crown and vanes together) is usually cast in one piece. 
The minimum thickness varies from a half to three-quarters of an inch in the 
lower portions of the vanes, to three-quarters to an inch in the upper portions. 
The material is usually cast iron, but steel and bronze are growing more 
common, especially in cases where high heads are met with. 

The wheel crowns are usually cast of iron, steel, or bronze, and are from 
1 to 2-|- inches in thickness, according to the size and speed of the turbine. 
Certain recent accidents suggest that it would be advisable to investigate 
whether the wheel can resist the stresses produced if (owing to the failure of 
the regulating apparatus) the wheel “ runs away,” and attains a speed which is 
approximately equal to twice that for which it is designed (see p. 943). A 
large factor of safety is of course unnecessary when provision is made against 
such abnormal occurrences. 

The whole wheel must be firmly fixed to the shaft. Pfarr (see Hutte, 
vol. 2, p. 35) states that L = o'6 + ^ inches approximately, where L, is the 

o 

length of the key boss. 

The guide crowns and vanes need less careful consideration. If the vanes 
are fixed, steel plates will suffice. If the vanes are movable for purposes of 
regulation, they are usually made of cast iron. Where bronze is specified, 
bronze bushes and turning pins must also be provided. 

Clearance Space .—The space between the wheel and its housing largely 
influences the loss due to leakage (see p. 905). The exact value depends 
entirely upon the accuracy of the construction. 

We may assume that ei = p^ths of an inch in small, and gths of an inch in 
large turbines. 





REGULATION 923 

Bearings. —The design of turbine bearings is not a difficult matter once the 
magnitude of the forces involved has been realised. 

In small turbines, the end pressure produced by the combined weight of the 
wheel and shaft and the water pressures, is usually carried on a submerged 
footstep bearing. Lubrication is then difficult, but if the bearing is bushed 
with lignum vitre the water provides all requisite lubrication. Typical drawings 
are given in Unwin’s Machine Design. In somewhat larger turbines the 
bearing is enclosed, and is lubricated by oil delivered under pressure. This 
method appears to be less satisfactory than that employed in many modern 
turbines, where, as already stated, the whole of the end thrust is taken up by 
oil or water pressure on the under surface of a balancing piston. The under 
surface of the piston and the upper surface of the bottom of the cylinder in 
which it works should be provided with grooves shaped in plan somewhat like 



the vanes of a centrifugal pump. The object of such grooves is to encourage 
a rapid flow of oil, or water, underneath the piston. Details aie given by 
Unwin (ut supra), and also by Van Cleeve {Trans. Am. Soc. of C.R., vol. 62, 
p. 199). The inflowing oil should be cooled by passing it through small, thin 
walled pipes, which are exposed to a stream of water. 

Methods of Regulation.— The methods of regulating the horse-power 
and the speed of a turbine are very various. Gelpke enumerates seven, and 

more could be collected. 

The following classification may be adopted : 

(a) Regulation by moving the guide vanes. 

(h) Regulation by obstructing the entry into, or exit from, the guide vanes, 
(c) Regulation by valves, or sluice gates in the approach channels, 01- 
pressure mains. 





















CONTROL OF WATER 


924 

Under ( a ) we need merely consider the method of Fink, where the vanes 
are rotated round fixed axes. The variants where the ends of the vanes are 
shifted sideways, or where a portion only of the vane moves, are equally 
expensive in construction, and produce shock losses of the character already 
discussed. 

The only objection to the method is its cost. 

The calculation of the power requisite to move the vanes can be theoretically 
effected by investigating the pressures on either side of a guide vane, and 



Sketch No. 260. —Regulation by Movable Guide Vanes of a Turbine 

near to Type I. 

These sketches show the difficulties introduced by any departure beyond the limits of 
Gelpke’s types, when the turbines are regulated. The underlying assumption is that w x 
remains constant and equal to however much the vanes be moved. Even under this 
favourable assumption the shock losses in No. 259 are very great. 

If in addition the value of w . 2 is corrected for : 

(a) Decrease in w x owing to greater friction in the guide vanes ; 

( b ) Shock loss on quitting the guide vanes ; 

(r) Loss caused by decreased hydraulic efficiency, owing to shock losses at entry 
to wheel; 

it is obvious that w 2 will decrease rapidly as the guide vanes close up and the shock 
losses will become still larger. 

taking the moments of the unbalanced pressures round the fixed axis. As a 
matter of practice, however, the friction of the various bearings in the link work 
connecting the piston of the regulating apparatus with the vanes influences the 
result to such an extent that it is advisable to assume that the full pressure 
caused by the head H, acts on one side of the vanes only, and to proportion 
the links and regulating apparatus for the forces thus produced. A certain 



























THE FALL INTENSIFLER 


9 2 5 


excess of power is thus obtained, which will be useful if the lubrication of the 
pins or link bearings becomes defective. 

(P) Until lately the standard American method of regulation was a 
cylinder gate working between the wheel and guide crowns. The loss of 
efficiency caused by the sudden expansion of the water stream as it issues 
from beneath the gate is obvious. In some cases, partial crowns were fixed 
between the vanes, and the loss was thus materially reduced (see Sketch 
No. 250). The method is cheap, and the gate requires little power to move it. 
It may therefore be adopted in cases where the first cost must be kept low. 

(c) These methods practically amount to reducing the effective head. It is 
doubtful whether they are ever advisable. 

The Fall Intensifier . —The fall intensifier, like the Venturi meter, is 
an application of the principle of the diverging tube, and is due to Clemens 
Herschell. The circumstances favouring its practical application are best illus¬ 
trated by a description of the proposed installation at La Plaine, near Geneva. 
This power station is worked under a low head. At low water seasons (approxim¬ 
ately 100 days per year) a head of 43 feet is available, and all the water is 
passed through the turbines. For the remaining 265 days the flow of the river 
exceeds the quantity that can be economically employed for power development, 
and owing to a rise in the tail water level, the available head diminishes, and 
in high flood is only 26 feet. It will consequently be plain that the turbines 
which suffice to utilise the low water flow, and under such circumstances develop 


N, horse-power, will in flood time only produce —5 N = o'48 N, approximately. 

43 * 

Thus, under ordinary conditions, some device such as cone, or double 
turbines, would be required ; and even so the questions relating to the speed of 
the turbines would need somewhat careful consideration. 

Sketch No. 261 (Fig. 2) shows Herschell’s proposal diagrammatically. 
During low-water periods the water passes through the turbines by the channels 
ABCD. The circular gate at D, is closed during floods, and the water entering 
the turbines travels by the route ABCPG. At the same time the gate Q, is 
opened, and the whole, or a portion of the excess of water now available, passes 
through the fall intensifier RQPG. 

The theory of the process is as follows: 

Let H, be the visible head, i.e. the difference between the upstream and 


downstream flood water levels. 

Let us assume that a vacuum of h, feet of water exists at p. 

Then, the turbine works under an effective head equal to H +h, and when 
the form of the passages and the design of the turbine are known, we can 
calculate Q*, the quantity of water used by the turbine. 

So also, the passage RP, works under a head H + /*, and discharges a 
quantity of water Q*, say. The diverging passage PG, discharges a quantity of 
water equal to Q^-f-Q*. Thus, the velocities at P, and G, say v p , and v 0i can be 
calculated when the dimensions of the intensifier are known. 

Then, theoretically, we have : 


Vr 


-h = V Ji-+h 


2 g 


O (T 
*V> 


2 ) 


or, h 2 -\-h 


<- / 2_ t 

'p 


7- 


o or 
*•'«£> 


where h 2 is the depth of the centre of G below tail water level. 
Practically, h 2 +h, is say 070, or o‘8o of the theoretical value. 





CONTROL OF WATER 


926 

At La Plaine it would be advisable to make //, equal to about 43 — -6=17 
feet, and probably if we assume that at low water the turbines are run so as to 
develop o‘8o of the maximum possible power (this being the point where the 
greatest efficiency is secured), and in floods so as to develop the maximum 
possible power under the smaller head, the effective head during floods might 

be reduced to x feet, where .r^=o*8o x 43 2 , or .r = 37 f ee t sa Y* Lhus, efficient 
working with well designed turbines might be secured if h, was only 10, or 11 
feet, although it will be evident that if turbines of Types I. or Ii. are used, the 
speed must also be investigated. 





(1) Low Head Turbine Installation at Berrien Springs (after Engineering Record). 

(2) Herschell’s proposal for Fall Intensifier Installation. 

(3) Wheel Vanes of Francis Turbine (a) and Free Deviation Turbine (£). 


If Sketch No. 261 were a scale drawing, it is plain that G. should be at, or 
close to, tail water level so as to keep ft 2 , small. The necessary data regarding 
the efficiency of diverging tubes of the size now contemplated, are not available. 
Experience with draft tubes of turbines suggests that v v , should not exceed 
2’5 to 3 times v 0 , and, consequently, if h 2 + h= 15 say, we get: 

-g— (27 s — 1) x 070= 15, or v Q — 13 or 14 feet per second. 

Thus, the velocities contemplated are not larger than those which are 
frequently employed in turbine work. 

Herschell (The Fall Intensifier) has published the results of certain tests of 
the principle, which prove that it works satisfactorily in practice. The details 











































































PELTON WHEELS 927 

♦ 

of the channels near P, are far more important than any tests, and I find it 
hard to believe that the experimental arrangements give any indication of the 
methods which are employed in practice. Further details of practical installa¬ 
tions must be secured before a really intelligent design can be made. It will, 
however, be obvious that when the real efficiency of the arrangement can be 
approximately predicted, the method will be largely adopted. At present, in 
considering its application to any given case, we are quite unaware as to 
whether we shall have sufficient surplus water to produce the required vacuum 
at P. A certain amount of safety can be secured if the turbines are designed 
to work most efficiently at a low fraction of their full load (say 070 full load). 
Whether these conditions can be secured in any given case depends upon local 
conditions, and full records of the variations in head, and of the quantity of 
water available, are required. 

The fall intensifier is a cheap solution, and really amounts to a substitution 
of the two large gates at D, and Q (see Sketch No. 261), for a certain number 
of turbines. The intensifier itself is a hole in the foundations of the power 
house, and is therefore not a very expensive piece of work. 

Pelton and Spoon Wheels. —The Pelton type of turbine may be regarded 
as a turbine in which the guide vanes are replaced by one or more (not usually 
more than three) jets which are circular or rectangular in section. The water 
issuing from these jets impinges upon a series of moving buckets which are 
analogous to the wheel vanes and wheel passages of the ordinary Francis turbine. 

In typical Pelton wheels the water does not pass through the wheel, but 
escapes on either side of the buckets at approximately the same distance from 
the axis of the wheel as it entered the buckets. In the Loffel wheel, or turbine 
with free deviation, the water passes through the wheel and escapes axially in 
the same manner as in a Francis turbine. Pelton and Loffel wheels are more 
easily constructed than Francis turbines, as the open buckets can be cast and 
machined separately, and can afterwards be bolted to the wheel rim. The 
regulating mechanisrn is cheaper, as at most three orifices have to be dealt 
with. As a general rule, the size of the jet is altered either by a slide, or better 
still by a central spear (see Sketch No. 262). In some cases regulation is 
effected by turning the jet slightly away from the wheel, so that only a part of 
the jet strikes the buckets, and the remaining portion is discharged into the tail 
race without doing work. Water is consequently wasted, but if the supply 
main is long it is frequently inadvisable to shut off the water suddenly 
(see p. 808). 

The values of C, which indicate that Pelton or Loffel wheels are desirable 
are given on page 888. The efficiency of these wheels is slightly less than that 
of a Francis turbine. Consequently, even in California (the original home of 
the Pelton wheel) a Francis turbine is now frequently employed where five or 
ten years ago a Pelton wheel would have been installed. 

The symbols employed in the calculations of Pelton and Spoon wheels are 
similar to those used for turbines, but are detailed in order to prevent obscurity. 

b , is the axial breath of the bucket, in feet. 
d, is the diameter of the jet orifice, in feet. 

dj is the diameter of the jet at its vena contracta, or section of minimum area. 

D, is the diameter of the wheel, in feet, measured to the tip of the buckets. 
ej represents the total energy of the jet. 

e ’is the energy of a small portion of the jet at a distance r, from the axis of the jet in the 

cross-section at the vena contracta. 


CONTROL OR WATER 


928 

/z, is the radial height of the buckets. 

H, is the pressure in the supply main, in feet of water (see p. 882). Practically H = 
head utilised by the wheel. 

Q, is the quantity of water passed by the jet, in cusecs. 

s„ t is used for the efficiency of the nozzle, etc. (see p. 935)* 

z/ 2 , is the velocity of the bucket at the point where the jet strikes it. 

zi, is the velocity of the water relative to the bucket, in feet per second ; is used to 
denote the relative velocity just after complete entry, and therefore v z = v.> less im¬ 
pact losses. 

wj , is the velocity of the jet at the vena contracta, in feet per second. 

w 2 = Wi — Wj, approximately, is the velocity with which the jet arrives at the bucket. 

5 2 , is the angle between zz 2 and w„ or wj. 

e, is the hydraulic, and 77, the mechanical efficiency of the wheel. 

9 , is the impact angle ; theoretically, 9 , is a space angle, but Finkle uses 9 for the impact 
angle measured in a plane perpendicular to the axis of the wheel. 

</>, is the foam and friction loss angle ; as a definition we may put ^ = cos 0. (See p. 935 -) 

v 2 * 

Size of the Jet .—Let H, be the pressure in the supply main, as measured at 
a point close to the wheel, where the velocity is small in comparison with 
\t 2gH, say not over o'o5, to o'i \t 2gW ; so that H, is approximately equal to 
the geometrical head from the water level in the forebay to the jet orifice as 
corrected for the friction losses in the supply main. The velocity of the water 

in the jet is equal to : _ 

w y — °’95 to 0*98^2^11. 

The velocity of the bucket should be about one-half this, say : 

z/ 2 = o - 45 to o'5oV2^H. 


Thus, D 2 , the diameter of the wheel at the point where the jet strikes the 
bucket, is given by 


7 tD 2 7 Z 

60 


= w 2 . 


If the value of w 2 , when the efficiency is greatest is experimentally investi- 

gated, it will generally be found that - . — ■ varies from o’qo to crqS. The 

v 2 o-H 

higher values occur in the more efficient wheels in which the design of the 
buckets when tested according to Finkle’s rules, is good. The lower values 
usually occur in less efficient machines where Finkle’s process indicates that the 
buckets are badly designed. The rule is not without exceptions, but it will 
frequently permit the best speed of the wheel to be selected. So far as theory 
can be applied to the question, this experimental fact seems to indicate not so 
much that the buckets are badly designed, as that bad designers crowd the 
buckets too closely together. 

The size of the jet orifice is best determined as follows: 

Let H -\-hf be the total static head from top water level to the nozzle, so 
that hf represents the head lost in the supply main when Q cusecs 
are passing. 

Let l be the length and D' the diameter of the supply main, and 77 = C V rs 
its skin friction equation. 

Then, w r = / 2 /( H +^/) 


At 


d 


4 


1 











SIZE OF JETS 929 

where c v is the coefficient of velocity for the nozzle. The energy of the jet is ; 

e . = 62 . 5 Tf? = "-62-5 [ igcj D' 5 ^(H T hf) I 


2 o' 
w «b 


8 ‘ f t ^^ + D'» J 


and this is a maximum when : 


C 2 


d= 


D' 5 


w 


« f .r 


This gives Wj = oS\6c v \f 2 g (H +///). 

This solution is that appropriate when the cost of the supply main is a large 
fraction of the total cost of the installation. 

Gelpke, apparently considering only the efficiency of the wheel, gives a 
formula which is approximately, 

* 3 . 

9-5 

The horse-power of the wheel, if 77 = 0-80, is given by ( ^, and if J be the 
diameter of the jet at its minimum section, 


11 


7T 


Values of the r 


• (d V 

ratl ° \i) 


Q = -Wjdf. 

are given on page 937. 


We can thus determine whether one, or two, or more nozzles are required in 
order to supply the requisite volume of water ; and D 2 , and n, should then be 
adjusted in order to as far as possible conform to the two relations given above. 
Square or rectangular nozzles are not common, but their area is made equal 


7T • • 

to —d 2 , where d, is obtained as above. 

4 

The jet nozzle should be so directed that the directions of Wj and zz 2 , the 
velocity of the wheel at the point where the centre of the jet meets the bucket 
tip circle make an angle of about 30 degrees. 

If regulation is effected by deflecting the nozzle away from the wheel this 
should be allowed for by somewhat increasing this angle. Gelpke gives a table 
showing that this angle S 2 is least in large wheels, and increases to about 40 
degrees in small wheels, regulated by deflecting the nozzle. His figures appear 
to represent German practice well, but American designers usually use smaller 
values of d 2 . 

* . 

(i) P elton Wheels— Let h be the height of the buckets measured 
radially, and b their breadth measured axially, then: 

Gelpke states that approximately h=v*]d ’ b = y$d, where d, is the diameter 
of the jet. 

His rule gives: 

The area of contracted section of jet . 

—_---5-—=013, approximately. 

Projected area of bucket 

Le Conte states that the best efficiency in eleven Californian machines 
occurred when this ratio was 0-0979. 

f 

The maximqm value of the ratio was 0-1417. 

The minimum value of the ratio was o"o86i. 


59 









93° 


CONTROL OF WATER 


So also, in the above eleven installations, the ratio, 
d_ Diameter of jet 
b 


, ranged from 0*253 to 0*346, the average being 0 282. 


Width of bucket’ 

The number of buckets depends on the ratio of dj or d to D 2 , and on the 
angle § 2 . It is best determined by drawing the jet and the bucket circle, and 
spacing the buckets so that the outer edge of the jet is neither obstructed by 
the tip of the bucket behind that on which it impinges, nor does the inner 
edge impinge so deeply into the bucket as to produce too short or too rapidly 
curved a path across the bucket. In general this produces a bucket with a tip 
somewhat recessed so as to prevent obstruction, and yet enables a close spacing 
of the buckets to be secured. 

Gelpke gives a table of z 2 in terms of D 2 ranging from z 2 =l 6 , when D 2 is 
12 inches or less, up to z 2 = 24 when D 2 exceeds 60 inches. 

On trial I found that its value is largely dependent on Gelpke’s ratio for — 

D 2 

being adhered to. Since I believe this ratio to be only adapted to favourable 
developments (i.e. where the ratio ^ is small, see p. 929), it is always neces¬ 
sary to check results either by a drawing as above, or by Finkle’s more elaborate 
method. When Gelpke’s ratio is adhered to the spacing produces very excellent 

designs, but when applied to such ratios of as occur in Le Conte’s examples, a 
wider spacing is desirable. 

The breadth of the housing of the wheel should be approximately equal to 
3 b, or 10 d. 

The entry diagram can now be drawn, and this should be investigated 
for say three elements of the jet and three positions of the bucket as it moves 
over the selected spacing (see Sketch No. 263). Also, though in preliminary 
calculations it may be neglected, we should finally determine the impact angles 
as space angles, i.e. take into account the axial deviation of the jet as it is split 
by the central knife edge of the bucket. 

It will be plain that there must be a slight residual velocity v 4 sin S 4 at 

exit, producing an exit loss of head represented by h 4 = — --. Usually 

^ 4 = o*o5H. 

As a rule, however, the detailed geometrical construction given by Finkle 
should be adopted. 

(ii )“Loffel? or Spoon Wheels.— In this type the form of the bucket 
resembles a spoon, and the water escapes axially. 

The Loffel wheel is less frequently used than the Pelton wheel, and appears 
to be slightly less efficient, owing to the fact that the escaping water is liable 
to drop back on to the rim of the wheel. 

Gelpke gives the following: 

b = 2 >d h— 1 *2 $d. approx. 

and the distance between the entry points on two consecutive buckets is 
given by ; 

/=o*40 to 0*45 - - . 

smoj 





S POO AT WHEELS 


93 i 


so that the number of buckets is —~, and is roughly twice that of a Pelton 

(/ 

wheel of the same diameter ; see, however, page 930. 

The conditions for shockless entry and radial exit are theoretically somewhat 
more easily satisfied in a Loffel wheel than in a Pelton wheel, and this 
theoretical advantage appears to account for its adoption in Germany. 

It is at present impossible to state whether the Loffel wheel really deserves 
adoption when the value of C, is such as to permit a Pelton wheel to be built. 
At present, in the form of the inside feed turbine with free deviation (see 
Sketch No. 261) it fills up the gap between 0 = 32, which corresponds to the 



SKETCH No. 262.—Loffel Wheel of 2 feet diameter, proportioned by Gelpke’s rules, 
with 2^-inch jet regulated by central spear proportioned according to the Doble 
Co.’s standard. 


Pelton wheel of the largest capacity, and C = 6i, which corresponds to a 
Francis turbine of very small capacity. So far as can be judged, even this 
limited sphere of utility is being rapidly encroached upon as designers 
acquire experience. 

The circumstances of any given wheel can be investigated by Tinkle’s 
construction. 

Detailed Designs of Pelton Wheels .—The formulae and figures detailed 
above were the only information that I possessed in the period during which I 
enjoyed opportunities for testing Pelton wheels (I have never had personal 
experience of a Spoon wheel). I then came to the conclusion that the efficiencies 






















93 2 


C O NTR OL * OF WATER 


usually stated were probably but rarely attained, but my experience being 
solely concerned with small wheels, I did not feel justified in making any 
definite statement. The following investigation of Finkle’s, in my opinion, 
hums the fiist real step towards a logical design of Pelton wheels of high 
efficiency. When the methods are applied to drawings of existing wheels the 
hydiaulic efficiency obtained is usually i to 3 per cent, lower than that 
calculated from actual observations. Thejresults, however, convince me that 
efficiencies of o So are far less commonly attained than is - *generally stated to 



6 the case, and that the difference between the efficiencies of a well designed 
elton wheel and a stock piece of machinery is probably considerably greater 
ian that which exists in Francis turbines constructed by reputable firms It 
wil also be plain that a highly efficient Pelton wheel can only be obtained 
with certainty by utilising the results of similar experiments. 

r 11 S ° I*’’, aS }. Can i udg ' e ’. Mr Eckart’s experimental methods should be 
iollowed. but his mathematical investigations are less powerful than those 
undertaken by Mr, Finkle. 1 e 

































EFFICIENCY OF FELTONS 




933 


It is not proposed to discuss the mechanical design of a Pelton or Spoon wheel. 
The constructional form of the wheel,(unlike that of the usual (i.e. Types I. to IV.) 
Francis turbine, is admirably adapted for securing rigidity and strength with but 
little trouble. The small size Pelton wheel is manufactured in considerable 
numbers by firms who are specialists, and, although I have frequently found reason 
to criticise the hydraulic design, the mechanical proportions are always good. 
Even when the strength is excessive, the fly-wheel effect produced by a heavy 
rim is always beneficial. Larger and specially constructed Pelton wheels are 
usually built on the tension spoke (bicycle wheel) principle, and no case of 
trouble arising from insufficient strength, or, what is probably equally important, 
insufficient rigidity, has been recorded. 


Investigation of the Efficiency of a Pelton Wheel . — The 
general methods of investigating the influence of the forms and sizes of the 
buckets and the jet upon the efficiency of a Pelton wheel, and other types of 
impulse turbines, are precisely the same as those used in similar work concerning 
Francis turbines. A very elegant geometrical method has been given by Finkle 
(EngineeringNews, December 24, 1908). This is a development of the method 
which is usually adopted in German Technical Colleges. In some respects the 
theory is open to objection, and the experimental data required for a full discussion 
are most defective. Nevertheless, the results of the method give a very clear insight 
into the various ways in which efficiency is lost, and there is no doubt that a 
bucket form which gives satisfactory results when examined by Finlde’s process 
will prove to be highly efficient. I therefore give an explanation of the method, 
and shall criticise certain of the assumptions made by Finkle, not because I 
discredit them (for I realise the defects of our present knowledge, and am 
aware that Mr. Finkle had more precise data upon Pelton wheels of the size 
considered than any which are generally accessible), but as an indication of the 
lines upon which experimental research should proceed. 

Let AB (see Sketch No. 263), represent the velocity due to the total head 
available at the nozzle of the wheel, i.e. the total geometrical head from the 
forebay to the nozzle less all losses by pipe friction, bends, etc. 

BC“ 

On AB, describe a semicircle, and set off BC, where ^32“the fraction of 


the head lost in the nozzle = 0*06, according to Finkle. Then AC, represents 
the velocity of the issuing jet, and AC = 0*97 1 2g\\ approximately. More 
accurately : 

AC 2 _ Energy^ofjet 

AB 2_ Dischargex Nett available head’ 


and Eckart (Ins/, of Meek. Eng., 1910) finds experimentally that: 


Diameter of jet 
in inches. 
AC 


Ratio 


AB 


— 1 2 .1 r 3 9 AS 7 

— 4(T4 5b 4 °B4 

= o'958 0*968 0*982 


6 £| 

0*986 


so that Finkle’s value which refers to a large and very well designed nozzle 

running full bore, is probably slightly low. 

Now, along AB set off AK equal to the velocity of the bucket, and draw 
AD =AC in a direction making the same angle with AK, as the velocity of the 
bucket makes with the velocity of the jet (angle DAK = §2)* Since the cioss- 




CONTROL OF WATER 


934 


section of the jet bears a finite ratio to the size of the bucket, in a detailed study 
of a large wheel it will be necessary to select a certain number (three in Finkle’s 
example) of points, or more acurately representative elements of the jet, and to 
obtain the angle DAK, and construct a separate diagram for each of these 
elementary jets. This is, of course, best done by drawing the jet and bucket to 
a convenient size, and where the necessary data exist, the variation in AD, or 
AC, that occurs over the cross-section of the jet, as well as the easily calculated 
variation in AK, might be taken into account. As a general rule, however, AD, 
is taken as constant. 

Thus KD, represents the velocity of the jet relative to the bucket. Now, 
the bucket cannot be so correctly designed that the direction of its surface at 
the point of impact of the elementary jet w T ill accurately coincide with KD. We 
therefore calculate or measure the impact angle d = DKE, which represents the 
(space) angle between KD, the ideal direction of the relative velocity, and KE, 
the path which the water actually follows on the bucket. This evidently 
requires certain assumptions to be made regarding the manner in which the 
water leaves the bucket, and Finkle sketches out (see Sketch No. 263) three 
paths corresponding to three positions of the bucket for each of the three 
elementary jets. The assumption made appears to be that the discharge is 
uniform over each element of the discharge edge PQR, of the bucket. This 
may be accepted as true, and in view of the high velocity of the water is probably 
more accurate than the similar assumption made regarding partial turbines in a 
Francis turbine. Now, describe a semicircle on KD, cutting KE, in E. 
Then KE, represents v 3 the velocity with which the water starts to travel along 
the bucket, and in theory v 3 — v 2 cos 6 . 

The question of loss by impact at entrance)has already been discussed. We 
have no direct evidence upon the subject in the case of Pelton wheels, and such 
evidence as is afforded by the characteristic curves of turbines tends to show 
that the theory followed by Finkle is (for small values of 6 such as occur in a 
well-designed bucket) erroneous, and overestimates the loss. Nevertheless, if 


the drawing shows that 


DE 2 

AB 2 


(the impact fraction of the hydraulic loss) is large, 


the bucket must be considered as badly designed, and a better shape must be 
sketched out. It is hardly necessary to state that 6 must be calculated by the 
spherical trigonometrical methods already indicated. 

Next, set off the angle EKF = <j) and describe a semicircle on KE, cutting KF 
in F. If cf) be properly selected, KF, represents the relative velocity of exit of the 
water from the bucket. Finkle takes (/> = 2i degrees, in all the nine cases, and 
this is evidently an experimental value. As a matter of fact, it is fairly plain 
that (f) largely depends upon the form and curvature of the path in which the 
water travels across the bucket. In a well-designed bucket each elementary jet 
is deflected through approximately the same total angle while crossing the 
bucket, so that the water particles which lose the least energy from friction 
probably lose more energy owing to the sharper curvature of the path which 
they traverse. Thus, the assumption that $ = a constant, is a rational one. 

Hence (subject to the “error” discussed later), KF, represents v 4 , the 


relative exit velocity of the water, and 


EF 2 

^-g2, represents the fraction of the 


energy lost by “foam and friction.” Now draw AG, along AB, to represent the 
velocity of the bucket at the point where the water (the velocity of which is 




FINKLE S DIAGRAM 


935 


represented by Kf) leaves the bucket; and set off GH = I<F, so that the angle 
AGH, represents the angle between the velocity of the bucket and the velocity 
KK This must be measured from the drawing of the bucket, and the bucket 
is usually designed so that n~ / 3 4 = AGH = io degrees approximately. Then AH, 
represents the absolute velocity of the water when it quits the bucket, and 
AH2 ^ , 

> represents the fraction of energy lost by exit velocity. We may therefore 

utilise the result of this construction in order to determine the final value of the 
exit angle AGH. 

The overall hydraulic efficiency of the Pelton wheel can now be estimated. 
The fractions of the energy available just before the nozzle, which are afterwards 
dissipated without doing work, are as follows : 

BC 2 


(i) Lost in the nozzle . 

(ii) Impact loss at entry 

(iii) Foam and friction loss . 

(iv) Exit velocity loss 

Thus, the hydraulic efficiency is 


Sn — 


AB 2 


DE 2 
AB 2 
EF 2 
,5V ~" AB 2 


Se. = - 


AH 2 


AB- 


BC 2 + DE 2 + EF 2 + AH 2 
AB 2 


The sketch shows one of Tinkle’s nine diagrams, but is not a representative 
diagram, since I desired to show the various losses clearly and therefore 
selected a case with relatively large values of and s r . 

Finkle does not explain his methods, and the following criticisms may there¬ 
fore be due to misconceptions. In the first place, the impact angle 6 is 
apparently obtained as though the impact were in two dimensions only. Since 
the various paths Iz, . . ., Oo , are apparently freely sketched out, this is not 
very important. The angle obtained may not refer to the precise portion of the 
jet considered by Finkle, but some stream does experience the assumed 
deviation. Secondly, since u A or AG is not equal to zz 2 or AK ; v 3 or KE is 
not equal to z/ 4 or KF even if no foam and friction loss occurs. This appears 
likely to produce a certain error for the real meaning of Finkle’s assumption, 
<£ = 21 degrees, is that when a stream of water enters a bucket with a certain 
measured (after shock has occurred) relative entry velocity, the relative exit 
velocity is observed to be 0-933 of the entry velocity. Now, these observations 
were almost certainly taken on a fixed bucket, so that the fact that the ratio was 
obtained by observation does not entirely justify the neglect of the theoretical 
alteration of the relative velocities (see p. 865). 

Finkle’s original paper is well worth consultation, but as he does not state 
what experimental foundation his figures possess, I do not quote them. 

Eckart {Inst, of Meek. Eng., 1910) has investigated the matter experi¬ 
mentally, by means of a special Pitot tube (see p. 72). He measures the 
velocity of the jet at several points, and puts : 







CONTROL OF WATER 


9 3 6 


where aj, is the area of the jet at the point where the measurements are taken, 
and tv, is the velocity at a distance r, from the centre of the jet. Where R is 
the radius of the jet, the energy of the jet is : 

.! .v ■: • : ; ! i ' ■ - oi i ' >• • <-"• ,; )ft ■ i ; ! 

ITT herdr 
J 0 


c= 


CL j 


W 


where e = — 62foot-lbs. 

o /r 


O cr 


62* t; 3 
Thus, approximately €j ——- W . 

J 

j - r ' T Miiin o' it 'hi 1 

Eckart stages that in his tests the accurate value of e y, was always somewhat 
less than that given by the approximate formula, the difference being as 
follows : 

f when the diameter of the minimum section'! 
i'44 per cent. - . , . ) Ali inches. 

• 1 l of the let was ) 


r68 

1*24 

o‘8i 


55 


55 


55 


5 ) 


5 ? 

55 

5 ) 


55 


55 


55 


r 3 9 

564 

A3 7 
°64 
6 2 
6 4 


6 5 2 


55 


55 


55 


AC 2 


We thus obtain (see p. 933) the accurate values of the ratio already 


given. 


Then, putting w 2 = AK = the velocity of the bucket at the point of contact, 
and 2/ 2 =KD=the velocity of the water at entrance, relative to the bucket, 
§0 = angle KAD : 

77 2 2 = W/ + Z/ 2 2 — 2 WjU 2 COS 8.J 

• 1 , • I" < 1 i 1 . » . 

which is the algebraic expression of Finkle’s geometrical construction. 

Eckart states that § 2 = 4 degrees 41 minutes, or cos 8 2 — o’gg68. 

The power of the wheel is obviously : 

62' c 

P= —- u 2 (Wj cos S 2 — u 2 — v 2 cos / 3 2 ) 

& 

where / 3 2 = the angle AKD, and we assume — 

Eckart now measures t/ 4 = KF, or GH, the velocity of the water when 
leaving the bucket, and states that the loss of head due to friction and eddies 
in the bucket is represented by : 


/T = 




=s r U 


zg ~g 

The underlying assumption is that 6 = 0 in a construction similar to 
Finkle’s, and theoretically, therefore, the total loss is slightly underestimated. 
Practically, the error is slight, and the figures in the column “ Other Hydraulic 
Losses ” show that even if the whole amount entered in the column is due to 
this cause (which is not probable), the value of 6 need only be considered 
when very careful measurements are made. 

Next, put AG = 7/4 = the velocity of the bucket at the point of exit, and let 
the angle of exit = AG H = 7r —/ 3 4 . 

The absolute velocity at exit, or the residual velocity is, ?£/ 4 = AH, and 
w 4 2 = (t/ 4 — 7/4 cos ^ 4 ) 2 -f^4 2 sin 2 / 3 4 , which expresses Finkle’s geometrical 

‘ZU ^ 

construction. The head lost is —R. 








937 


CENTRIFUGAL PUMPS 


Eckart’s value of b 4 is 14 degrees, or cos /3 4 = 0*9703. 
The experimental results are as follows : 


Diameter of minimum section of jet 





(inches). 

Coefficient of contraction of jet . 

. 2 3 
4g4 

0-994 

r 39 

06 4 

O-95 1 

5 wi 

0*891 

642 

0*847 

Coefficient of velocity .... 

°' 97 1 

O-976 

0*984 

0*989 

Coefficient of discharge 

0-965 

0*929 

0*877 

0*838 

! Efficiency of nozzle, equal to - . J — . 

V 2gH 

00 

LO 

CN 

b 

O-968 

0*982 

0*986 

Loss in eddies and friction in bucket 





(per cent.). 

2 3 

23-2 

27*7 

29*2 

Loss in residual velocity (per cent.) 

i*i 

I 'O 

i*8 

1*9 

Other hydraulic losses (per cent.) 

i *5 

i*6 

11 

o*8 

Hydraulic efficiency (per cent.) . 

74*4 

74-2 

69*4 

68*1 


The results are not as good as those which Finkle believes that he has 
attained, but they are actual measurements, while Finkle’s results are calcula¬ 
tions, though apparently founded on observations on other Pelton wheels. 

Centrifugal Pumps. — Symbols. —The symbols used in discussing 
centrifugal pumps are precisely those used in discussing Francis turbines 
(see p. 875). When it is desired to distinguish between the hydraulic 
efficiency of a pump and that of a turbine, the symbols e p and e t are em¬ 
ployed. Also, since the water passes through the pump in the reverse 
direction to the flow of water in a turbine, the suffix 2 refers to exit from 
the pump and 4 to entry into. The notation has not been altered, as suffix 2 
will be found to refer to the outer circumstances of the wheel both in pumps 
and turbines. 

The centrifugal pump is a reversed turbine. The water flows through the 
pump in the opposite direction (from the centre to the circumference), and the 
wheel rotates in the opposite direction, doing work on the water ; while in the 
case of a turbine the water does work on the wheel. 

Using suffix 4 to denote entry into (i.e. the inner portion of) the wheel, and 
suffix 2 for exit from (i.e. the outer portion of) the wheel ; we have : 

H u.g — U\ j 'ic /. 2 2 ~7v 4 2 1 — 

e ~ 2 g 2g 2g 

where e is the-hydraulic efficiency of the pump. This may be expressed in 
■words as follows : 

The gross head pumped against (allowance being made for pump efficiency), 
is equal to the sum of: 

(i) The pressure produced by the centrifugal force. 

(ii) The pressure required to produce the change in the absolute velocities 
at entry and exit. 

(iii) The diminution of pressure caused by the change in the relative 
velocities at entry and exit. 

The statement is not a proof, but the form is easy to remember. 
























93 3 CONTROL OF WATER 

The value of e, however, differs considerably from that obtained in turbines. 
This difference is believed to be solely due to the exigencies of practical 
design. A turbine is assumed to work under a constant head, and if the hea 
varies greatly, the quantity of water passed through the turbine is adjusted so 
as to secure the best efficiency. A centrifugal pump is expected to pump 
against a head that varies over a far greater range than is usual in turbine 
work, and to deliver the maximum possible quantity of water at all heads. 
Thus, the pump must be compared with a turbine which is often run at an 
unsuitable speed, and is systematically overloaded. The design of the pump 
must therefore be adapted to these unfavourable circumstances. Thus, e —067 
is a mean value, in the same sense as f=o'8 o for a turbine. The efficiency of 
a well designed centrifugal pump may be estimated as follows : 

(a) For the ordinary type of portable centrifugal pump which is expected 
to pump against heads varying from 10 to 30 feet, take € P — ei— 0*20, wheie 
f p is the efficiency of the pump, and et is the efficiency of a turbine of the 
same size, when running under a head equal to the mean head pumped 
against. 

(, b ) For a fixed centrifugal pump, working against a large, and not very 
variable head, take : 

€p = € l O IO 

The rules are rough, and it is probable that e p does not exceed o’go, to 0*45 
in the case of contractors’ pumps working under ordinary conditions ; while 
most firms will guarantee 6 = 075 to 078 (not including pipe friction) against 
a steady head. 

The efficiency of the high pressure centrifugal pumps, which are now 
employed for draining mines, is greatly in excess of that given by the above 
rule ; and the difference between e p and e t in these cases is amply explained by 
the fact that the velocity of the water in the long rising mains is far greater 
than the velocity of the water in the supply mains of turbines. 

The best method of sketching out the preliminary design of a pump is as 
follows : 

Let H x be the maximum head pumped against. 

Let Ho be the minimum head pumped against. 

Select a value of <? and calculate : 

1 *25 — = K 1} and 1*25 ^ = K 2 . 

Now, let Q 1? and be the quantity of water delivered, and the speed of 
the pump, when the head is Hj, and Q 2 , and ;z 2 , be the values of Q 1? and n u 
when the head is H 2 . Determine the size and type of a turbine that will use 
Q 1} cusecs, and run at ;z l5 revolutions under a head K l5 and also of a turbine 
that will use Q 2 , cusecs, and run at n 2 , revolutions under a head K 2 . The two 
turbines thus obtained probably differ radically. 

Let us assume that the K x , turbine is the larger of the two. Calculate the 
type and size of a turbine that uses o'SoQt (say) cusecs at n lt revolutions. 
We thus usually get a smaller turbine which more closely resembles the K 2 
turbine in type. .Similarly, calculate a turbine which passes i‘2oQ 2 (say) 
cusecs, at n 2 , revolutions under a head K 2 . These two turbines should not 
differ very greatly, and the size and type of the pump can now be selected. 
The velocities u 2 , u 4 , v 2 , v 4 , and w 2 , w 4 , can now be estimated, and we can 


SHOCK LOSSES IN PUMPS 


939 


determine whether the general equation is satisfied for the two circumstances 
Hi, Q\, n u and H 2 , Q 2 , n. 2 . Slight modifications may be required, but, as a 
general rule, we can proceed to estimate the losses due to friction, and shock, 
and can sketch out the forms of the vanes. 

The process is empirical, and it is quite possible to select values of 
Hi, Qi, n u which are entirely incompatible with the conditions H 2 , Q 2 , ;/ 2 . If 
such a case occurs, in practice, we must assume that the pump will be extremely 
inefficient under one or other of the conditions, and should accordingly design 
on that assumption. 

Sketch No. 264 shows three typical forms of vane with radial entry, and a 
spiral pump housing, or body. The spiral housing must plainly be so designed 



that the velocity of the water at every point is equal to cos S 2 . Thus, when 
the pump is delivering Q, cusecs the area at a point P, distant 6 degiees fiom 

Q 0 

the point O, is plainly 

Losses by Shock.— In Sketch No. 264 the loss by shock at entry is nil, 
as the vanes are so directed that the entry is radial. If the quantity of water 
delivered is altered, and the speed of the pump is not altered, w 4 , is altered and 
shock occurs, and its value can be calculated by the velocity diagram. 

The conditions at the point of exit are somewhat different. There are no 
guide vanes. Thus, a loss of head equal to 

w<L sin 2 3 2 

2,T 


always occurs. 


/ cos — 
Also a loss ^: 


^ occurs, where 11> 1 = 


Ql 

277 area at P 

























940 


CONTROL OF WATER 


This last loss varies over the whole exit circumference of the pump, but can 
be calculated by taking the average values at three or four points. 

In some modern high-pressure centrifugal pumps guide vanes analogous to 
those of a turbine are provided outside the wheel. Sketch No. 264, Fig. 2, 
shows the plan of a typical example. 

The tangents to the inner end of these vanes should be parallel to the 
direction of w 2i and their outer tangents should be as nearly as possible perpen¬ 
dicular to the line joining the outer end to the centre of the wheel. The losses 
are obtained by putting w e the velocity of exit from the guide vanes for tv 2 , and 
Sj the angle the end tangent makes with a perpendicular to the radius for § 2 in 
the equations given above. There is also a certain extra loss by skin friction 
on the guide vanes. One very efficient type of pump is also provided with 
internal guide vanes. 

If the question be investigated mathematically, it will be found that guide 
vanes permit a high value of the head to be obtained with wheel vanes which 
are nearly straight and much shorter than in the ordinary type of pump. 
Several theories regarding the exact form of these vanes are alluded to later, 
but so far as experiments go the precise form does not appear to be very 
important. 

The practical result is that a guide vane pump is some 5 to 10 per cent, 
more efficient than the. ordinary type when delivering the designed quantity of 
water and running at the designed speed. The efficiency curve, however, is 
very sharply pointed, and thus the pump is ill adapted for working under 
variable heads or at speeds other than the designed speed. The question is of 
importance, since our present knowledge of the exact values of shock losses and 
losses in curved passages is not sufficiently precise to enable the mathematical 
processes already discussed to disclose the full advantages obtained by guide 
vanes. In three cases that have recently come under my notice the makers 
tendered guide vane pumps and guaranteed and obtained values of the 
efficiency which were higher than those predicted by the usual rules. 

In the one case that I was able to test exhaustively it appeared that the 
losses in the wheel passages were little if at all greater than those due to skin 
friction. The wheel vanes were nearly straight, and the workmanship of the 
pump was excellent. The one doubt that still remains is whether the efficiency 
will not decrease very rapidly when the pump becomes worn. I have not as 
yet felt justified in recommending a guide vane pump for silted water. 

Neumann (Theorie der Ze?itr'ifitgal Pumften) has proposed to make these 
guide vanes conform to an evolute of a circle, the radius of the generating 
circle being fixed by the initial angle of inclination of the guide vane> as 
calculated from the equations of relative velocity. 

Bergeron (/fc'Z/z/tf de Mechanique, 31st October 1910) states that this form is 
not so good as the equiangular spiral which produces a very efficient shape 
when tested experimentally. Bergeron also considers the correction caused by 
the fact that both the exit channels from the wheel and the entrance channels 
into the guide chamber are of finite size. Both his own experiments and those 
of Wagenbach ( Ztschr . des Gescimte Turbifienwesen, 30th June 1908) show that 
fi 2 is in practice somewhat less than the value obtained by drawing the triangle 
of velocities. 

Thus, H, the height to which the pump can lift the water, is somewhat less 
than the theoretical value in vanes which are directed either backward or 



94i 


DELIVER V AND HEAD 


radially, and is somewhat greater than the theoretical value when the vanes are 
directed forward. 

In general, when high efficiency is desired it is advisable to use backwardly 
directed vanes, but the required lift can be attained (even if the lesser value of 
the efficiency be taken into account) at the least speed of pump rotation by 
using forwardly directed vanes. 

Variation of H as Q is altered. —Consider the equation ; 

pH 

= W 2 U 2 COS 8 2 — W^ll^ COS §4 

When the entry is radial cos §4 = 0, and cos is always small. Thus, for 
speeds which are not very different from that of radial entry ; 


= w 2 u 2 cos S 2 = uf + tl 2 V 2 cos /So 

Therefore u 2 = - V2 C0S/3a + / DiSEt ^ 

2 V 4 e 

Now, for vanes which are directed backwards at exit (see I, Sketch No 264), 
cos ( 3 2 is negative. 

For vanes which are radial at exit (see II, Sketch No. 264), cos /S 2 = °, or 



For vanes which are directed forward at entry (see III, Sketch No. 264), 
cos /So is positive. 

Now, v 2 can be expressed in terms of Q : 


v 2 


Q 


z 2 a 2 b 2 


FI 


Thus, if we plot — as ordinate, and Q, as abscissa, we get the three lines 


H 


AiHjAgH and A 3 H, which represent the values of— in terms of Q, when u 2 , or 


is constant. 

HA„ refers to a vane which is directed backwards at exit (cos /S 2 being 
negative), and therefore slopes downwards as Q, increases. 

HA,, refers to a vane which is radial at exit (cos / 3 2 = o), and is therefore 
horizontal. 

HAo, refers to a vane which is directed forwards at exit (cos ( 3 2 being 
positive), and therefore slopes upwards as Q, increases. 

H ^ , . , uf 

The value of OH, i.e. — when Q=o, is plainly y—. 

€ g 

Now, as a matter of experiment, e varies as Q alters, owing to shock, and 
losses due to the fact that entry is only radial for one particular value of Q. 
The values of H, as actually observed, therefore lie not on the straight lines 
HA 1} HAo, and HA 3 , but on the approximately parabolic curves BjKj, B 2 K 2 , 

and B.jKJ’ It is also an experimental fact that, very approximately, OB l5 OB 2 , 

2 

and OB, are each equal to 2 . A general idea of the relation between H, and 
Q, can thus be obtained. The results can be rendered quite sufficiently accurate 








942 


CONTROL OF WATER 


for ordinary practical purposes by calculating the theoretical curves of , as 

indicated, and calculating e for any given value of Q, as follows : 

Put e m for the observed value of e when the pump passes the quantity of 
water, say Q m , which produces the best efficiency at the given speed, or for the 
calculated value of e under these circumstances. 

Estimate the shock losses at entry and exit for the new value of Q, say 
Then the investigation of turbine efficiencies given on page 900 applies, and 
the new value of e becomes : 


(QiY- 

\Qm) 


cr 2 — cr 4 = e i say 


H 


The value of the head produced is given by where H 1} is the value of 

, as calculated by the theoretical straight line equations already given. 


The results of this process are quite sufficiently accurate, provided that Q l5 
is not less than say o*6Q m , and is not greater than say i*4Q m . If, however, the 
method is applied to calculate H, when Q 1 = o - iQ w , or when Q 1 = 2Q„„ errors 
may be expected, and the head which will be obtained will usually be less than 
the truth when Q, is a small fraction of Q in . The head is greater than the truth 
if Q 1} considerably exceeds Q w - 

For preliminary estimates the following rule will be found to agree well with 
the makers’ catalogues 

z/ 2 = 8*5 to 9-2 Vh 


the lower values evidently refer to more efficient pumps. 

In very well designed pumps with guide vanes such values as : 


u 2 — 7 'S t0 8*2 V h are attained. 


The theory given above includes all points in which the design of a 
centrifugal pump differs from that of a turbine. It may, however, be noted 
that in cases where the pump is below water level, so that troubles caused by a 
vacuum existing at the entrance to the pump need not be feared, a certain gain 


in efficiency can be secured by making the ratio considerably larger than 

Ua 


is usual to turbines. The theory is obvious, since divergence losses do not 
occur, and K (see p. 902) depends only on frictional losses. The size of the 
pump can thus be materially reduced. The extra losses caused by the 
increase in the velocity of the water in the pump, and (unless a diverging 
mouthpiece be provided) in the rising main, are easily calculable. 

The question of multiple stage pumps is not considered, as the difficulties 
in design caused by the double and triple wheels are entirely mechanical. 
The efficiency of multiple stage pumps is high, but is probably not higher than 
that of a carefully designed single stage pump working against a practically 
constant head. 

Governing of Turbines. —Our present knowledge does not permit any 
very definite statements to be made on this subject. The requirements of a 
governor are : 


(i) Sensitiveness, i.e. it should change the position of the regulating apparatus 
with as small an alteration of the number of revolutions of the shaft as possible. 

(ii) Rapidity of action, i.e. the governor should be powerful enough to move 




GOVERNORS 


943 


the regulating apparatus rapidly. This condition must be carefully considered. 
While an instantaneous opening of the apparatus is not objectional, an instan¬ 
taneous closure would produce water-hammer, thus the time of closure can with 
advantage be greater than the time of opening. 

(iii) Non-hunting properties, i.e. the governor should bring the turbine to 
its proper speed rapidly, with as few oscillations about this speed as possible. 

The following investigation is given by Pfarr ( Turbinen ). 

Let rtN represent the horse-power initially developed by the turbine, and 
let this be suddenly diminished, or increased, to bN ; let <?M and bM 
represent the corresponding turning moments given out by the turbine 
shaft, in foot-pounds. 

Let n a represent the speed of the shaft when the governor holds the 
regulating apparatus at the position corresponding to the supply of 
water required for horse-power. 

Let iib be the corresponding speed for b'S horse-power. The more 
sensitive the governor the less n a ~nb. 

Let T represent the line required to close off or open out the regulating 
apparatus completely, i.e. from a—\ to b — o. T is smaller the more 
rapid the governor. 

Let s represent the time between the alteration of load and the first 
motion of the governor, i.e. s is smaller the more sensitive the 
governor. 

Let I represent the moment of inertia of the shaft and all rigidly attached 
masses, i.e. wheels and dynamo if this is direct driven, about its 
axis, in lbs.-feet 4 . 

Then if we assume ; 

(i) No change in the effective head H by waves or oscillations in the 
pressure main ; 

(ii) That the governing apparatus once in action works at its maximum 
speed, and shuts off or admits the water uniformly : 

The maximum (for a diminution of load) or the minimum (for an increase 
of load) speed is given by 

?W= »« + {(a- b)s+(a-b) 2 ~} 
n m -m = n a ~ {(£ - a)s + (b- a) 2 ~ } 

and, as already stated, T usually differs for closure and opening. 

The assumptions in my opinion are so far removed from the practical 
condition that the equation is only useful for comparative purposes. In 
particular, nearly all good governing apparatus do not work uniformly, but at 
a speed approximately proportional to the change from the required speed ?i h . 
This could be allowed for in the mathematical investigation were it not that 
most makers cannot supply the values of s, T, n a or n,„ with any accuracy. 

In addition, the formula in no way discloses the hunting possibilities of the 
governing apparatus. These Pfarr has investigated graphically. So far as 
I am aware the results do not agree with those obtained by tacheometric studies 
of the speed oscillations, but the difficulties regarding j, T, etc. will amply 
explain this. 



944 


CONTROL OF WATER 


The present position, therefore, is that the civil engineer must accept 
makers’ guarantees, and is frequently obliged to buy a turbine he would not 
otherwise select, in order to obtain a reliable governor. His difficulties can 
be greatly minimised by careful design of the supply mains and providing relief 
valves. 

The best method, however, is the water tower, which I therefore investigate 
in detail. ' 

SYMBOLS 

A suffix notation is employed for / 3 , C, Q, v andj during the arithmetical integration. v n 
represents the value of v n , io n seconds after the change of load occurs, and 
A v n — v n+x - v n . 

C = —is the coefficient of skin friction for the main, C n (see p. 946). 

\r s 

d, is the diameter of the main in feet. 

F, is the area of the cross-section of the main in square feet. 

F«j, is the area of the cross-section of the water tower in square feet. , 

H, is the total head in feet, measured from forebay to the tail water channel of the turbine. 
Zi, is the head in feet, expended in producing a uniform velocity v through the length l of 
the main. 
k (see p. 952). 

/, is the length of the main in feet from forebay to water tower. 
vi, as a suffix indicates a minimax value. 

P (see p. 953). 

Q, is the quantity of water received by the turbine in cusecs. 

Qb = F^. Q& = Fz>&. Qo (see p. 954). 

R (see p. 954). 

t , is the symbol for time ; dT, indicates the period of time, usually 10 seconds, during 
which a change Av or Ay occurs. 

Vb and Vb are the initial and final velocities of the water in the main. 

Vi and V 2 (see p. 954). 
x (see p. 954). 

y, is the height in feet of the water surface in the water tower above the water level in the 
forebay. 
z m (see p. 952). 

p v ' 2 =Zi=v^ (—+^ 4 ) ( Se ep. 94 6). Pn (seep.946). 


Problem of a Water Tower or Vessel at the Lower End of a long Pressure 
Main.— Consider a pressure main d, feet in diameter, and /, feet in length, and 

t r d 2 

of an area represented by F = —, which is delivering (e.g. to a power station), 


a quantity of water equal to Q h , cubic feet per second, where Ft/&=Q & . Sup¬ 
pose (one turbine having been shut off, or set to work) that the demand 
suddenly changes to Q/= Fv f . It is quite evident that the acceleration or 
retardation of a mass of 62 - 5F/, pounds of water from velocity v b , to velocity 
will take time, and that there will be a sudden fall, or rise of pressure, producing 
shocks and irregular running of the turbines. 

In order to avoid such irregularities, it is usual to construct a water tower, 
or some other device close to the lower end of the main, in order to equalise the 
supply. The change will then occur gradually. 

The theory is rather complex, and I propose to develop it, and incidentally 
to give some idea of the amount of irregularity that still remains uncompensated 
for. 


Let F„,, be the surface area of the equalising device. Let_y, be the height 
of the water surface in this device, measured from the level corresponding to 





WATER TOWER 


945 


Q=o, i.e. the level of the water in the forebay at the upper end of the main. 
Thus, when the velocity, is steady, y, is always negative. 

Let v, be the velocity of the water in the main at any time t , after the 
change in demand occurs. 

Then, assuming that a quantity Q, is furnished to the turbines, we have: 
Y^dt— Yvdt—Y xv dy .(i) 


and h = (iv 2 = v 1 ( — + 

\2g 


Al_ 

CV 



the head required to maintain a uniform velocity 


v , in the main. The force accelerating the mass of water in the main is con¬ 
sequently represented by 62’5F( — y—h), since y, is positive when the water 
surface in the water tower is above the water level in the forebay. 



Thus, we get: 

: . (ii) 

Eliminating v , between equations (i) and (ii), we can get a differential 
equation for y. The solution of this equation can only be obtained on the 
assumption that Q, and / 3 , are constant. Now, if Q = Q/ = a constant, the 
equalising reservoir, or chamber, works satisfactorily. Provided that this can 
be relied upon, there is no particular reason for an engineer to waste his time 
on mathematical gymnastics. 

Thus, for practical purposes, some process is required which enables us to 
see what actually takes place, and to determine how much Q (the supply to 
the turbine) really does vary. 

The following approximate process is open to mathematical objections, and, 
if carelessly handled, may lead to results which differ materially from the truth. 
The method amounts to tracing a curve on the assumption that a small arc of 
the curve can always be replaced by its tangent, provided that we calculate the 

60 





















CONTROL OF WATER 


946 


inclination of the tangent at sufficiently frequent intervals. Errors are thus 
accumulative, but can be sufficiently minimised for practical purposes by 
shortening the time intervals whenever the tangent is steep, i.e. Ay, or Av, is 
large. I have calculated several cases which permit of accurate solutions, by 
the approximate process, and find that errors in the absolute magnitude of y, or 
v, are not very great (4, to 6 per cent, at most), although the time at which 
they occur is frequently some 10 per cent, in error. Now, we are really only 
concerned with the minimax values of y, and the time at which they occur is 
not highly material. In the accurate solutions, however, we must assume that 
Q, is constant. As a matter of fact, we really wish to find whether the tower is 
sufficiently large to cause Q to remain constant. We must also assume that ft 
is constant, which (even if we have experimented on the pipe, and know the 
actual value of C), is erroneous ; as C, probably varies 7 or 8 per cent, in large 
pipes, when v, varies from 1 foot to 5 feet per second. Thus, I consider that 
the approximate method is just as likely to give results which agree with 
experiment, as the accurate mathematical solution. In practice C, is usually 
not determined by actual experiment, but is calculated by the rules which 
have already been given. The magnitude of the differences which are then 
produced by merely selecting different methods of calculating C, far exceeds 
that which is likely to be produced by using the approximate in place of the 
accurate method. 

We may, as a rule, take AT=io seconds, and may assume that_y, and v, 
change by jumps at the end of each such period. 

If y n , v n , Q n , and ft n , be the values of y, v, Q, and ft, at the end of 10 n, 
seconds from the time when the changes in demand begin, replacing dy , by Ay, 
the change in y, during the 10 seconds interval between 10 n, and io/z+io 
seconds after the change in demand occurs, is given by the equation: 


JT qj Q 

From equation (i) Ay n = — ^ AT.(iii) 

•T W 
cr 

From'equation (ii) Av n = — (y n + ftnVn) AT.(iv) 


and y n+ i-yn+Ay n \ 

^n+\ — AZ4i J 


are the values of y, and v, at the end of io/j+io seconds. 


Then, by substituting these values in equations (iii), and (iv), we can obtain 
y n + 2) v n+ 2j and so work on for as long a period as rs requisite. 

The calculation of ft n , is obvious : 

ftn = where C n is the variable value of C, appropriate to d, and v n , 


and if the entry to the pipe is not bell-mouthed, the term —, may become —, as 

2 g 2 g’ 

already discussed (see p. 414). 

It will also be plain that if h = KV n , better represents the friction equation of 
the main, this form can be introduced into the calculations. 

1 he method will be rendered clearer by the following example, which is 
founded on the design for the Baden State Railways Power Scheme in the 
Murgtal (Die Wasserkraft Anlage im Murgtal, 1910). Slight alterations have 
purposely been made, as the original object of the work was to estimate the effect 
of such vaiiations by comparison with the results given in the treatise referred to. 
The supply main is of the following dimensions : 



ARITHMETICAL INTEGRATION 


947 


Length /= 10,040 teet. Cross-section F = 88*23 square feet. Cross-section 
of the water tower, F w = 1217-5 square feet. The full supply (^ = 494 cusecs, or 

Vh ~ 561 teet pei second. The power house is suddenly shut down, so that 
Q/=o, and v f =o. 

The value of / 3 , is given as 0-709, or y b = -22-30 feet. 

The time of vibration of the system (when unaffected by friction) is : 



Or in this case : 



10040 

32-2 


7 . $ = 210 seconds. 
88-23 


According to Johnson (Proc. Am. Inst, of Mech. Engr .., vol. 30, p. 442), the 
time as influenced by friction is not very far removed from: 


77 \/g + ^+^ = 272 seconds. 

It is therefore evident that intervals of 10 seconds should be sufficiently 
close to introduce no very great error in the results. 

The equations are, putting AT =10 seconds: 

F 882-3 

4 yn= IO X=^V H = ~—f-V n = 0-7257/ n 

r w 1 ~ 1 / b 

A v n = - —f(y n +l 3^n 2 )= - ^-f-(yn+o'7ogv n 2 ) 

c 1004 ' 

= — 0-032 I/« —0*0228?7 n 2 . 

The actual calculation requires great care, and is best effected by means of 
a table ruled as below : 


Time 

y feet 

Ay feet 

0725^ 

v feet p. s. 

AzTeet p. s. 

0*0321/ 

0 - 02287 ^ 2 

0 

IO 

20 

- 22*30 

- i8 ’ 2 3 

- 14*16 

4-07 

4*07 

o' 0’ 

5 ' 6 i 

5-61 

5 ’ 4 8 

0 

-Q' 13 1 

0*716 

°' 58 S 

0*7l6 

■ 

0’7l6 


In the first line, the given values of y 0 , and v 0 {i.e. y h and v b ), are inserted in 
columns 2 and 5. Column 4 is obtained by multiplying v 0 by 0-725. Since 

Or 

0 /=o, there is no term in Ay of the form —so that column 4 is not needed 

I* w 

ill this case, and the result Ay=4-07, might be written at once in column 3 of line 2. 
Columns 7 and 8 of line 1 are now filled in as shown. 

The determination of the signs of these terms is difficult. The term in v 2 , 
always has a sign opposite to that of v, and the term in y (as shown by the 
equation for Ay), is positive if v, and y, have different signs, and negative if 
they have the same sign. Thus, in this particular case Av 0 = o, and line 2 is 
filled in with Ay 0 = 4 '° 7 > A7/ 0 = o. 




































94 8 CONTROL OF WATER 


T 

y feet 

A y 

v feet 
per Sec. 

Av 

Remarks 

0 

- 22’30 

4*07 

5 ‘61 

0 N 


10 

- 18*23 

4*07 

5 ' 61 

- 0*136 


20 

- 14*16 

3*96 

5*47 

- 0*227 

The signs of the terms of Az/ 

3 ° 

— 10*20 

3*81 

5' 2 5 

- 0*302 

>■ are: 0"02 28z; 2 negative, 

40 

- 6 *39 

3'59 

4’95 

-°‘353 

0*0321 y positive. 

5 ° 

— 2*80 

2 *81 

4*60 

-°‘ 33 ° 


5 8 '4 

0*0 

0*28 

4*27 

— 0*060 1 


60 

4- 0*28 

1*98 

4*21 

— 0*404 h 

Change of section occurs. 

70 

+ 2*26 

1*77 

3 ' 81 

- 0-404 


80 

+ 4*03 

i* 5 8 

3 ‘ 4 I 

-°* 394 j 


90 

+ 5 '6* 

1*40 

3*02 

-0*388 


100 

4 - 7' 01 

1*22 

2*63 

-0*382 


110 

4- 8*23 

1*02 

2*25 

~ °’375 

The term 0*02 28& 2 is negative, 

120 

+ 9‘ 2 5 

0*87 

i*88 

-0-377 

so is the term 0*03214^. 

130 

4- 10*12 

0*70 

I ' 5 ° 

-0*376 


140 

4-10*82 

0*52 

1*12 

- 0*375 


* 5 ° 

+ 11 ‘34 

+ °'35 

075 

-0*372 ! 


160 

4- 11*69 

+ 0*18 

°‘ 3 8 

- 0*379 


170 

+ 11*87 

0*0 

0*0 

-0*380 L 


180 

+ 11-87 

- 0*18 

-0*38 

-0*376 

' The term 0*0228Z/ 2 becomes 

190 

+ 11*69 

“ 0*35 

- 0*76 

-0*362 

positive, since v is now 

200 

+ 11*34 

-o* 5 2 

— 1*12 

— 0*336 

negative, the term 0*03214' 

210 

+10*82 

-o*68 

- 1*46 

— 0*298 

remains negative. 

220 

+ 10*14 

— 0*82 

— 1*76 

-0-255 


230 

+ 9 ‘ 3 2 

-0*94 

- 2*02 

— 0*202 


240 

+ 8-38 

-1*03 

— 2*22 

- 0-157 


250 

+ 7 '35 

— 1*10 

-2*38 

- 0*107 

) 

260 

+ 6*25 

- i*i 5 

— 2*48 

— 0*061 


270 

+ 5 ' 10 

— 1*18 

- 2*54 

- 0*017 1 


280 

+ 3*92 

—1*19 

-2*56 

+ 0*023 


290 

+ 2*73 

- 1 *18 

- 2*54 

+ 0*061 


3 °° 

+ 1 ‘55 

—1*16 

- 2*48 

+ 0*094 


3 10 

+ o *39 

-°'39 

-2*39 

+ 0*040 

For 3-5 seconds. 

3 1 3 ‘5 

0*0 

— 1 * 11 

~ 2*35 

+ 0*080 ! 

For 6*5 seconds. 

3 2 ° 

— I'll 

— 1*64 

- 2*27 

+ 0-153 

Change of section occurs as 

33 ° 

- 2*75 

“ r 54 

— 2*12 

+ 0*190 

before. 

340 

- 4*29 

- 1*40 

~ I *93 

+ 0*223 

The term 0*02 2SZ/ 2 is still 

35 ° 

- 5' 6 9 

— 1*24 

— 1*71 

+ 0*249 

positive, but 0*032 ly is also 

360 

- 6 93 

- 1 *06 

— 1 *46 

+ 0-273 

► positive, since y has changed 

37 o 

- 7*99 

- o*86 

- 1*19 

+ 0*288 

sign. 

38° 

- 8*85 

- o*66 

- 0*90 

+ 0*306 


39 ° 

- 9 ' 5 I 

- °’43 

— °*59 

+ 0*313 


400 

- 9‘94 

— 0*20 

- 0*28 

+ 0*321 

y 

410 

— 10*14 

+ 0*03 

+ 0*04 

• . . 

1 The term 0*02 2 8 v 2 becomes 

420 

— 10*11 

... 

... 

• • • 

J negative, since v is positive. 


The calculations were made with a 50 cm. slide rule, and the third place figures in Av 
are plainly liable to error. The agreement with calculations effected on an arithmometer 
is, however, very close, and the slide rule appears to be sufficiently accurate for practical 
purposes. 






















































INCREASE OF LOAD 


949 

The columns headed^, and v, can now be filled in in line 3, which refers to 
a time 10 seconds after the alteration in demand. 

From the above values we can calculate the entries in columns 4, 7, and 8, 
of line 3, and, determining the signs as already indicated, we fill in columns 3 
and 6 of line 4 with 

A /i = 4’°7 j and Av x = —0*131. 

For 20 seconds (line 5) we consequently find that : 

_y 2 = — I4’i6 and v 2 = 5*48 

and the work can proceed as far as is required. 

In the actual problem the water tower is stepped, and its area for positive 
values of y, is F'^^iqoi. Consequently, when y, is positive, we have 
Ay = 0*4642/. The change occurs at T = 58*4 seconds, and again at 313*5 
seconds. The table shows the solution for the first 410 seconds, and the 
maximum and minimum values of y , and v, are found to be as follows : 

Maximum ofy = +11*87 feet when T= 180 seconds. 

Minimum of y — — 10*14 feet when T = 4io seconds. 

Maximum of v= -4-5*61 feet per second when T = o seconds. 

Minimum of 2/=—2*56 „ „ „ 280 seconds. 

The case might be further investigated, but it is fairly plain that no greater 
oscillations can occur. 

Let us now consider a case where the demand is suddenly increased from 
247 cusecs to 494 cusecs. We have : 

22 * 'X 

—y 0 =—— = 5*57 feet v 0 = 2‘So feet per second. 

4 

Assuming that 494 cusecs is actually delivered to the turbine by the 
combined contributions of the pipe and the water tower, the equations for 10 
seconds interval are as follows : 

Ay n =-4-05+ 0*72 $V n 
Av n = — 0*0312 y n — 0‘022&v n 2 


The sample table for the first 40 seconds is as follows : 


T 

y 

0-725 v„ 

A yn 

V n 

1 A V n 

o m Oj2iy n 

0'0228v n 2 

0 

- 5’57 

2*03 

— 2*02 

2-80 

° 



10 

— 7*60 


- 2*02 

2‘8o 

+ 0-065 

0-244 

0-179 

20 

— 9'62 

2’o8 

-i *97 

!>. 

00 

*M 

+ 0*121 

°‘ 3°9 

CO 

CO 

1 —( 

b 

30 

“ 11 '59 

2*17 

- r88 

2*99 

+ 0*168 

0-372 

0*204 

40 

- i 3'47 

2*29 

— 1*76 

3 ’ 16 

+ 0*204 

0*432 

0*228 




































95° 


CONTROL OF WATER 


Thereafter the tabulation is : 


T 

y 

Ay 

V 

Ay 

5 ° 

— 1 5‘ 2 3 

- 1*62 

3 ’ 3 6 

0*232 

60 

- 16*85 

-i *45 

3*59 

0*247 

70 

-18*30 

— 1*27 

3*84 

0*251 

80 

- 1 9 '57 

- 1*09 

4*09 

0*247 

9 ° 

— 20*66 

— 0*90 

4*34 

0*234 

100 

-21*56 

-0*73 

4*57 

0*2 l8 

110 

— 22*29 

-o ‘57 

4*79 

0*193 

120 

- 22*86 

-0*44 

4 * 9 8 

0*168 

130 

-23*30 

-0*32 

5* I 5 

0*144 

140 

- 23*62 

— 0*22 

5* 2 9 

0*120 

15 ° 

-23*84 

-0*13 

5 * 4 i 

0*095 

160 

- 23*97 

— 0*06 

5 * 5 ° 

0*080 

170 

-24*03 

-0*03 

5-58 

0*068 

180 

- 24*06 

+ 0*05 

5*65 

0*051 

190 

— 24*01 

4- 0*08 

5 ’ 7 o 

0*031 

200 

- 23*93 

+ 0*10 

5*73 

0*02 I 

210 

-23*83 

+ 0*12 

5*75 

0*01 I 

220 

-23*71 

+ 0*13 

576 

0*004 

230 

-23*58 

+ 0*13 

5*76 

— 0*002 

, 


In view of the small difference between these values, and the steady motion 
values y= —22*3 feet, 7/= 5*60 feet per second, it is unnecessary to carry the work 
any further. 

The total head in the case to which these examples refer exceeds 300 feet, 
and the maximum oscillation being only about 33 feet (Example No. 1) the 
variation in the head is only 11 per cent. Thus, even if the governor did not 
move during the first 180 seconds, the variation in Q (the quantity passed on 
to the turbine) would at the worst be but 5 per cent., so that we may consider 
that this regulation is very satisfactory. 

Let us, however, assume that the water tower is not widened out at y — o, but 
has a cross-section of 1217*5 square feet all the way up. Let us also assume 
that the regulation is by hand, and that when the full demand corresponding to 
a load represented by v b = 5*6o feet per second ceases, the admission valve of 
the turbine is adjusted so as to pass only 49*4 cusecs, under an effective head 
of 287*7 feet- We find that the maximum effective head is 317*8 feet, and that 
the minimum head is 272*3 feet. The maximum delivery to the turbine is 

consequently 49*4 

This variation is sufficient to materially influence the calculation, and in 
such cases a 9th and 10th column should be introduced in the arithmetical 
work, in which we calculate Q, from the formula: 


J 


3i8 

288 


= 52*0 cusecs, and the minimum is 48*4 cusecs. 



H+j 

H 





































TOWER OF VARIABLE SECTION 

Then, the equation for Ay, in place of being : 


95 1 


Ay 


Qf : 


_ II_ V _QA at 

~\f/ f 7 ,/ at 


where ^ , is a constant, is represented by 


Ay 




[ F io~ F ?t ,\/ H j 


AT 


The question is of most importance when H, is small (say 50 to 60 feet). In 
such cases, it is usually an easy matter to make the ratio large, so that y, is 
only a relatively small fraction of H. 

Returning to the general problem. It will be plain that the process given 
a ove peimits us to determine the rise and fall of the water level in the water 
towei, or suige tank, when ¥ w , is determined. The problem met with in 
practice, however, is more usually as follows. We assume a certain value for 
Vb—Vf, coriesponding to the fraction of the total load of the power station that 
is likely to be suddenly thrown off, or put on, say, v\ ) —Vf=kv m , where v m , is the 
velocity coriesponding to full load, and k, is a fraction determined by the 
variability of the load. 

The piactical problem for a given k, is then to determine F w , so that the 
extieme oscillations of the water level may be such as to produce the cheapest 
solution. 

The question has been very carefully investigated by Johnson (Trans. Am. 
Soc. of Mech. Eng ., vols. 30 and 31). Certain very useful equations are also 
given by Johnson, Harza, and Larner, in the paper and its discussion. 
Having very carefully compared these with the results of the arithmetical 
methods developed above, I consider that Harza’s methods are most suitable 
for practical design. Harza considers the equations : 


i—fO'+M. 


and s= 


dy _ Ft'— Q 


IV 


and in addition assumes that the governor of the turbine acts instantaneously, 
so as to keep the power delivered to the turbines constant, and thus arrives at 
a third equation : 

Q( H —y)— Q/( H —yi) 


whereby, is the value corresponding to a steady velocity 1 y, and H, is the total 
head measured from the forebay above the main to tail-water below the turbine. 

An accurate solution of these three equations is impossible, and Harza’s 
method of attacking the problem is not in accordance with the mathematical 
process of successive approximation. He obtains approximate solutions by 
neglecting the friction term (/ 3 ?v 2 ), and the governor motion (i.e. the third of the 
above equations). These solutions are used later on for substitution in certain 
terms of the accurate equations, but these substitutions are not effected in a 
logical manner. 

A very careful examination of the method leads me to believe that it is 
satisfactory, provided that fiv 2 , does not exceed o‘ioH, or o'^H. If, however, 
fiv 2 (where v , represents the greater of the two velocities) be a large fraction of 




CONTROL OF WATER 


95 2 

H, the development is illogical. This opinion is justified by the fact that cases 
can be constructed where Harza’s equations lead to results which aie hopelessly 

; 2 

erroneous. In such examples -vp, is always a large fraction. 

Harza’s equation is consequently applicable to all practical cases. In view 
of our present small experience of the problems concerning water towers, the 
final results must be checked by the arithmetical process already given. This 

, ( 3 v 2 

checking is the more necessary, the greater the value ot -77-. 

Subject to these remarks, let us assume that: 

y m , is the first minimax value of y, i.e. the value of y, at the crest of the 
first surge (in the case of a decrease in load), or at the bottom of the first suck 
down (in the case of an increase in load) that occurs after the change 
of demand. 

Let z m , be the alteration in water level produced by this first surge, or first 
suck down. So that: 

z m =y m +Pv h 2 for a surge, 

z m — —y m — fab 2 for a suck down. 

Then, Harza ( Trans. Am. Soc. of Meek. Eng., vol. 30, p. 478), gives the 
following : 

Zrn 2 - 2 H z m = - j + H ^ ^(7V\,7//) j 


where (as is indicated by the sign rs J), the right-hand side of the equation is 
always to be made negative. That is to say : 

vf—vf, and v b — v f , are to be taken if v b , be greater than Vf, 

and vf — vf, and Vf—v b , if Vf, be greater than v h . 

Now, this equation can be used to determine the extreme oscillations of the 
water surface in the water tower, as follows : 

(i) Ascertain the greatest height to which the water rises in the water tower 
by assuming that the water in the forebay is at its maximum level, and con¬ 
sidering a fraction k of the load as shut off. Thus, take v b , successively 
equal to v m , o'gv m , o'%v m , etc., and V/, therefore, as equal to (1 — k)v m , (0*9 — k)v m , 
etc., and V/— o, when v b , is equal to, or less than kv m . Determine the values 
of z n v, the first surge up for each case, and the absolute height of the water- 
level which is then attained from the equation : ym = z m —( 3 vf. 

It is an easy matter to determine the absolute maximum oi y m . 

(ii) Take the water level in the forebay at its lowest possible, and similarly 
calculate the sucks down, and the minimum absolute water level. The only 
change is that the power is now switched on, instead of being cut off, so that 
Vf, is greater than v b . Thus, e, the total possible oscillation of the water level 
produced in a tower with an area equal to F u ,, is determined. 

The cost of a tower of an area F u ,, and a height e, can be estimated, and a 
new area F w , may be assumed, and the new e, determined. Consequently, the 
dimensions of the most advantageous tower can be selected, and more accurate 
values of y m , may be determined for this tower only by the arithmetical process. 

As an example, take : 

H = 5o feet, /=5oo feet, F = 50*3 square feet, F,<,=402*4 square feet, and 




PRELIMINAR Y R ULES 9 5 3 

<-m — 7 feet pei second, with kv m — 3 feet per second, and /3 = o’l. Consider the 
case of a shut down. We have: 

s 2 - 1 005 ” = - 1 -94 { z/ 6 2 - ( Vb - 3)2} -1 39 (v b -v b + 3 )=- V 

say, where v b — 3 , is never negative. 

The tabulation is : 


v b 

Feet per Second 

P 

Z ,n 

/H 2 

y —z — Bv , 2 

m m " b 

7 

481 

5'°7 

- 4 T 

+ 0*17 

6 

469 

4’93 

~ 3 * 6 

+ I *33 

5 

45 8 

4*8 1 

- 2 ‘5 

+ 2*31 

4 

446 

4-68 

— i*6 

+ 3*08 

3 

484 

4’45 

-0-9 

+ 3'55 

2 

286 

2-96 

-0*4 

+ 2-56 

1 

141 

1 '47 

- O'l 

+ I’37 


Thus, the maximum possible level of the water is about 3*55 feet above that 
in the forebay, and occurs when the load is completely shut off and three- 
sevenths of the power was previously being delivered. 

If, on the other hand, we assume a complete shut down, i.e. v b ~y, and 
Vf= o, we get : 

z— i2’i5 feet, and_y = 7’25 feet 


The amount of the suck downs produced by sudden increases in demand is 
calculated in the same way : 


7J 

•b 

P 

L 

/V 

y m 

O 

434 

4‘45 

0 

- 4*45 

1 

446 

4*68 

O’l 

- 4 ' 7 8 

2 

45 8 

4‘8i 

o *4 

- 5 * 2 i 

3 

469 

4‘93 

o'9 

- 5' 8 3 

4 

481 

3*07 

i*6 

- 6*67 

5 

326 

3 ‘ 3 8 

2*5 

- 5 * 88 

6 

164 

1 '67 

3*6 

- 5*27 


So that here the interval near v b =4 feet per sec., must be examined more 
closely. 

According to Larner {Trans. Am. Soc. of Mech. Eng., vol. 31, p. 117), the 
value of jj/ max obtained by Harza’s equation may differ as much as 19, or even 
27 per cent, from the truth, and is usually less (on the average 5 per cent, less) 
than the truth. It therefore becomes necessary to find some method of 
obtaining a value which z, does not exceed. 








































954 


CONTROL OF WATER 


This is done as follows : 
Calculate the quantity : 


_Vf(U — f3v/ 2 ) 

1 H -pV b 2 —Zm 


where z m , is derived from Harza’s equation, and v f , is assumed to be greater 
than Vb> 

Then, Johnson and Larner (ut supra ) find that : 


*i‘—' |-(v 1 -%) 2 -/3 \vs-vjy 

g r l0 

is always greater (on an average 12 per cent, greater) than z m as obtained by 
the arithmetical method. 

If Vf , be substituted for V 1} we obtain a value z ?, which is always less 
than z m . 

Larner has further developed the matter, and shows that if we substitute 
V 2 = — R(V 1 — Vb) for V l5 in the above equation, we get a value of z , which 
rarely departs more than 3 per cent, from the truth- R, is determined as 
follows ; 

FI 


Put x■ 


F^iooo 


Then, x 2 — 6ox +70237 (R —R 2 )= —1872 

These last three expressions are purely empirical, and consequently have no 
such claims to reliability as Harza’s rules. 

In actual practice, k, the fraction of the load which is suddenly shut off or 
switched on, varies from 0^05 to o'20 in American examples. The Murgtal 
towers, on the other hand, are designed for k=o‘$o, when the load increases, 
and k— roo in the case of a shut down. 

Differential Water Tower. —On referring to the first of the tabulated 
examples, it will be noticed that the oscillations have been considerably reduced 
by the widening which occurs at the level y — o. 

Mathematically speaking, when _y = o, or is materially reduced, and 

in the case under consideration y—o, happens to be the equilibrium value of y. 

The principle thus disclosed may be applied in a more general manner 
by feeding the water tower with a properly adjusted auxiliary supply equal to 
Q 2 , cusecs. We then have the following equations : 


^=^-Q/+Q 2 

dt F w F w F w 

d ir- g gy+w) 

Now, if we could adjust Q 2 so that when y = V/, -r = o and ^ =0 

dt at 

simultaneously, the oscillation would end at once ; for both v, and y, would 
then reach their equilibrium values, and, being momentarily steady, would 
remain so. 

The above adjustment, however, cannot be effected, and the best that can 
be done is to endeavour to make ^ small, when is also small. That is to 


1 




DIFFERENTIAL TOWER 


955 


say, the first time that/, is close to —/37y 2 , ^ or should be made as small 

dt AT 

as possible. 

Johnson ( ut supra ) has endeavoured to apply this principle. He separates 
the water tower into two portions, as follows. One, the ordinary water tower 
communicating directly with the pipe, and the other a riser communicating with 
the ordinary tower by means of constricted orifices. These ports, or orifices, 
are designed so that they can deliver a quantity of water represented by : 

Q 2 = F (vf—vi) cusecs 

under a head x m which is the maximum alteration in level of the water in the 
ordinary water tower {i.e. is equivalent to z m , in Harza’s approximate theory). 
This he assumes as occurring when v = zy. 

So far as I understand the matter, Johnson’s mathematical assumptions 
are incorrect, although the equations are correct if the assumptions be true. 
His actual practice, however, is founded on the results of arithmetical work, 
and is consequently far less likely to be erroneous. 

The practical development is fairly obvious. Consider the second example 
(p. 949) : 

When/ = — 227 feet, 7/, the velocity in the pipe, is only 479 feet per second, 
and in consequence/, continues to decrease. Thus, when v , has its correct value, 
/, is too great negatively, and 7/, and /, continue to recede from their equi¬ 
librium values. Let us, however, assume that when /= — 22*3 feet =//, a 
properly adjusted quantity of water is delivered so as to keep/ steady. Then, 
when 7/, attains the value 77, /, still retains the value appropriate to steady 
motion with v—Vf , and equilibrium is secured without any further oscillations. 

The mathematical development of the motion under these assumptions is as 
follows : 


dy F 7 /-Q f +Q 2 
dt F w 


so that Q 2 =F(t/ 



since/, is assumed to remain constant, and equal to / 3 t/ f 2 . 

2V F g(3 Vp + V 

Hence, — j — /=log e - ’-fa constant 

’ l b v ¥ —v 

and the total quantity of water that must be supplied to the tower from the riser 
is given by the equation : 


A 




dv FI , / , \ 

= 5- loge (t/ f + 7 /) 




The limits for both integrations are given by : 
v=v x , and v=v F , where v x , is the value of v, when /, first becomes equal to 

7/p, e.g. v x — 479 f eet P er secon d m the example above referred to. 

Thus, the time before equilibrium is actually attained is theoretically 
infinite. In practice, however, we cannot arrange so as to deliver the variable 
quantity Q 2 . We must therefore select the value of /, which differs slightly 
from — / 3 t/ f 2 , say: 

//= — / 37 / F 2 + one foot, say 
= — / 3 z/ F 2 , say. 






CONTROL OF WATER 


95 6 

We can then calculate T, the time between the limits v=v b , and v = u v and 
A, the corresponding total quantity of water which is delivered. We can thus 
arrive at the size of the riser chamber, and estimate the head under which the 
delivery orifices work, which will be slightly less than / 3 (z/ F 2 — v b 2 ). The size 
of these ports can thus be determined, and a preliminary design can be 
arrived at for the riser. The exact circumstances of the motion can then be 
arithmetically investigated, the levels in the water tower and in the riser being 
determined, and the accurate value of Q 2 , calculated for intervals of say ten 
seconds. The final design can only be arrived at by ascertaining the circum¬ 
stances in this manner for the cases which produce the greatest oscillations in 
the water level in the tower. These are probably : 

(i) The rejection of all the load, when the load is k , of the full load. 

(ii) The switching on of a similar fraction of the load when (i— k) of the full 
load is already on. 

The practical results obtained by this method have not as yet been published. 
Johnson speaks very highly of its efficiency, and appears to consider it advisable 
in all cases. He also states that F w , can be reduced to at least one half of the 
required area in an ordinary water tower. Trial calculations of my own 
confirm this statement, but they also indicate that the oscillations, while never so 
great as in an ordinary water tower, are by no means so small as is assumed 
in the mathematical theory. For this reason I do not give any examples, and 
I consider that the mathematical theory is merely a rough approximation. 
More exact rules for the preliminary design of the riser, are greatly to be 
desired, for at present its proper proportioning is so laborious as to render the 
principle almost useless. 


CHAPTER XVI 


CONCRETE, IRONWORK AND ALLIED HYDRAULIC 

CONSTRUCTION 

Concrete.— Standard specification of cement. 

Treatment of Cement. —Air slaking. 

Proportioning of Concrete. —Practical definitions of Sand and Aggregate—Determina¬ 
tion of the void spaces—Practical proportioning of concrete—Results—Possible 
exceptions—Effect of fineness of the cement—Coarse and fine sands. 

Mixing of Granular Substances. —Theory—Feret’s tests—Fuller and Thompson’s 
investigations—General rules—Impermeability—Definition of “ Sand ” and “ Stone ” 
—Sizing curve—Removal of medium size “Sand,” and medium size “Stone”— 
Practical examples—Effect of artificially drying the materials. 

Sand. —Specification—Tests—Criticism—Washing—Clay and vegetable loam—Alkaline 
salts in sand and water—Effect on permeable concrete. 

Aggregate. —Chemically detrimental substances—Limestone aggregates. 

Concrete. —Machine and hand mixing—Tests—Specification—Methods of deposition 
—Wet and dry concrete—Deacon’s plastic concrete—Ramming—“Plums,” or 
displacers—Wet concrete. 

Shuttering. —Stresses produced by concrete—Stiffeners—Design of framing—Sheeting. 
Rendering. —Specification—Criticism—Other methods of obtaining an hydraulically 
smooth face—Facing of concrete—Working against shuttering—Brickwork facing— 
Removal of cement by brushing or by washes. 

Expansion Joints .— Asphalte or bitumen — Reinforcement with steel. 

Grouting with Cement. —Specific gravity and properties of grout—“ Laitance ”— 
Repairs by grouting—Delta barrage—Pressures produced—Construction by grouting 
—Weirs below the Delta barrage—Failure of the process—Percentage of cement 
used—Methods of economising cement. 

Artificial Methods of producing Impermeable Mortar. —Sylvester process— 
Gaines’ alum and clay process. 

Metallic Construction as applied to the Control of Water. — General 
conditions—Joints. 

General Design. —Deflection of metallic structures—Rules for Design—Strength of 
structures—Working stresses—Bearing pressures—Roller bearings—Ball bearings, 
not advisable. 

Special Cases.— Worm gearing—Stanching rods—Plating—Rules for joint rivetting— 
Deflection and strength—Deflection of a trussed frame. 

Water Towers.— General investigation of stresses in the external plating—Supporting 
girder. 

Concrete.—T he following discussion is almost entirely concerned with 
impermeable concrete. The question of obtaining the strongest concrete 
(under either tensile or compressive stresses) does not in reality greatly concern 
the hydraulic engineer. So far as our knowledge goes, the mixture which 
produces the most impermeable concrete does not greatly differ from that 
which produces the strongest concrete. If in any particular case the difference 
should prove to be marked, it is doubtful whether the adoption of the strongest 
mixture can be justified, for it is uncertain whether concrete which is markedly 


CONTROL OF WATER 


95 8 

permeable by water will not rapidly lose strength through the removal of the 
cementing material by solution in the percolating water. 

I do not propose to enter into such questions as the manufacture, composi¬ 
tion, or specification of Portland cement. These matters have now been 
reduced to standards, and, except in the case of very large orders, an engineer 
cannot (at any reasonable price) force his own particular ideas on the manu¬ 
facturer. Speaking as one who saw a great deal of the final results of the 
older method, where the consultant specified, and the manufacturers produced 
a more or less close approximation, I regard the present practice as more 
likely to give good results, even when (as was the case in several works I 
was employed on) the consultant had a thorough practical knowledge of the 
manufacture of cement, and knew both what he really required and how to 
manufacture it. When contrasted with the usual circumstances of a “ scissors 
and paste ” specification, accompanied by hearsay knowledge of manufacturing 
processes, there can be no comparison whatsoever. 

The matters which the engineer should control are the treatment of cement 
after its reception, the proportioning of the quantities of cement, sand, and 
gravel that go to form the concrete, and the specification and enforcement of 
the processes comprised in the term “ mixing of concrete.” 

Treatment of Cement. —This depends greatly on the quality of the 
cement. The cements of the period 1890-1902, contained “particles of free 
lime,” or at any rate were improved by being exposed (under cover from rain), 
in layers 6 inches to 9 inches deep, and turned over twice or thrice in a period 
of a month to six weeks. This process was termed “ air slaking,” and is still 
practised in many cases. I believe that air slaking is less necessary now that 
cements are ground so much more finely than in former years. It is also 
extremely doubtful whether air slaking may not be injurious to a very finely 
ground rotary kiln cement. 

At present the practical effect is that air slaking should be considered for 
cement which is made close to the place where it is used, and the advice of 
the makers (or better still, of the analyst and tester, if such are retained) should 
be taken, and confirmed by tests of its expansion after setting. If cement is 
used after a sea voyage (imported cement) air slaking is not usually necessary, 
but samples should be tested. I may state that I have had experience of three 
cases of sea-borne cement which appeared to have been deteriorated by air 
slaking. Each sample, however, was the product of a newly started rotary 
kiln, and such occurrences are consequently less probable nowadays. The 
whole question has been very carefully investigated by Bamber ( P.I.C.E ., 
vol. 183, p. 85), and it would appear that the above opinions concerning the 
inutility of air slaking are, if anything, not sufficiently severe. If tensile tests 
alone are relied upon, the process always appears useless, and is sometimes 
detrimental. So far as my experience goes, modern cements, when they fail 
to conform to the Institution of Civil Engineers or British Standard Specifica- . 
tion, usually fail only by not being sufficiently finely ground, and this test 
should always be applied first. 

Proportioning of Concrete.—Concrete consists of Portland cement, sand, 
and aggregate, by which last term is meant the larger non-cementing material, 
stones, broken bricks, gravel, cinders, slag, etc. 

We may consider sand as comprising the non-cementing material that 
passes a sieve of four or eight meshes per lineal inch, according to the quality 


CEMENT 


959 

of the available raw material. Aggregate is the material which is larger 
than this size. 

In practice, it is frequently found that sand and aggregate occur in Nature 
mixed together, and it is more convenient to make the concrete by adding 
cement to the unseparated mixture. In the following discussions of the pro¬ 
portioning of concrete mixtures, I therefore use the term sand for whatever 
the engineers propose to use as sand, and aggregate for whatever it is proposed 
to use as aggregate. A very varied experience has led me to believe that 
there are very few, if any, circumstances where the ratio of the cost of cement 
to that of properly separating the materials, is such that a considerable 
economy in cost cannot be obtained by separating the raw excavated materials 
and carefully proportioning the mixture. The only exceptions are cases where 
it is desired to fill a small cavity with firm material, very weak concrete (made 
with material excavated from the cavity) being used ; and, even under such 
conditions, it is only the cost of bringing the sieves and grading apparatus 
to the site that turns the scale. 

The correct method of proportioning concrete entirely depends upon the 
voids existing in the sand, the aggregate, and the cement itself. These are 
best determined as follows : 

(a) Cement .—Take a measured bulk of cement, mix with water so as to form 
a paste, and measure the bulk of the paste. This will usually be between o'8o, 
and o'9o of the bulk of the cement. I propose to assume o - 85 as a mean value. 
In practice, the engineer should consider whether he proposes to employ a 
very wet or very dry mixture for concrete, and should proportion the amount 
of water added accordingly. He should remember that if a very wet concrete 
mixture is employed, the figure obtained for the bulk of mortar in a small scale 
experiment will probably be slightly below the truth, when contrasted with 
that obtained on the quantity of cement used in making a batch of concrete. 
For example, in my own experiments I have obtained 0*84, using 1000 c.c. (say 
60 cube inches) of cement, and afterwards found from 0*85 to o*86 when using 
7 cube feet of cement. 

The following table shows the effect of varying percentages of water on the 
final volume of the resulting compacted paste, as found by Fuller and 
Thompson (Trans. Am. Soc. of C.E., vol. 59, p. 67) in small scale experiments, 
on 300 grammes (say 12 cube inches) of pure cement: 


1 Percentage of Water 

mixed with the Cement. 

Volume of Paste 

eicenta^e y 0 j ume Q f (j r y Cement Powder 

I 

20 

37 

23 

90 

26 

92 

o 2 

96 

5 ° 

119 

100 

114 


Thus, in small scale experiments, the wetness of the paste has a considerable 
influence on the results obtained. The effect is less marked in practical trials 

















960 


CONTROL OF WATER 


on a large scale, since the permissible variations in the percentage of water are 
not so marked, but it must nevertheless be allowed for. 

It is also advisable to note that if small measuring vessels, such as test 
tubes, are used, the cement or sand may pack abnormally, and appear more 
bulky than when tested in larger vessels. It is therefore as well to work with 
at least 50 cube inches of material, and to use vessels at least 3 inches in 
diameter. These difficulties are avoided by working by weight (as Fuller and 
Thompson did) and not by volume. I recommend volume working for the 
trial proportioning, simply because the cement, sand, and aggregate, will be 
measured by volume when the concrete mixture is deposited. Thus, in 
practice, it is advisable to weigh a cube foot each of cement, sand, and 
aggregate, before .determining the voids, so that any error caused by abnormal 
packing can be detected. 

(b) Sand .—Take the sand as it will be used (not artificially dried), pour a 
known bulk into a water-tight vessel, and fill in water from a graduated glass, 
until the water just appears over the top of the sand. The shrinkage of the 
sand which occurs in wetting should be disregarded, and the volume of water 
used should be taken as the voids in the original bulk. The figure obtained 
varies considerably. I have found figures as low as o'23 on extremely fine and 
somewhat dirty sands, such as occur in the Punjab. Sands freshly dredged 
from the sea, or from rivers (where the finer particles have been removed by 
the action of currents), show figures as high as o'48 or o'5o, the usual value 
being between 0^35 and 0*45. I propose to assume 0*40 as an average. 

(c) Aggregate .—A sand of which the individual grains are markedly porous 
should be considered as unfit for making good concrete. Porous aggregates 
are often employed, but I doubt whether they ever make really first class im¬ 
permeable concrete. Their use, however, is quite justified in circumstances 
where bulk, rather than strength, is desirable, {e.g. for partition walls, or for 
filling up cavities where percolation can be disregarded). Therefore, if the 
aggregate is porous, it should first be wetted and allowed to absorb all the 
water possible ; then freed from the visible water, and tested for voids, just as 
the sand was. Aggregate being an artificial material (in a sense that sand is 
not), the voids are even more variable than in the case of sand, and the method 
of filling employed in practice should be closely followed. For example, a 
difference of 3, or 4 per cent, in the voids may be caused merely by carting 
over a rough road, or by carriage by rail. What we wish to ascertain is the 
voids as they exist in the aggregate, when measured by the workmen in pre¬ 
paring the concrete. I assume o'35 for calculations. 

A very close approximation to the mixture which produces the densest, and 
therefore the least permeable concrete, can be obtained by the following- 
method. 

The cement paste should fill the voids in the sand, and the mortar thus 
obtained should fill the voids in the aggregate. As a rule, an excess of 
10 per cent, is allowed in each case, in order to compensate for irregularities in 
mixing. 

Thus, take the assumed 0^40 of voids in sand. We require o*4o(rio) = 
o‘44 of cement paste. Thus, 1 part of cement (producing 0^85 parts of paste) 

o*8 c 

fills the voids in , = i'93» sa Y 2 parts, of sand, and presumably makes 

o 44 

2(1 — o*4o) + o' 85 = 2'o5 parts of mortar. 


AGGREGATE 


961 


The voids in 1 part of aggregate are 0*35, or, adding 10 per cent., 0*38, so 

2 *0 C 

that 2*05 parts of mortar fill the voids in —| = 5'°4, say 5 parts of aggregate. 

o’3b 

The proportion which just produces “ no voids ” is, therefore : 

1 cement: 1*93 sand : 5*04 aggregate ; 
or close enough to 1 cement : 2 sand : 5 aggregate. 

The following figures indicate the bulk of the ingredients, and of the wet 
concrete when proportioned by these principles. The cement passed a speci¬ 
fication of not more than 7 per cent, residue, on a sieve of 5776 holes per square 
inch, and passed entirely through a sieve of 1600 holes per square inch. 
The aggregate and sand were procured from good Thames ballast by sifting 
through a sieve of 4 meshes per linear inch, i.e. say o'15 inch size. All above 
being aggregate, and all below, sand. 


Proportioning . 


Cement. 

Sand. 

Cube Feet. 
Aggregate. 

Total. 

Wet 

Concrete. 

Excess Of cement 


9’37 

lo'64 

28'oo 

48*01 

3 6 * 3 6 


f 

7 

11*10 

28'4o 

46*50 

32*30 



7 

io*5° 

28*00 

45 * 5 ° 

32*25 

Properly pro- 


7 

IO'OO 

28*00 

45*00 

30*80 

portioned 


7 

io'8o 

28'0O 

45*80 

34 *io 



7 

io‘8o 

28*00 

45*80 

33 *So 



7 

io’8o 

28*00 

45*80 

34 *oo 

Deficiency of 

r 

7 

i 3'3 

35 ' 9 ° 

56*2 

41*2 

cement 

1 

3*5 

io'8 

28*00 

42*3 

33*3 


The contrast between a properly proportioned mixture, and one containing 
an excess or deficiency of cement, or sand, is very marked. In the first class the 
total volume of wet concrete exceeds that of the aggregate by about 17 per cent, 
on the average, while in the others the excess is rarely less than 20 per cent. 
The contrast would be even more marked were it not that the volume of sand 
in each of these mixtures had been experimentally proportioned so as to secure 
as small a percentage of voids as was possible consistent with the general ratio 
of cement to aggregate. Also, the last three cases of the properly proportioned 
concrete are in reality somewhat misleading, since the properties of the sand 
had changed to such a degree as to necessitate a slight alteration in the pro¬ 
portions. In practice, the new proportions were ordered wherever 28 cube feet 
of aggregate (with the sand and cement) produced a volume of wet concrete in 
excess of 33*60 cube feet, {i.e. 20 per cent, excess). The figures, however, show 
the results attained under somewhat careful supervision, and are therefore more 
useful than an enumeration of laboratory tests. 

The following figures are the average results of some loo large scale tests 
on “ bankers,” of roughly 1 cube yard capacity. Since they include many cases 

61 














































CONTROL OF WATER 


962 

where the mixtures are known to be only roughly proportioned for minimum 
voids, it is desirable to check them at the first opportunity. I find the figures 
useful in preliminary estimates, and if confined to such purposes they will not 
prove misleading. 


A Mixture by Volume of 

Produces 

Set Concrete 
Parts. 

Cement 

Parts. 

Sand 

Parts. 

Aggregate 

Parts. 

I 


4 

4*6 

1 

2 

4 

4'5 

1 

3 

6 

6*6 

1 

4 

8 

8-9 

1 

5 

10 

11-25 


The method seems to deserve careful criticism. In the first place, the 
experience upon which it was founded is largely based on cement which would 
now be considered as extremely coarsely ground. Thus, in 1880, Grant 
( P.I.C.E ., vol. 62, p. 101), states that 15 to 27 per cent, of good English 
Portland cement was retained in a sieve of 2500 holes per square inch. 

In 1891, Carey {P.I.C.E ., vol. 107, p. 47), whose ideas on this subject were 
very advanced, used cement giving a residue of 9 per cent, on such a sieve. 

In 1897, Butler {P.I.C.E., vol. 132, p. 346), gave the following percentages 
or the residues found in actual samples : 


Sample. 

Number of Holes per Sq 

uare Inch. 

32,400 

5776 

2500 

F. 

33 

16 

4 

G. 

35 

20 

8 

H. 

28 

11 

4 

I. 

39 

15 

2 '5 


The British Standard Specification (1910) is as follows : 

“ Residue on a sieve of 5776 holes per square inch not to exceed 3 per 
cent., and on a 32,400 hole sieve not to exceed 18 per cent. 

American Portland cement is probably equally finely ground. Typical 
figures in 1905, for the residue on a sieve with 40,000 holes per square inch, are 
from 21 to 36 per cent., with an average of 287 per cent. These figures cannot 
be considered as indicating the whole difference that has occurred in the last 
twenty years, since even more finely ground cements are now procurable and 
at no very great increase in cost. 



























GRANULAR SUBSTANCES 


9 6 3 

The sands usually employed in Great Britain and the Eastern United States 
are coarse in comparison with those commonly found in the vast alluvial plains 
characteristic of India, and the Middle United States. Consequently, I con¬ 
sider that the assumption that 0-85 of cement paste, and 2(1—0-40) of sand, 
always works out at 2*05 of mortar, needs experimental checking. 

As a matter of fact, the relation does hold to about ± 2 per cent, of difference 
(which is approximately equal to the possible error in the large scale measure¬ 
ments) with finely ground cement and coarse sand. 

I have found an increase in bulk of about 4 per cent, in the case of a some¬ 
what coarsely ground cement and fine sand, which, I believe, is beyond any 
possibility of error. With very fine sand (30 per cent, passing a 100 mesh 
sieve), and British Standard cement, I have sometimes found a shrinkage of 
5 per cent. I therefore consider that at present it is well worth while to test the 
mortar carefully, and to make sure that its bulk does not differ from that shown 
by the calculation. Should the resulting bulk differ materially, the discrepancy 
must be allowed for, and a series of trial mixtures of sand and cement should be 
made up, in order to select t,hat which produces the densest mortar. 

The fact that such differences may occur renders it somewhat doubtful 
whether the process given above is applicable in every case. It would appear 
that where the larger particles of the cement are of approximately the same 
size as the smaller particles of sand, the resulting mixture is very close to the 
densest possible. If there is a marked gap in the sizes of particles contained in 
the mixture of sand and cement, so that very few particles of, let us say, ^pjth of 
an inch in diameter, exist, the theory may require modification. At any rate, it 
is always as well to investigate the bulk of mortar produced, and, if necessary, 
to modify the proportions of cement and sand, so as to get a denser mortar 
mixture. 

It will also be plain that this method may lead to a somewhat peculiar 
proportioning of the materials. For instance, let us assume that the aggregate, 
instead of being almost entirely composed of particles exceeding a quarter of 
an inch in size, is “run of the breaker” stone, containing an appreciable propor¬ 
tion of stone dust. If this does not materially exceed say 10 to 15 per cent, of 
the whole volume of aggregate, the effect will be to diminish the percentage of 
voids in the aggregate, and therefore the amount of mortar used ; whereas, if 
this stone dust was screened out, and was added to the sand, an additional 
quantity of cement would be required to fill the voids in the screened dust. It 
is therefore desirable to consider the problem apart from any practical classifica¬ 
tion of the raw materials. 

Mixing of Granular Substances. —The rules now discussed are at first sight 
somewhat meaningless, but their physical basis becomes clearer when it is 
realised that they merely express the methods by which the closest possible 
packing of the individual particles of the mixture of cement, sand, and 
aggregate, which makes up the concrete, may be obtained. 

For simplicity, consider a granular substance composed of rigid spherical 
particles only. If all the particles are of the same size, we obtain a material 
which (absolute dimensions being neglected) may be compared to a number of 
billiard balls. If these balls are piled together in cubical order, so that the 
centres of each eight adjacent balls lie at the angles of a cube, it will be found 

that the volume occupied by the ivory of the balls is ^ = 0-52 of the total space, 


CONTROL OF WATER 


964 


and 0*48 of the total space is occupied only by air. A little consideration will 
show that since the length of the diagonal of a cube is : 

s! length of side, 

a smaller ball, of a diameter equal to ——=0-366 diameter of the original 


balls, might be fitted into the void space existing between each eight adjacent 
balls. There being one such void space for each one of the original balls, an 
extra portion of the original space, amounting to (o*366) 3 , can be filled up with 
ivory ; so that a packing of balls of unit diameter, with an equal number of balls 
the diameter of which is 0*366 units, will produce a space containing 0*52+0-049 
= 0*57 of ivory, and 0*43 of air. And, plainly, if the smaller balls are of greater 
diameter than 0*366, or are more numerous than the original balls, the packing 
cannot be made as close ; and if smaller than 0*365, or less numerous, some 
voids which could be filled will remain unfilled. 

Thus, adopting a regular cubical packing, we can take a bulk of 100 cube 
feet of billiard balls, containing 52 cube feet of ivory, and 48 cube feet of air ; 
and also a bulk of about 9*4 cube feet of smaller balls, each with a radius equal 
to 0*366 of the radius of the larger balls, and containing 4*9 cube feet of ivory 
and 4*5 cube feet of air. On packing the mixed balls regularly in order we 
obtain a bulk of 100 cube feet of the mixture, containing 56*9 cube feet of ivory. 
The process can be described as mixing 10 volumes of grains of unit diameter 
with 1 volume of grains, the diameter of which is approximately one-third of a 
unit, and obtaining 10 volumes of a denser mixture with 0*43 voids, in place of 
11 volumes of less dense unmixed substances containing 0*48 voids. 

The example is selected because a model is easily constructed, and the 
purely geometrical difficulties are not great. It is otherwise somewhat mis¬ 
leading. As a matter of fact, the closest packing of a set of spheres of equal 
size is obtained when a regular tetrahedron is taken as the basis of arrange¬ 
ment. I am unable to prove, or, to discover a proof which shows that this is 
absolutely the closest possible packing ; but, assuming that the statement is 
correct, we find that: 


The volume of ivory 


7 T V 2 
~ 6 ~ 


= 074 of the total volume. 


The volume of air = 0*26 of the total volume. 

The diameter of the smaller spheres which can just be fitted into the inter¬ 
stices =0*225 of the diameter of the original spheres. 

The extra volume of ivory thus filled in = 0*011 of the original volume. 

The volume of the space occupied by these smaller balls before mixture 
= 0*015 °f the space occupied by the larger balls. 

Thus, the process is expressed by mixing 60 volumes of spheres of unit 
diameter with slightly less than 1 volume of spheres of about 0*22 diameter, in 
order to obtain 60 volumes of mixture with 24*9 per cent, of voids, in place of 
61 volumes of unmixed material with 26 per cent, of voids. 

The granular substances used in practice are not made up of spherical 
grains, nor are the individual grains of uniform diameter, but the figures 
already given show that void spaces exist. The practical test of pouring dry 
sand into a bucket “ full ” of road metal, will at once dispel any doubts con¬ 
cerning the possibility of making a denser substance by mixing two granular 
substances of different size of grain. The figures arrived at in the two 




FERET S TESTS 


965 

examples considered above will also serve to show the general principles. The 
mean sizes of the two substances must not be too close together ; and any 
admixture of grains, say one half the diameter of the larger grains, is certainly 
useless, and may be detrimental. 

A practical example is afforded by the tests of Feret ( A.P.C ., July 1892). 

The dust produced by crushing Cherbourg quartzite was sized into three 
classes. 

G, containing grains which passed a sieve of 4 meshes per square cm., {i.e. 
roughly 10 mesh per lineal inch), and which were retained by a sieve of 36 
meshes per square cm., (15 mesh per lineal inch) (approximately from o'2o to 
o’o6 inch in diameter). 

M, passing a 36 mesh sieve, and retained on a 324 mesh (or 36 meshes per 
lineal inch) sieve (approximately from o'o6 to 0-02 inch in diameter). 

F, passing a 324 mesh sieve (approximately all grains less than 0'02 inch 
in diameter). 

Each of these “sands” contained about 50 per cent, of voids. 

The three substances were then systematically mixed in various 
proportions. 

The densest mixture was o'6 G, to 0*4 F, with about 36 per cent, of voids. 
No mixture of F, and M, only, had less than 42 per cent, of voids ; and no 
mixture of G, and M, only, had less than 47 per cent, of voids. 

Similar information could be collected from many sources ; and, as will 
be seen later, the exact figures concerning the proportions which produce the 
densest mixture, and the voids in the individual materials, and the various 
mixtures, are very variable. 

The general results are, however, quite in accordance with the hints afforded 
by the mathematical theory. Roughly speaking, taking the average size of a 
cement grain as unit, the densest mixture is obtained by selecting sand grains 
of sizes, say, 4 and 16 times this unit size ; and the stones of sizes, say, 64 and 
256 times this unit size. It is obvious that this sizing (if the bulk proportions 
are properly selected) secures a dense “ sand,” and a dense “ stone ” ; and that 
the cement should pack nicely inside the sand, and the sand inside the stone. 

This aspect of the question has been investigated by Fuller and Thompson 
{Trans. Am. Soc. of C.E., vol. 59, p. 67), who regard the cement, sand, and 
aggregate as graduating one into the other, so that when they speak of particles 
less than o’oo3 inch in diameter, both particles of sand and cement are 
included. Similarly, a few of the larger grains of cement may be included in 
the size exceeding o‘oi ins. in diameter. 

The principles now set forth refer to all concrete mixtures, but the actual 
figures are probably only applicable to sands and aggregates that do not differ 
greatly as regards the general size and shape of grains from those used in the 
experiments. The experiments show that a substitution of angular aggregate 
and angular sand, for round aggregate and round grained sand, can alter the 
proportions of the best mixtures to the extent of 5, or even 10 per cent. 

The following conclusions are, however, generally confirmed by the experi¬ 
ments of Feret (although the details are possibly subject to certain exceptions), 
and may be considered as a basis for special tests in any given case. 

(i) A mixture in which the particles have been graded so as to give a 
concrete of great density when water and cement are added, produces a 
concrete of greater compressive strength than a mixture containing the same 


CONTROL OF WATER 


966 


proportions of cement and natural materials, (i.c. sand and aggregate), but 
which yields a less dense concrete, owing to a less favourable grading of the 
sizes of the particles. 

(ii) The density (and usually the strength) of concrete is affected but 
slightly, if at all, by decreasing the quantity of medium size stone in the 
aggregate, and increasing the quantity of coarsest size stone. An excess of 
medium size stone appreciably decreases the density and strength of the 
concrete. 

(iii) Variations in the size of the sand particles have more effect on the 
strength and density of the concrete, than variations in the size of the stone 
particles. 

(iv) An excess of fine, or medium sand, decreases the density, and also the 
strength of the concrete ; and, where the proportion of cement is small, a 
deficiency in sand of fine size has the same effect. 

(v) The substitution of cement for fine sand does not affect the density of the 


Is 


— 

S 

s 

no. ot 

4 

Sieve 

Meshes Per Li. 

ica! Inch 


_ 

Tl 







_ 


% 

si 









! 



.S 

s A 






t 


! 

1 

t 

j 



— Cotve day 
—- Jerome Par 

Sand Effect 
K Crushed Sto 

ve S/je ■ 008 inch Uniformity Co a 
te do- -0045 Inch do- d, 

'ficientr$h-!>-9 

• m - 5 - 8 


1 



Sf$e in Inches 

Confinuatfon 

Percer. 

of Curves - 

rage smaller than 


1 

1 

1 

1 

• 1 

t 




0-2Q 

Cotve 

93 

day Jerome Park 

•7 96-9 



! \ 
1 / / 1 




0~$6 

0-48 

95 

96 

■0 99'1 

■P 99'7 


kJ , 

u 

! 

*to 



0-60 

0-75 

Wf 

/ OO 

-y 1 uu 


n 

Jni 

f 

e 

P 

_ 

* 

\ Scale \ 

\ of l 

* Grain Diameters ; 

; in Inches | 


Sketch No. 266.—Fuller and Thompson’s Ideal Sizing Curves. 


mixture, but increases the strength, although in a slightly smaller ratio than 
the increase in the proportion of cement. 

(vi) The correct proportioning of concrete as regards impermeability con¬ 
sists in finding (with any given percentage of cement) the concrete mixture 
possessing a maximum density. The requisite strength is secured by an 
increase or decrease of the cement (thus, in effect, substituting cement for the 
finer particles of the sand). 

(vii) With a given sand and stone, and a given percentage of cement, the 
densest and strongest mixture is attained when the volume of the mixture of 
sand, cement, and water, is such that it just fills the voids in the stone. In 
other words, in practical construction as small a proportion of sand, and as large 
a proportion of stone, should be used, as is possible without producing visible 
voids in the concrete. 

In the above definitions the size of separation between “ sand ” and “ stone 55 
is taken as one-tenth the size of the largest stone. For example, for stone 
running up to 2\ inches all material below 0*22 inch in diameter is sand, (i.e. 
















































SIZING CURVES 967 

all passing say a $ inch mesh), and for inch stone, all material below 0*05 ins. 
in diameter, ( i.e . all passing a sieve of 15 meshes to the linear inch). 

The teims excess 5 and “ deficiency ” are relative, the standard being the 
“ideal” sizing curves given by Fuller and Thompson. These curves are 
piobably applicable (with a fair degree of accuracy) to most mixtures of broken 
stone, and sand, or gravel, but further trials are greatly to be desired. The 
exact form of the curve is affected by the shape of the individual grains ; and 
when angular “ sand,” procured by crushing stone, is mixed with rounded 
a g£T re gate, other and larger modifications probably occur. According to Fuller 
and Thompson, the best mixture is one in which the cement and sand together 
form about 34, to 38 per cent, of the whole volume, and about 7 per cent, of 
this is less than 0*003 ' ns> diameter, say 200 meshes to the linear inch. 

The ideal grading is shown in Sketch No. 266, where the sizing or grading 
curve starts with 7 per cent, of the whole mixture less than 0*0027 ins., and 

runs as an ellipse to a percentage of 30 + 2*2 D, for a size —, where D, is the 

diameter of the largest stone, in inches. The stone is then graded uniformly, 
as is shown by the straight line ; and it will be noticed that slight differences 
exist, according as the “ sand ” and “ stone ” are angular or rounded. 

Now, these definite figures, and the elliptical and straight line laws, are 
both probably only of limited applicability. The generally applicable deduc¬ 
tions (not only from these investigations, but also from those of Feret) are 
as follows : 

Taking D, as the maximum diameter, sizes of stone between o*6 D, and 
0*3 D, are unfavourable, and should be partially removed by sieving. 

So also, 0*1 D, being the maximum diameter of sand, sizes between 0*06 D, 
and 0*03 D, require diminution. For example, when the maximum stone is 
2\ ins. in diameter, stones of a size between 1*5 ins. and 0*75 ins. may be 
found to be in excess when compared with the curve. Sand grains of a size 
between 0*15 ins. and 0*075 i ns - will probably be in excess when compared 
with the curve, and should consequently be removed as far as possible. 

As an example, let us take Sketch No. 267, which shows a sizing curve for 
Thames ballast. Here the sizing of the mixture, as dug from the excavation, 
is as follows : 

About 73 per cent, of the whole material is less than 0*20 ins. in diameter 
(Fine), and about 14 per cent, is between 0*20 ins. and 0*48 ins. in diameter 
(Medium). About 13 per cent, is above 0*48 ins. in diameter (Coarse). 

A close approximation to the ideal cu'rve is obtained by a mixture of the 
following proportions, namely : 

Containing 38 per cent, of Fine, 14 per cent, of Medium, and 48 per cent, 
of Coarse. 

Now, D, being 1*5 ins., the effect of the proposed grading is to diminish 
the percentage of the particles of sand less than 0*20 ins. in size (Fine) to 
about one half of that which occurs in Nature, the desired object being the 
diminution of the medium sized grains of sand. 

The percentage of gravel over 0*48 ins. (Coarse) is about four times that 
which occurs in Nature, and this causes the natural proportion of small gravel 
(Medium) to fit the curve very nicely. 

If the matter is carefully studied, it will be found that this division of 
the natural “ballast” into three classes, and a proper selection of their pro- 


968 CONTROL OF WATER 

portions, will permit a large rejection of medium sand and medium gravel 
particles to be made. 

These rules do not always produce the densest mixtures. The variations 
likely to occur are illustrated by Feret’s experiments. Here the material was 
separated into: 

G, containing material between 2*36 ins. and 1*57 ins. 

M, „ „ 1*57 ins. and 0*79 ins. 

F, „ „ 079 ins. and 079 ins. 

These substances separately contain about 52 per cent, of voids when the 
material consists of broken stone, and 40 per cent, of voids when it is 
rounded gravel. 

The mixture possessing the smallest percentage of voids (and, in con¬ 
sequence, presumably the best mixture) is composed of 1 G, to 1 F, in broken 



stone, and contains 47 per cent, of voids. In the case of gravel, the propor¬ 
tions are 3*5 G, to 1 F, and the voids fall to 34 per cent. 

The results differ from Fuller’s proportions in that the class M, is totally 
eliminated, and are obviously less adapted for practical mixtures. The large 
difference, both in the proportions and the voids in the densest mixtures, which 
is produced by the substitution of gravel for broken stone, indicates that neither 
of the experimenters has succeeded in obtaining a rule which is universally 
applicable. Consequently, any blind application of Fuller’s curve is un¬ 
desirable. It must not be forgotten that both experimenters worked with an 
artificially dried material. The absolute values of the voids therefore differ 
considerably from those existing in a “ dry material,” as used in practical work. 

I have carried out special tests on the subject, and find that if we call 
the mixture containing the smallest percentage of voids, the “optimum” 
mixture, then the proportions of the “ optimum ” mixture for artificially dried 


















































SAND 


969 


materials differ very slightly from those of the “ optimum ” mixture for “ dry ” 
materials, as found in practice, although the absolute percentages of voids in 
the two mixtures may be very different. 

It will be found that a fair approximation to the best mixture (as obtained 
either by the methods of Fuller or Feret), can in many cases be secured by 
passing the natural material through a trommel with holes about o'20 ins. 
in diameter, and taking from 2 , to 5 measures of coarse, to 1 of fine material, 
in place of the natural mixture, which usually consists of 1 of coarse material 
to 3 or 4 of fine. The exact proportions are best arrived at by a series of 
trial mixtures. When the densest mixture has thus been discovered the result 
should be checked by tensile tests of the mortar thus obtained. In practice, I 
find that a comparison of the sizing curves of the available material with 
Fuller and Thompson’s ideal sizing curve, as plotted in Sketch No. 268, will 
afford valuable preliminary indications. This is, of course, the usual sand and 
stone classification. 

The more complicated “Fine, Medium, Coarse” process indicated in. 
Sketch No. 267 is of practical importance. When the usual sand and aggregate 
are thus divided into three classes, it is often possible to obtain a good “void¬ 
less” (z.e. practically impermeable) concrete with a mixture of—1 cement : 9 or 
10 of a scientifically graded mixture of the three classes. Whereas, the usual 
practical mixture, obtained by taking only two classes (i.e. sand and aggregate 
as they are generally used), is—1 : 2 : 5, or 1 : 7 of the combined material. 

When considering the sizing of materials it is often desirable to know 
what size of particle will pass a screen of say 40 meshes per linear inch. The 
question is very easily solved in meshes down to say 10 per inch, by actual 
test and measurement. Below 10 meshes per linear inch I have found that 
the following rule is very close to commercial practice : 

The maximum diameter of a particle which passes a commercial sieve 


of fly meshes per linear inch, is not far removed from 


62 

n 


inches, and is still 


more closely represented by if > 7 , is less than 40, and y, if n is greater 


than 40. 

Sand.—The usual specification for sand is as follows : 

The sand to be clean, sharp, angular pit sand, free from clay or mud, or 
other impurities which adhere to the grains. The practical tests employed in 
judging sand are : 

(i) If it stains the fingers when rubbed, it is considered to be dirty, and is 
consequently washed. 

(ii) The angularity of the grains is judged by examination by the eye, or 
by a lens. 

The specification is really one which secures a sand which is well adapted 
for making good mortar for bricklaying purposes, and is founded on the 
properties of clean pit sand, as distinguished from river sand, which is generally 
less angular, and contains fewer fine grains. Sea sand is usually even more 
rounded and more devoid of fine particles than river sand, and, being coated 
with salt, is unsuitable for mixing with cement. 

The specification therefore usually enables the sand which is best adapted 
for concrete work to be selected from the two or three classes of sand which 
occur in Nature. It is, however, quite useless for selecting the best pit sand 


970 


CONTROL OF WATER 


when three or four sources are accessible, and it in no way indicates the best 
method of preparing the raw sand. 

The specification does not describe an ideal sand for concrete, although a 
sand passing this specification will no doubt produce a good mixture, and 
forms a good raw material from which a still better sand can be selected. 

The sand required for concrete is a hard, non-porous substance, containing 
grains of all sizes, roughly in the proportions indicated by the sizing curves 
already given. This may be accurately specified by sizing tests ; but, as a 
rule, the smaller the percentage of voids the more closely the sand conforms to 
the sizing curves, and the better it is fitted for concrete. The material should 
not contain any free lime, or salts, which may act injuriously on the cement. 



Thus, a good, up-to-date specification can only be obtained by systematic 
preliminary tests on the local sand ; and the following form is probably 
necessary in cases where large quantities of sand are used : 

The raw material for sand to be procured from approved pits ; and, if directed, 
to be washed and graded into two sizes by passage through screens of (half an 
inch) and {\ of an inch) mesh. 

The required proportions of cement, fine sand, coarse sand, and aggregate, 
will be selected by the engineers, according to the results of sizing tests con¬ 
ducted, as shown in the annexed schedule ; and payment for the cement will be 
made according to the weight actually used. 

The difficulties are obvious, and a similar specification of the aggregate is 
also required. The concrete mixtures at Staines were proportioned on these 
principles, although in a less scientific manner (the date being 1899) ; and, 
since it was my duty as engineer’s assistant to conduct the tests, I can state 
that a specification similar to the above, if properly used, is not unjust to the 
contractor. 







































SAND TESTS 


97 T 

The whole of the above experimental work may at first sight appear to be 
somewhat unnecessary. 1 he real justification for the discussion is that with 
care from 6d. to is. can be saved in the cost of each cube yard of concrete, 
even under British conditions ; and, in localities where cement is really costly, 
the saving is frequently sufficient to enable cement to be used in place of less 
satisfactory local lime or other mortars. 

Similar investigations for hydraulic lime, and lime and clay cements 
(Natural Portland) are badly needed. 

The information at present available almost entirely consists of tension 
tests of various mixtures, and is not sufficient to enable any definite statements 
to be made. The principles above developed should be followed when investi¬ 
gations are made ; but, as a rule, the requisite strength is obtained with 
difficulty, and, if it is obtained, and the cementing material is finely ground, it 
is probable that the resulting concrete will be very nearly “ voidless.” 

In this connection I would observe that no modern engineer can afford to 
neglect such cementing materials as hydraulic lime and trass, or the weak 
hydraulic limes produced by burning kankar in India and hardpan in Australia. 
I do not, however, consider that I have sufficient chemical knowledge to 
discuss the principles involved in the selection of these materials and the 
production of concrete made by their use. 

I therefore merely state that certain French firms supply a hydraulic lime 
with which concrete—as reliable as a Portland cement concrete—can be 
produced ; and that certain German firms sell trass, from Andemach, which 
is equally reliable. 

The resulting concrete is not as strong as Portland cement concrete, and at 
present I merely use these materials when a cheaper result can be produced. 
It must also be remembered that the above firms are by no means the only 
possible sources (the grey lias lime of England being equally useful). The only 
reason for specially mentioning these firms is that they market a properly tested 
material of uniform quality, and therefore form as good a source of supply as 
any reliable manufacturer of Portland cement. 

The following details may be useful in drawing up a logical specification : 

In the case of modern cements, it has been fairly well established that a 
round sand gives the strongest concrete when tested in compression, the 
angular sands giving better results in tension tests only. Now, concrete 
structures are designed for exposure to compressive stresses ; thus, to insist on 
an angular sand seems somewhat unnecessary. In some cases (e.g. retaining 
walls, and broad foundations), we know that the concrete does actually sustain 
tensile stresses, and then angular sand may be advantageous. I do not consider 
that it is permissible to reject an otherwise satisfactory sand merely because it 
is not angular, since a want of angularity really means that the sand is not very 
fine, for it will generally be found that the finer the sand, the more angular are 
the individual grains. 

The following tests of sands by Feret show the influence of the shape of the 
grains on the percentage of voids : 

Sand with laminated grains contains 34*6 per cent, of voids. 

Sand with flat grains (crushed shells), 31-8 per cent, of voids. 

Sand with angular grains (crushed stone), 27-4 per cent, of voids. 

Sand with rounded grains, 25-6 per cent, of voids. 


972 


CONTROL OF WATER 


These results are only comparative, and in Nature the percentages of voids 
are usually larger, but an angular sand may be expected to have from 2 to 5 
per cent, more voids than similar rounded sands. 

Hazen states that a sand with a uniformity coefficient of less than 2, as a 
rule contains 45 per cent, of voids ; and if the uniformity coefficient is between 
2, and 3, the voids fall to 40 per cent.; while with a coefficient of 6, or 8, the 
voids fall to 30 per cent. The figures are interesting, as showing the extreme 
importance of removing the medium sized grains. Hazen probably refers to 
angular sands. 

My own experience is distinctly adverse to the washing of sand in order to 
remove clayey particles, unless such particles exceed say 5 per cent, in bulk, or 
are collected in comparatively large masses. 

In practical tests of sand (such as is met with in the Thames valley), the 
unwashed material generally produces a stronger mortar when tested by 
1 cement : 3 sand, tensile tests (probably because the finer and more angular 
particles are not removed), and the mortar is usually less permeable by water. 
An engineer desirous of making the best use of the available material should 
consequently specify that washing may be ordered if necessary ; but should 
definitely state that sand which tests well (either in tension or in compression, 
or for permeability, according to the purpose for which it is required), need not 
be washed simply because it contains clay. 

The best method of preparation has been much discussed. So far as I can 
sum up a matter which obviously depends largely upon local conditions, I am 
inclined to believe that while vegetable mould should invariably be removed, 
the presence of a small proportion of clay (say 2 to 5 per cent., or even in some 
cases 10 per cent.), is usually beneficial, especially where impermeability, rather 
than strength, is the main requirement. I attribute those cases where sand is 
improved by the removal of small quantities of clay, not so much to the removal 
of the clay, as to the washing away of salts coating the grains of sand. And 
there is little doubt that a washing which is sufficiently violent to remove the 
smaller grains of the sand, almost always results in a sand which produces a 
weaker (in tension) mortar. 

In this connection, it is necessary to refer to the alkaline salts (such as 
sodium carbonate, sulphate, or chloride), which occasionally occur, either in 
sand, or in water used for mixing concrete. The presence of such salts 
necessitates great care in proportioning and mixing concrete. 

In some localities I have found it absolutely impossible to make a good 
concrete with local sand and well water. Such extreme cases are easily 
recognised, since the cement either sets very rapidly, or refuses to set within a 
reasonable period. The more dangerous cases, however, are those where the 
concrete works properly, and is deposited without arousing any suspicion, and 
then rapidly disintegrates. 

So far as can be judged, the conditions are very similar to those producing 
the disintegration of concrete by sea water, so much discussed ten or fifteen 
years ago. The solution of the problem is—I believe—the same. Concrete 
which is rapidly destroyed by the action of alkaline salts always appears to 
have been markedly permeable, and its destruction is probably due to the 
crystallisation of salts in the interstices. If this be so, it is plain that a 
properly proportioned impermeable concrete will probably disintegrate at the 
surface only, and the practical effect of the presence of alkaline salts will be to 


AGGREGATE 


973 

prohibit the use of other than impermeable concrete. Where impermeable 
concrete would be too expensive, coatings, or layers of asphalte, or bitumen 
sheeting, are indicated, in order to prevent percolation. I have also found a 
mere coating of tar to be satisfactory for a period of at least three or 
four years. 

In this connection it is advisable to refer to the “working qualities” of 
mortar. These are not easily defined, but are fully appreciated by bricklayers 
and masons. A mortar “works well” when it fills the joints readily, and 
adheres nicely to the bricks or stones. Now, as a matter of experience, if the 
ordinary specification of “ clean angular sand ” is rigidly adhered to, and this 
sand is mixed with a good modern Portland cement (or even in some cases 
with hydraulic lime), the resulting mortar, especially if rich in cement, does not 
work well. 

As a practical matter, therefore, it is frequently advisable to secure a good 
working mortar for brickwork or masonry, even if it is not quite so strong in 
tension or otherwise satisfactory under test, in order to obtain good workman¬ 
ship. The quality of the inspection and the control over the labour will, of 
course, be important factors in arriving at the final decision. 

Similarly, the rejection of odd lots of mortar left over at meal intervals, or 
even over night, is an unending source of friction, especially with quick setting 
cements. While I do not consider the practice an ideal one, I have frequently 
found that if this half-set mortar be mixed in small quantities with freshly made 
mortar, the resulting mixture works very well. In one case, where the results 
of tensile tests were favourable, and the normal mortar worked very badly, I 
found better results were obtained by systematically mixing about the last tenth 
of each batch with the new batch. 

Aggregate.—The most important point is to be certain that the aggregate 
does not contain any chemical calculated to act on, or disintegrate, the cement. 

The deleterious substances most commonly found are :—Soluble sulphates 
in cinders or slag; or, where the cinders are not properly cleaned, in unconsumed 
coal. Such salts sometimes occur in brick bats, which, when otherwise 
satisfactory, form a good concrete aggregate if broken to size. So also, lime in 
the old mortar adhering to the bats may cause trouble. 

The only other case commonly found is that of a limestone aggregate, which 
is occasionally destroyed by acid moorland waters. (See Barrett, P.I.C.E ., 
vol. 167, p. 153.) 

The qualities required in a good aggregate are very much akin to those 
of a good sand, the size of the individual grains being the only marked 
difference. 

The ideal aggregate is a hard, angular stone, with rough surfaces affording 
a good grip for the mortar. A granite road metal may be taken as typical. 

Hard water-worn pebbles are generally held to be less favourable sub¬ 
stances, but they nevertheless form a good concrete, and usually contain a 
smaller proportion of voids. The fact that a water-worn pebble remains hard 
is a very fair indication that it will not disintegrate when used for aggregate. 
In actual practice, any hard material can be used. Very good results have 
been obtained with burnt clay, although this is probably better adapted for a 
concrete with a matrix of hydraulic lime, rather than Portland cement. 

CONCRETE. _As a rule, on all works of sufficient size to justify the cost of a 

machine and its driving power, machine mixing alone is employed in concrete 


974 CONTROL OF WATER 

work ; though I do not consider its advantages justify an engineer in specifying 
it exclusively. 

Mixing machines are of many types. The cubical box rotating round a 
diagonal possesses certain theoretical advantages, but well mixed concrete can 
be turned out by nearly all existing types of machine. A very good test 
consists in placing the sand, aggregate, and cement, separately in the mixer, 
mixing the cement with about io per cent, of some easily recognisable colour¬ 
ing matter, insoluble in water (I usually employ brick dust, sifted so as to be of 
the same fineness as the cement), and then seeing how this colour has spread 
over the mixed mass, testing both dry and with water added. 

The most logical test is to take samples of the mortar, or concrete, from 6 
or 8 different portions of a batch, and to make up separate tests from each 
sample (either briquettes for tension, or cubes for compression). Then 
thoroughly mix the whole batch by hand, and take the same number of samples 
from the mixed heap for testing purposes. If the first set of tests either vary 
materially inter se, or are markedly (say more than 5, to 10 per cent.) weaker 
than those of the hand mixed set of tests, the machine may be considered as 
defective. When applying this method, it is as well to bear in mind that a 
batch mixer gives very similar results, however it may be worked, provided 
that the number of turns is the same ; while a continuous mixer is far more 
sensitive to careless working. Thus, not only are the above tests more easily 
faked for special purposes, but a continuous mixer always needs more rigid 
inspection. 

The usual specification for hand mixing is as follows. The concrete to be 
mixed on a close boarded, or impervious floor, and when dry to be turned over 
at least twice ; then three times after water is added, until thoroughly and 
satisfactorily mixed. 

I consider that concrete should be deposited with as little disturbance as 
possible. I am aware that it was formerly the practice to drop the concrete 
from stages (sometimes specially erected) through a height of 20, or 30 feet. 
Engineers who persist in this practice do not realise that modern cement is a 
substance composed of particles which are far finer than any ordinary sand, 
and are therefore easily sized out, and separated from the sand and aggregate. 
Personally, I am so adverse to any undue disturbance that I view the practice 
of running concrete down a shoot with disfavour, and prefer to deposit it 
in tipping buckets, or better still, in flap-bottomed grabs. It must, how¬ 
ever, be realised that a hard, coherent filling is all that is required in certain 
cases, and under such circumstances any undue restrictions merely delay 
progress. 

The question of very dry, versus very wet concrete, has been the subject of 
much discussion (see p. 396). I believe that a very dry concrete, rammed until 
it quakes, and slightly sweats water, is the ideal mixture. But I am equally 
convinced that competitive contractors cannot be expected to sacrifice their own 
interests, and that administrative working does not justify useless extravagance. 
Thus, since a very dry concrete, insufficiently rammed, produces worse results 
than a wet concrete slapped into place, I believe that the best results are 
obtained by considering the permissible degree of wetness of the concrete as a 
function of the thickness of the work, and its irregularity. For thin walls of 
irregular section, encumbered by metallic reinforcement or expansion joints, 



DEACON'S METHODS 


975 

the use of dry concrete will lead to friction with the workmen, slow progress, 
displacement of the reinforcement, and (despite the best supervision) possi¬ 
bilities of unperceived cavities always remain. Such cavities are most likely to 
occur between the reinforcing rods, and are positively dangerous in such a 
position, since they give rise to corrosion and a lack of adhesion between the 
concrete and the steel. Consequently, the concrete should be wet, and the 
wetness cannot be considered to be excessive unless clear water is found to rise 
to the top of the concrete. The above degree of wetness is only permissible 
when the shuttering is cement-tight, which is best secured by the use of 
tongued and grooved boarding. 

At the other extreme lie wide walls, such as a dam, where the workmen 
can stand and ram, or trample all over the surface of the concrete. 

In such cases the concrete should be mixed fairly dry, and should be 
rammed into place. 

The methods adopted by Deacon ( P.LC.E ., vol. 126, p. 24), may be taken 
as a model, subject to the remarks that they are expensive, and if carelessly 
carried out will produce worse results than concrete which is too wet. 

The cement was slow setting, the specification stipulating that a thermo¬ 
meter when inserted into a jam jar containing freshly made cement plaster 
should not rise more than 2 degrees Fahr. in the first 15 minutes, and 3 degrees 
Fahr. in the first 60 minutes, after making the plaster. This cement was 
mixed with three times its volume of a mixture consisting of 1 part of sand, 
and 2 parts of stone dust from the breakers, which passed through a sieve of 
8 meshes per inch ; and about 6 to 8 per cent, of water was added. The 
mortar thus obtained resembled putty in consistence, but (the amounts are 
not given, but the mortar and the concrete were proportioned in the manner 
indicated on p. 961 so as to be “ voidless ”) when rammed became “jelly like,” 
and resembled a “quicksand,” and was almost impermeable to water. The 
concrete was rammed with beaters made of 5-inch iron plates, 1 foot square, 
with the edges turned up fths of an inch all round. 

With the cement of the present day a greater quantity of water would 
probably be required, but the consistency aimed at is that employed by a 
skilful cement tester when making briquettes for testing purposes. The results 
are good, and with careful supervision 1 foot thickness of concrete made by 
these methods is water-tight under a head of 30 feet, but such results are 
unlikely to be attained by a contractor. 

As a rule, wide walls of the character now considered are constructed of 
concrete, with stone plums or displacers. These are large blocks of sound 
stone (Deacon used blocks up to 6 tons in weight, and his average size was 
about 2 tons ; but, in bridge piers, and such work, 2 to 6 cubic feet is more 
usual) roughly trimmed so as to remove concavities, and set in the concrete, 
generally point end downwards. 

Deacon beat the blocks into place with fifty or more blows from two- 
handed wooden mallets, 6 to 7 inches in diameter, and 14 inches long ; but 

such blocks are usually wriggled or levered into a good bedding in the 

concrete by means of crowbars (see p. 404)* As a rule, these plums are 

separated from each other by at least 4 inches of concrete, so that the plums 

rarely form more than 40 per cent, of the volume. Deacon, however, having 
made a plastic concrete by the method described, found that the plums could 
be packed far more closely, and consequently adopted 1 inch as the minimum 


CONTROL OF WATER 


976 

distance. Blunt tools (“ swords ” and “ slicers ”) were used for ramming the 
concrete into the narrow joints between the blocks. 

It is pure hypocrisy to treat wet concrete as though it were dry, and vice 
versa. The only effect of ramming wet concrete is to bring more “ laitance ” 
to the surface, and to cover it with what is really dead and useless cement, 
which has been drowned by the excess of water. If the concrete is not 
rammed, a smaller quantity of this laitance is produced, and that which is 
produced remains distributed throughout the entire mass. All that wet 
concrete really requires is to be worked with a spade, or blunt tool, in order 
to force it into corners of the shuttering, or between the reinforcing bars. 
Similarly, dry concrete, if not rammed, is liable to form arches, and void 
cavities, are left; also it appears that ramming is actually necessary in order 
to bring the water into contact with the cement, and start the setting of 
the concrete. 

Shuttering. —The design of the forms, or moulds for retaining the 
concrete while setting, deserves consideration. The forms are exposed to 
the pressure of the unset concrete, the pressure, of course, varying not only 
with the wetness, but with the height of fresh material deposited at a time. 
The usual practice is to calculate the stresses as though the concrete were 
a liquid weighing 70 to 80 lbs. per cube foot. General experience therefore 
leads to the following rules, which are introduced mainly to prevent excessive 
deflection of the shuttering. 

A board, 1 inch thick before planing, should be supported by a stud piece 
every 2 feet. If inches thick, every 4 feet, and, in the case of 2 inch boards, 
every 5 feet. 

The experiments of Ashley ( E?igineering News , 30th June 1910) show that 
a wet concrete in walls 3 feet thick produces pressures corresponding to a 
liquid weighing from 63, to 79 lbs. per cube foot, and that these pressures 
increase according to the hydrostatic law {i.e. vary as the depth of wet 
concrete), until at least 6 feet of concrete has been deposited, so that the 
lower boards are exposed to a pressure of 470 to 480 lbs. per square foot some 
five hours after the start of the work. 

In very wide walls (say 5, to 10 feet wide), with extremely wet concrete, 
pressures equivalent to a liquid weighing 150 lbs. per cube foot may be attained. 

Schunk (Engineering News , 9th September 1909) says that if R, be the 
number of feet depth of concrete deposited per hour, the pressure increases 

at this rate until a time T = C + ^, minutes has elapsed. Therefore, the 

maximum pressure may amount to 2-5 CR+375 lbs. per square foot, and, if t, 
be the temperature of the concrete, we have as follows : 

t — 80 70 60 55 50 40 degrees Fahr. 

C = 20 25 35 42 50 70 

so that pressures of 1500 lbs. per square foot may occur at low temperatures. 
The circumstances appear to have been abnormal, and it is but rarely that 
R, exceeds 2 feet per hour, but the matter must be provided for when the 
work has to be pressed forward. 

In grouting work, pressures equivalent to a fluid weighing 125 lbs. per 

cube foot must be provided for, but in such cases the pressure is necessary, 

and is not likely to lead to inconvenience. 

It must be remembered that not only can the individual planks of the 


RENDERING 


977 


shuttering deflect, or break, under these stresses, but that the whole form must 
be supported on rigid frames or struts. Sketch No. 269 shows a good, and a 
bad type for the lining of a canal. The frame on the left-hand side is de¬ 
formable, and even in so small a canal as is here illustrated, cases of an 
excess thickness of 1^ inches of concrete occurred, while half an inch was 
the general value. The details for making frames cement tight need con¬ 
sideration ; in general, tongued and grooved boarding suffices, but if the boards 
are firmly braced together and well covered with soft soap good results are 
obtained with plain edges, especially after the shuttering has been used once 
or twice, and has absorbed moisture, and has had the interstices filled with 
old concrete. 

The precautions required when concrete is deposited on a surface of old, 
set concrete, have been discussed under the heading of Puddle Walls (p. 316). 
While these are effective when properly carried out, all designs in concrete 
should be carefully considered with a view to preventing the occurrence of 
permeable joints. I am fully persuaded that concrete can (with care) be made 
perfectly water-tight. Where cement is expensive, it is highly probable that 
economy can be secured by trusting to walls of a thickness which is not 



Sketch No. 269.—Shuttering of Staines Aqueduct. 


greater than the stresses demand, combined with a sandwiched layer of 
asphalte, or bitumen sheeting. It is, of course, understood that the layer 
outside the sheeting cannot be relied upon to take any portion of the stresses, 
and may therefore be of weaker, and, if necessary, even of permeable concrete, 
just to form a filling. 

Rendering.—Concrete linings to canals and channels are frequentlv rendered 
with a mortar of cement and sand. 

The following specification is typical: 

The concrete walls when well set to be carefully picked over, and rendered 
with two coats of Portland cement, and clean sharp sand, in equal proportions. 
Each coat to be well worked in, and rubbed down with a trowel. The first 
coat to be approximately |fths of an inch thick, and the contractor to remove 
all projections in the concrete where these would cause the coat to be less 
than ith of an inch, and to fill all deficiencies so as to bring the surface to a 
true line and level. The second coat to be §ths of an inch thick. 

The phrase “sharp sand” is merely an interesting relic of the past, since 
impermeability is now the true desideratum. Sharp sand does secure a nice- 

62 


















































CONTROL OF WATER 


978 

looking coat, much admired by local builders, which a rounded sand will 
probably fail to do. In practice, it is unusual to insist upon angular grains, 
even when specified. 

My own experience of such work is unsatisfactory. The facing is good, but 
it is of course costly. Its hydraulic advantages are over-rated. The extra 
smoothness of channel is easily procured with the usual concrete specification, 
by employing planed shuttering, covered with soft soap, and working the 
concrete against the shuttering during deposition, with a spade or fireman’s 
sheer. The rendering is also supposed to make the wall quite impermeable. 
Properly laid rendering is certainly impermeable, but if there is a really open 
joint in the concrete wall, so that the rendering is exposed to any degree of 
hydraulic pressure, it does not possess the necessary strength, and is con¬ 
sequently fractured. 

In cases where impermeability is not absolutely essential a facing of extra 
rich concrete can be deposited simultaneously with the poorer backing, by 
means of a temporary shuttering formed of a piece of plank lifted up as the two 
mixtures are deposited. The fact that this temporary internal shuttering does 
not entirely prevent a mixture of the two grades of concrete, is advantageous, as 
a graduation from the poorer to the richer quality finally exists, which secures a 
union of the two grades, thus preventing any separation caused by differences 
in expansion under heat, or elasticity. 

In general, the richer facing is placed where visible; but from every point of 
view (except that of appearance), the correct position of the richer facing is on 
the pressure side of the wall, i.e. on the water face if it is desired to retain the 
visible water, but on the earth face if the exclusion of ground water is required. 

Facing of Concrete .—I have already referred to the methods of giving 
concrete what may be termed an hydraulically smooth face. Any attempts to 
produce a face resembling dressed stone in smoothness are likely to fail. The 
desired appearance can be secured by carefully trowelling, or working the 
concrete against the shutterings, but the result is rarely permanently satisfactory. 
The smoothness is attained by bringing a skin of cement and fine grains of 
sand to the surface. This almost invariably develops hair cracks, and after a 
year or so the surface resembles a badly disintegrated stone. These cracks 
rarely penetrate below the fine skin, but they effectually destroy the desired 
appearance. If such a facing is demanded, it is best obtained by rendering the 
surface, as already explained. If the appearance of concrete is disliked, two 
better methods exist. Either the whole mass of concrete may be faced with 
masonry, or brickwork, well bonded to the concrete by headers (a useful 
specification being one course of headers to three of stretchers in brickwork, 
and an equivalent if masonry is used). The cost is not excessive, for the facing 
work can be raised, 1 to 2 feet according to its thickness, above the concrete 
before each batch is deposited, thus rendering shuttering unnecessary. The 
more logical method, however, is to produce a rough cast stone face by removing 
the cement and sand to an average depth of about ^th of an inch, by means of 
washes of acid, and brushing over with wire brushes, thus leaving the aggregate 
exposed. In such cases, if a facing layer of concrete with a nice-looking 
aggregate (eg. broken syenite, or granite) is used, a very excellent appearance 
is obtained. 

Expansion Joints. —It will be found that all “monolithic concrete ” (mass 
concrete) structures crack under the influence of temperature stresses. These 


EXPANSION JOINTS 979 

cracks usually occur at intervals of about 40 feet along the length of the work. 
Two remedies suggest themselves. 

The most usual is to place expansion joints at every 30 feet of length along 
the work. The design of expansion joints is simple ; or rather, the simpler 
their design, the better they work. The concrete mass is divided by chase 
joints at every 30 feet in length, and near every marked change in section. 
These joints are run in with asphalte, bitumen, or other elastic material. The 
trade terms for such substances are very varied, and in many cases are 
apparently meaningless. It is best to specify the use, and to ask for a 
guarantee from the sellers. 

The following is a useful specification : 

The expansion joints shall be i\ inch wide, filled in with asphalte, or other 
approved substance. The filling shall be sufficiently elastic to give and take 
with the expansion and contraction of the concrete, without rupturing. Samples 
shall not be decomposed by soaking in water in 2 inch square pats, £ inch 
thick, for three months. Such pats shall not crack when exposed to a tempera¬ 
ture of for days, or flow under pressures of at a tempera¬ 

ture of 

The filling in of the blanks is obvious, and similar tests can be specified in 
order to cover any peculiar circumstances. Thin steel plates, or lead flashing, 
built into the concrete on either side of the open joint (say £-inch wide joints) 
have also been found to give satisfactory results. 

The second method consists in reinforcing the concrete longitudinally with 
sufficient steel to take up the tensile stresses (see Sketch No. 204). The usual 
calculation is as follows : 

The “elastic limit” of steel rods being 60,000 lbs. per square inch, and the 
tensile strength of concrete 200 lbs. per square inch, the area of steel should be 
3^oth of the area of the concrete. 

I do not feel very much impressed by a calculation which departs so far 
from the ordinary practical rules, but mass concrete reinforced with this propor¬ 
tion of steel does not usually crack, and the cracks that do occur can be 
explained by sudden alterations in the section of the work. 

A mass of concrete reinforced in this manner at all sudden variations of 
section and in all thin portions, especially those which are exposed to changes 
of temperature (e.g. the top of a dam, or the parapets of an arch), will rarely be 
found to crack badly. 

Where the character of the work permits, very good results are obtained by 
splitting the concrete up into blocks which do not greatly exceed 30 feet in any 
dimension, laying alternate blocks, and filling in the void spaces later on. The 
joints between the blocks are then in reality cracks of a regular nature, which 
will be found to open and close as the temperature changes, so that the method 
merely regularises the cracks, and does not in any way prevent them. If the 
concrete is faced with brickwork, or ashlar, cracks do not usually appear on the 
face, but in many cases they can be discovered running through the concrete, 
so that the method is one of concealment rather than of prevention. 

The figures relating to the expansion of mass concrete are discussed under 
dams (see p. 398). The circumstances occurring in dams are probably less 
favourable than is the case with mass concrete buried in the earth, so that the 
details there given can be applied to buried masses of concrete with satisfactory 

results. 





CONTROL OF WATER 


980 

In the case of thin walls of concrete which are exposed to the atmosphere on 
both sides, it is doubtful whether any method other than systematic reinforce¬ 
ment, or efficient expansion joints at every 20 to 30 feet, will entirely prevent 
cracking. 

Grouting with Cement. —The theory of this process is very simple. If 
Portland cement is stirred with not too great a proportion of water it mixes 
with the water, forming “grout,” or liquid paste, which contains approximately 
equal proportions of cement and water, and has a specific gravity of about 2. 

This paste flows like a viscid liquid ; and, provided that it is not exposed to 
an excess of water, it sets hard under water, and binds together any stones, 
ballast, or sand, the interstices of which it may fill, into a solid mass of rich 
concrete. It must be carefully noted that if Portland cement is shaken up with 
an excess of water (say more than 1 part of cement to 5 parts of water), the 
resulting mass will not set, and the cement is “ killed ” by the excess of water. 
Consequently, if we can secure that the grout is not unduly diluted by water, we 
can inject it into the interstices of a mass of rubble, stone, or gravel, lying under 
water, and rest assured that it will produce a hard, continuous mass of good 
concrete. 

The above statements must be taken as referring to the majority of 
commercial Portland cements. The published data mainly refer to the com¬ 
paratively coarsely ground cements of the period 1890-1900. My own tests on 
the newer, more finely ground, rotary kiln cements indicate that these are less 
easily killed by water. So far as I am aware, the results of large grouting 
operations with such cements have never been published, although a consider¬ 
able degree of success was obtained under extremely difficult conditions by 
Walker on the Seiswan super-passage of the Sirhind Canal in 1905-07. I there¬ 
fore believe that modern Portland cement is well adapted for grouting opera¬ 
tions, and that a certain admixture of fine sand (to replace the coarse grains 
that existed in the older cements), is probably not only permissible, but is 
actually advantageous. The best, and only reliable test, is of course the practical 
one of grouting up a small mass of rubble, or stone, and sand, under water. For 
specification purposes, a small bulk of cement may be shaken up with say three 
or four times its volume of water, the resulting grout carefully deposited under 
water, and its setting properties noted. 

The advantages are obvious. A hole can be dredged in a river bed and 
loose stone deposited. The grout can then be injected into the stone, and, when 
it has set, a continuous uniform bed of concrete will result, which forms an 
excellent foundation for any work it may be desired to erect. Thus, if it is 
necessary to unwater an area in permeable soil, the area may be dredged out to 
the required depth ; rubble may then be deposited and the whole grouted up. 
When this has set, walls, or coffer dams, can be erected on the concrete, and the 
surrounded area can be pumped dry. If the concrete bottom is sufficiently 
thick, springs and boils are entirely prevented, and the saving in pumping 
plant may amply justify the expense in cement. 

The process is not, however, infallible; and certain conditions must 
necessarily be fulfilled. In the first place, grout, like any other liquid, will 
find its own level, and it must be prevented from leaking away. In the second 
place, if water is injected into the grout during its setting the cement may be 
more or less “killed,” and some or all-of the grout will refuse to set. The 
French term “ laitance ” is a good expression for this dead cement. 


DELTA BARRAGE 981 

The principles are best illustrated by two successful and one unsuccessful 
examples. 

The Delta Barrage (Egypt) was known to stand on a mixture of fine sand, 
broken bricks, and rubble stone, the latter being the remains of the concrete 
which Mougel Bey was obliged to deposit in running water, with the natural 
result that the cement was swept away. It was also discovered (see Hanbury 
Brown, P.I.CE., vol. 158, p. 1) that in other places where masonry or concrete 
had been successfully laid, layers of silt (in some cases more than 2 feet 
6 inches thick) existed, sandwiched in between the masonry. In other cases, 
this silt had been removed, leaving void spaces in the masonry. The work 
was rendered fit to sustain water pressure by systematically drilling 4-inch 
holes through the masonry and concrete, and also as far below the foundation 
level as these holes could be kept open. Grout was then poured down the 
holes until no more was taken in. The top of the holes was some 20 to 30 
feet above the water level in the river. There was no difference between the 
water levels above and below the barrage. Thus, not only was the grout in¬ 
jected under a pressure of at least 20 to 30 lbs. per square inch (the maximum 
value being 37 lbs. per square inch), but there was nothing to cause further 
water to mix with the grout once it had displaced the water originally existing 
in the void spaces and interstices between the rubble and sand. 

The success of these operations, and their effect upon the prosperity of 
Egypt, are the really important facts in the modern history of Lower Egypt. 
It must, however, be remembered that the circumstances were extraordinarily 
favourable. Mougel Bey was certainly one of the most skilful French 
engineers of the nineteenth century, and his designs (in view of their date) 
must be considered as one of those strokes of prophecy which the French 
nation so frequently produces. Had Mougel Bey not been ordered to deposit 
a certain fixed quantity of concrete daily, there is not the slightest doubt but 
that he would have constructed a barrage capable of adequately performing all 
that the present repaired barrage and its subsidiary weirs now effect. As a 
proof, it maybe stated that until the 26th December 1909, the head regulator of 
the Menufiah Canal, which forms part of the Delta Barrage, was as Mougel 
Bey built it, and performed its portion of the work of the barrage satisfactorily. 
We may therefore consider that the grouting merely repaired certain accidental 
failures in construction ; and, had the original design been radically bad, no 
amount of grouting would have produced good results. 

The discoveries made during these grouting operations produced a certain 
distrust (in my opinion unwarranted) of the barrage. Mougel Bey had 
designed the barrage to produce a difference of 13 feet 1 inch in the water 
levels ; and after grouting it actually had sustained 14 feet 3 inches. It was, 
however, decided to produce only 9 feet 10 inches difference in water level at 
the barrage, and an additional 10 feet 6 inches by a subsidiary weir some 3000 
feet downstream. An additional “command” of 6 feet or more was thus 
secured. 

Sketch No. 270 shows the design of the weir, which is only economically 
justifiable by the fact that the financial rewards of success were so enormous 
that any extravagance was permissible, provided that a real success was 
obtained without delay. 

The core wall was constructed as follows ( P.I.CE vol. 158, p. 17). A 
wooden frame (resembling a box with neither top nor bottom) 32 feet 9 inches 


CONTROL OF WATER 


982 

by 9 feet 10 inches, and from 19 to 26 feet high, was formed by driving groups 
of sheet piles 3 inches thick and 4 feet 11 inches (1*5 metres) wide, into the river 
bed. This box was lined internally with sacking, held in position by match 
boards nailed on at intervals of 1 metre. Four perforated pipes, 5 inches in 
diameter, were then fixed vertically at intervals of 8 feet 2 inches along the 
centre of the box. The box was then filled to the desired depth with a mixture 
of rubble stone, with 20 per cent, of road metal, and 15 per cent, of pebbles. 
The proportion of pebbles was possibly somewhat too great to yield the best 
results ; but, per contra, the wall is certainly thicker than required. 

An unperforated 3-inch pipe was then run down inside two of the 5 _ inch pipes, 
and floats adjusted so as to sink in water, but to float on grout, were placed in 
the other two. Grout was then poured steadily, and, as far as possible, con¬ 
tinuously down the 3-inch pipes, until the floats indicated that there was 
about 1 foot 8 inches (o‘5 metre) in the other 5-inch pipes. The 3-inch filling 
pipes and floats then changed places, and grouting from alternate ends was 



Sketch No. 270. —Weir below Delta Barrage. 


continued in this manner until from 5 to 7 feet (1*5 to 2 metres) of grout had 
been poured in. Work was then stopped until this bottom layer had set solid. 
Thereafter grouting was carried on steadily until the desired height had been 
attained. 

The pouring was thus regulated so as to cause the grout to rise uniformly 
all over the area of the box. In addition, the box was, as far as possible, made 
grout-tight. It will consequently be evident that the necessity for preventing 
the grout from mixing with the water was fully realised ; and, laitance being 
lighter than grout, it will be plain that any laitance produced floated up, and 
finally appeared as a scum at the top of the box. 

The work was quite successful, although it is hard to see how a wall of such 
magnificent dimensions could possibly fail, unless the construction was radically 
bad, and almost vile in quality. 

Let us now consider an unsuccessful piece of work. The Staines reservoir 
supply channel was of the section shown in Sketch No. 269. The concrete side 
considered as a retaining wall was avowedly weak, and the design is perfectly 
justified^once it is realised that the channel is only the first of a series, and that 
























































STAINES RESER VOIR 


983 


it will later be supported on either side by additional channels. In one place 
the channel crossed a bed of peaty soil overlying gravel, carrying water which 
was flowing somewhat rapidly at right angles to the line of the channel. The 
probability of failure had been recognised, and special designs for strengthening 
the wall were prepared as soon as the soil was exposed in the excavation. As 
a mattei of fact, the wall did not fail; but open horizontal joints were formed 
in the concrete, due to the cement having been washed out before it had set. 
It was theiefore decided to inject grout, and to see whether this would suffice. 
Grout was consequently pumped into the wall and soil, under a pressure of 
about 40 to 50 lbs per square inch. The results were unsatisfactory; and the 
wall was repaired with brickwork, and was strengthened against the abnormal 
thrust of the peat by jack arches. The failure of the grouting process had been 
predicted, and the reasons are obvious. 


In the first place, it was impossible to prevent water flowing from the gravel 
through the open joints into the channel, while the grout was setting. The 
gravel was apparently traversed by a stream of water under a pressure which 
was greater than that of the water in the channel. 

Secondly, the joints which had to be grouted were thin, and were 
horizontally directed ; and, in consequence, laitance accumulated in a layer at 
the top of each joint. Union between the grout and the horizontal under side 
of each block of concrete which roofed a joint was thus prevented. The peat 
also formed a very efficient filter for retaining the particles of cement. 

The principles of grouting work are now plain. A viscid liquid is dealt 
with, which does not readily fill thin cracks (especially if they are horizontal), 
and which carries on its surface a deposit of useless scum (“laitance 5 '). Thus, 
grouting is only likely to prove successful when the interstices which have to 
be filled are fairly large (although not so large as to cause the grout to be 
drowned), are not traversed by flowing water, and are not roofed by flat or 
concave surfaces, which will either catch the laitance, or will prevent the 
grout from expelling air or water. 

When rough rubble stone is grouted up in the manner described above, 
the volume of cement used is about 35 to 40 per cent, of the volume occupied 
by the stone. In coarse sand the expenditure of cement is generally slightly 
less (say 30 to 35 per cent.) ; but it must be realised that to satisfactorily grout 
any material which is finer grained than fine gravel is a difficult matter, and 
should only be attempted under very favourable circumstances. 

If regular blocks of stone are fitted together, so that horizontal joints do 
not occur ( e.g . brickwork laid dry, with the courses inclined at 45 degrees to 
the horizontal, or hexagonal blocks as shown in Sketch No. 270), the proportion 
of cement may be reduced to 10, or even 6 per cent. It is, however, obvious 
that the greatest advantage of subaqueous grouting work is then lost, as the 
blocks must be laid by a diver. 

Certain small scale operations (100 to 150 cube feet) of my own enable me 
to state that this procedure will produce far more satisfactory results than 
the usual method of depositing 3 to 1 concrete (actually 1 cement to 4 of sand 
and aggregate) in bags. The dry brickwork is not easily laid so as to fill up 
irregular cavities, and the method is best adapted for plugging square wells. 

Artificial Methods of producing Impermeable Concrete or 
Mortar. —The principle underlying these methods consists in mixing some 
extremely fine grained substance with the cement, or mortar, in order to fill 


CONTROL OF WATER 


984 

the void spaces which probably exist, either between the cement grains, or 
due to the concrete not being voidlessly proportioned. Theoretically, I believe 
the substance should be a colloid, but this term is at present employed 
somewhat loosely. 

The dangers are obvious. No doubt the substance can fill the voids, but 
there is no certainty that it will not go further and insert itself between the 
particles of cement, and prevent their union. Thus, any local excess of the 
“filler 5 ’ may produce weakness, and tests of samples mixed under laboratory 
conditions can hardly be regarded as showing what may happen if the large 
scale mixing is carried out with ordinary commercial care. 

The typical process is Sylvester’s. This consists in producing a filler by 
mixing about 1 per cent, of powdered Castile soap, and 1 per cent, of alum 
(reckoned on the volume of the cement) with the cement. The mortar 
produced is water-tight, and works nicely. I have been accustomed to use 
the process regularly when building brickwork walls in hydraulic lime mortar 
for fixing gauging notches, and these walls were invariably “drop tight,” even 
under the most refined tests. The walls, however, were always proportioned 
so as to be capable of resisting the water pressure even if the mortar possessed 
no tensile strength, and samples of the mortar taken from the workmen’s pans 
were invariably 5, or 10 per cent, weaker under tensile tests than similar 
samples which were not treated by Sylvester’s process. In careful laboratory 
work, however, this difference did not occur. The standard Indian practice is 
to apply the Sylvester process to a 1 inch, or 2 inch facing layer of the mortar 
only, or to lay the face course only of a brickwork wall in Sylvestered 
mortar. Even under this restricted application, the process has not found 
much favour, and is usually regarded as a substitute for careful workmanship 
in the whole wall. 

Gaines (Trans. Am. Soc. of C.E., vol. 59, p. 165) has proposed the following : 

(a) About 1, to 2 per cent, by weight of alum in the water used for mixing 
concrete, or, 

(b) To substitute finely ground powdered clay for from 5, to 10 per cent, 
of the cement. 

(c) A combination of both processes. 

The mortar produced is far more impermeable than untreated mortar of 
the same proportions, and the 7, to 28 days’ tensile tests show a gain in 
strength. This cannot, however, be considered as ensuring that the concrete 
thus made will be permanently stronger, since high initial tensile strength is 
often found to be accompanied by a comparative decrease in strength two or 
three years after making. 

The present state of the question appears to be that the impermeability of 
all concretes, or mortars, can be increased by an admixture of inert fillers of 
the character described above. In small works which are carefully inspected, 
where impermeability is the great desideratum, the processes may be employed 
with advantage. In large work, until further experience has been accumu¬ 
lated, the risk of a decrease in strength is too great to be lightly undertaken. 
Reference is made to the discussion concerning clayey sands on page 972. 

Wells .—The methods employed in sinking shafts, or tunnelling, under 
water, by means of compressed air, can only be advantageously treated by a 
specialist. The following section is therefore devoted solely to the considera¬ 
tion of the open brickwork well used in India. 


INDIAN WELL CURB 


985 

Sketch No. 271 shows a typical well curb. The brickwork is built on this 
curb to about 10 feet high ; and, when set, the well is sunk about 10 feet. A 
fresh height of brickwork is then built, allowed to set, and the well is again 
sunk. The object being to produce a cut-off wall, or stop against percolation, 
the well is square in section, and the distance between adjacent wells should 



not exceed 6 inches. The methods adopted in order to grout up, or close the 
space between two adjacent wells are discussed on page 9 ^ 3 " 

A well of this design can be sunk in sand, if fairly free from boulders or 
tree trunks, to depths of 30 or 40 feet below subsoil water level by removing 
the sand from its inside with a Bell’s grab, or any usual type of small dredger. 
Bell’s grab being adapted to work close up to the corners of the well is more 















































CONTROL OF WATER 


986 

efficient than the “ orange peel ” shaped grabs. The volume of sand removed 
is roughly about twice the volume of the well, and this fact is in no way 
disadvantageous, since the sand forms a very cheap loading for the well, and 
the quantity removed from the well usually suffices to produce the required load. 

For greater depths, or for gravel, or clayey sand, and especially if tree 
trunks or large boulders occur, the services of a diver are usually required, or 
compressed air must be used to enable the bottom of the well to be excavated 
in the dry. 

The usual Indian applications of wells are sufficiently illustrated by 
Sketches Nos. 182, 192 and 200. 

The Indian well-sinkers form a distinct trade, and are good divers, so that 
difficulties connected with the alignment and spacing of the wells but rarely 
arise in India. In countries where well-sinkers are less skilful the engineer 
must be prepared to send a diver to the bottom of one well out of every 
twenty, and then remove a cube yard of material, so that a diving dress must 
be provided. 

In India the filling of these wells is usually effected by depositing a layer 
averaging about 3 feet in thickness, consisting of rich hydraulic lime concrete 
laid over the bottom of the well. When this has set, the well should be filled 
with pure sand, or weak concrete, and this covering should be capped with 
2 or 3 feet of arched brickwork. 

Metallic Construction as Applied to the Control of Water.— 
The following notes may appear somewhat disconnected, but when the 
conditions under which a civil engineer procures ironwork at the present date 
are considered, it is believed that they will be found to contain all the informa¬ 
tion that can be utilised with advantage. 

Under present-day conditions iron structures are usually manufactured in 
large, well equipped workshops, employing draughtsmen who should be far 
better able to design the details of ironwork than any hydraulic engineer. If 
this is not the case, the hydraulic engineer has selected the wrong contractor ; 
and his best efforts will probably be so hashed in construction that the final 
result is worse than the contractor’s unaided inefficiency would produce. In 
certain cases, however, hydraulic engineers are still forced by local conditions 
to construct ironwork (usually small structures only) locally. In these cases, 
the tools and workmen available usually set certain limits to the possible con¬ 
struction. Thus, the problem of the design of the details, and possibly even 
of the large members, is not so much the selection of the absolutely best 
design, as of the best design that can be constructed by the available tools and 
labour. In such cases, therefore, low working stresses should be assumed in 
calculation ; and, in particular, ample rivet area should be provided. 

In making sketch designs for contractors, however, most hydraulic 
engineers appear to be unaware of the cheapness of planing, or surfacing work, 
when effected in a well equipped machine shop. As a general rule, whether 
steel or cast iron work (and even more so in the case of brass, or bronze work) 
is considered, wood, lead, or felt packing is nowadays quite unnecessary, and a 
good faced metal to metalwork joint is usually quite as cheap, and is almost 
invariably well worth its extra cost. This remark does not apply to grouted 
joints, or to injections of grout for filling up cavities. Cement grout is a good pre¬ 
servative of metal work, and can be renewed, if necessary, during ordinary 
maintenance. It is, however, obviously inadvisable to design a joint for thin 


METALLIC CONSTRUCTION 987 


lead packing, or metal to metal, and to afterwards expeqt an injection of grout 
to compensate for defective workmanship. Thus, joints which are intended to 
be grouted should be designed with that object in view. 

The following peculiarities of hydraulic construction are, however, frequently 
not entirely realised by the designers of ironwork, and are therefore set forth. 
The notes are divided into the two following classes :— 

Class I .—I believe that these peculiarities are absolutely certain facts, and 
would consider myself justified in insisting on the modification of any design 
that, in important portions of the structure, was not in accordance with these 
conditions. 

Class II .—I consider that these peculiarities are important, but I realise 
that the general agreement of engineering opinion concerning such matters is 
by no means well established. Some of them may therefore appear to be 
merely personal fads. In my own practice I have been accustomed to consider 
all of them as of only slight importance. In most cases they are merely matters 
to be discussed with the draughtsman, and his views may usually be accepted 
if he can show any reason for their adoption beyond: “That was how I 
happened to put it on the paper.” Subject to these remarks we have as 
follows : 

Class I. (General Design). —Most of the metallic structures employed by 
hydraulic engineers are of such a size in relation to the stresses produced that 
they are more likely to be deficient in stiffness than in strength. Thus, the 
first test of a structure is concerned with its deflection, rather than the stress in 
pounds per square inch. 

Using Inches as the Unit of Length.— Deflection. —Consider a structure 
loaded in a manner similar to an ordinary beam. 

Let 8 , represent the central deflection, in inches, in the direction in which 
the load acts. 

Let z, represent the angle of slope of the beam at its end. 

Let /, represent the span in inches. 

Let I, represent the moment of inertia of the cross-section of the beam, 
considered in (inches) 4 . 

Let M, represent the maximum bending moment which the beam has to 
sustain, in inch-pounds. 

Let E, represent the modulus of elasticity, in pounds per square inch. E = 
28 to 30 million pounds per square inch for steel. 

The case of a simply supported beam of uniform cross-section, under a 
uniform load of to, pounds per inch run, will be considered in detail. We 
have : 


8 = 


5 w / 4 5 M/ 2 


tvP M/ 


1 — 


since M = 


TVl 2 


384 El 48 El’ ' 24EI 3EI ’ — 8 

Now, the beam is assumed to support plating, or other water-tight material, 
and leakage only occurs where the plating is not continuous, i.e. at the supports 
of the beam, where presumably the plating is keyed or jointed into some other 
water-tight material. The strain that is produced at these joints is proportional 
to iS ; where S, is the length in inches of the seating of the beam on the wall 
or support. The value of z'S, that will permit troublesome leakage evidently 

depends on :— 

(a) The design of the joint. 

(b) The workmanship of the joint. 







CONTROL OF WATER 


988 

but, obviously, if these factors are assumed to be constant, and if S, is assumed 
to be some fraction of /, and the volume of the leakage that produces trouble 

is also assumed to be proportional to /, the value of forms a fair measure of 

the powers of the structure to resist leakage. 

The value usually found in existing hydraulic structures is : 

8 _ 1 1 

7 2000 L 2500 


Assuming that 


8 
l 

8M/5 


2308 7 X 384 


384 El 7x384’ 

Thus, for simply supported beams, I 


or, M/= 


we get 
El 


100,000 I. 


56x5 
Ml 

100,000' 

Similarly, for a beam the ends of which are built in so as to make i— o, we 

find that I = ——. 

500,000 

The formulas for a simply supported beam under a central load of W, 
pounds are : 

W/ 3 Ml 2 . W/ 2 Ml 


8 = 


48 El 12 El’ 


1 = 


16EI 4EI’ 


W l 

since in this case M = —. 

4 

We thus get, I = 


125,000 

These formulae must be applied with judgment, but the process of checking 
a design in the manner thus indicated may be applied with advantage not only 
to the whole beam spanning an opening, but also to those component members 
of a trussed girder which support plating, or other water-tight skins. 

Where the designer’s details are well thought out, as for instance in a case 
where stanching rods are used, or the seats of the beams are supported on 
spherical bearings (see Sketch No. 272), I have passed such values as 
Ml 

I = --—, in a simply supported beam under uniform load. 


70,000 

When cast iron is used, E= 14,000,000 approximately. 
Ml 

Thus, I=——— for a simply supported beam, and 1 = 


Ml 


200,000 


for a built- 

1,000,000 

in beam, and this last formula can rarely be applied, owing to the weakness of 
cast iron in tension. 

Strejigth of Structure .—The above rules usually lead to a structure which 
is of ample strength. In addition, the following rules require consideration : 

No metal exposed to water should be less than fth of an inch thick, and, 
unless the metal can be painted and examined at very frequent intervals, 
this thickness should be increased to fths of an inch. Also, most hydraulic 
structures contain bolts, and any bolt less than fths of an inch in diameter is 
liable to be strained by unduly vigorous tightening. Thus, all members which 
contain bolt holes must be at least fths of an inch thick, and 3 inches wide. 
Consequently, quite apart from stress calculations, anything smaller than a 
inch x 2\ inch x f inch angle, or a 3 inch x f inch flat, is unusual. 
















STONE V SL UICES 


989 

If, however, stress calculations become of importance, the values of the 
working stresses may be taken from the table given below, subject to the 
following remarks : 

The absolute values may be objected to, and for good material and first 
class workmanship I have myself used values 33 per cent, in excess ; and for 
important and badly inspected structures values 20 per cent, in defect, when I 
considered that general circumstances justified their adoption, but I believe 
that the following principles should always be borne in mind : 

(i) Owing to the fact that water loads (excluding water hammer, wave 
action, and shocks by floating bodies) produce no impact stresses, members in 


Stanching Rod, Step coaledrvi/h brass 



© 


-<r- 


$ 


9*61 Beam 
vP Plate Vs. 

,** Clearance r 

- -%ii 


fi 

*1 




& 


JO 


Si 



3 ' 


4' 


Each Snivel tearing transmits atm! 55,000lbs. 
Each Roller carries about 16,000lbs. 
on Lervis Bolls 2 %‘dia. by iZ’Jong 


OH Bolts /'« 18" tong 
Z" Steel Stanching, Rod 





Sluice Gate 



P Faced Plate vtHh countersunk nvdtfng 


site/ stanching ’o—J 
spnna £ 

■ 

tn /1 1 __ J_ 


Beams & h "Plate / Z'S/anchino Rod raised k lonered 
1 r n —— mrishfndsnt v nf Gate 



¥Clearance 


Raised Sill of Regulator 

Sketch No. 272.—Stoney Sluice Bearings. 


3 

«\i 


'^-independently of Gate Each Roller carries about 4000lbs. 

VBolts, heads csk-inJoU. FacingPlale 


compression require a larger factor of safety than members in tension (pro¬ 
vided that the rivet holes in these latter are either drilled or reamed out after 

punching). . . , . , , , , 

(ii) In order to prevent leakage, the shearing area of the rivets should be 

relatively greater than the bearing area when hydraulic work is compared with 

bridge work. 

(a) Tensile Stresses— 

Steel . 


Cast iron 


11,000 to 13,500 lbs. per square inch,—the larger 
value being used when shock is entirely absent. 
1850 lbs. per square inch. 














































































9QO 


CONTROL OF WATER 


(b) Compressive Stresses — 

Steel . . . Pin ends, 11500-44 - lbs. per square inch. 

„ . Flat ends, 11500 — 30 ^ lbs. per square inch. 

In neither case should the stress exceed 11,000 lbs per square inch, and - 

should never exceed 150, where l is the length, and r the radius of gyration = 

fj — of the member considered, in inches. This value may appear much less 

than the corresponding tensile stresses, but it must be remembered that the 
absence of shock in hydraulic works does not materially assist long columns. 

Cast iron . . . 10,000 to 11,000 lbs. per square inch. Cast iron 

should not be used for long columns. 

Riveting Stresses — 

Shear . . . 9,000 lbs. per-square inch. 

Bearing . . .15,000 lbs. per square inch. 

Bearing Pressures. —The question of the bearing pressures produced by 
water loads now deserves consideration. These are generally very large rela¬ 
tive to those occurring in ordinary construction. Thus, 300 lbs. per square foot 
is a very heavy load in bridge work, but a pressure of 300 lbs. per square foot is 
attained in water at a depth of 5 feet, and, if allowance is made for the fluctua¬ 
tions of the water level, is, practically speaking, the smallest intensity of load 
ever considered ; while such pressures as 6000 lbs. per square foot are by no 
means unknown. 

Thus, the pressures on, and consequently the frictional forces resisting the 
motion of, sluice gates and valves, are very large. 

The principle of the balanced valve can obviously be applied to such heads 
as 50 or 100 feet of water. 

If, however, an ordinary sluice gate is considered, the complications attend¬ 
ing the use of a balanced valve are plain. Thus, in the usual design the heavy 
pressures are accepted as a fact, and endeavours are made to minimise the 
coefficients of friction. The coefficient of friction of metal on metal is about 
0*15 to 0*20 for machined surfaces under water (not rusted) ; but, unless the 
sluice gate is frequently moved, sticking may occur. In practice it appears 
inadvisable to design the gearing which opens the sluice gates for stresses less 
than those produced by a force resisting motion of one half the total pressure 
on the gate ( i.e . coefficient of friction = o'5o). The ordinary power required, 
however, will not greatly exceed two-fifths of that calculated on this assumption. 

As a rule, the gate is mounted on wheels. Since the greatest force is 
required to start the motion, the initial friction should be diminished as far as 
possible. Roller bearings form the best solution. 

Ball bearings have also been used, but invariably give trouble by corrosion, 
not at the point of contact of the balls and the ball races, but at a small distance 
away from this point. As this action may occur even in ball bearings which 
are filled full of vaseline and are not exposed to water, it appears impossible to 
prevent it. 

Owing to the slow speed at which sluice gates and other hydraulic machinery 
move, the important value of the coefficient of friction is that which occurs 
when starting motion. According to Stribech (, Ztschr . D.I. V. t 1902, p. 1464) : 




ROLLER BEARINGS ' 991 

Let St be the total number of rollers, b inches in length, and d inches in 
diameter, which carry a total load of P lbs., from a shaft of r inches radius. 
I hen, the maximum pressure is given by 

, 5 P 

^ = zbd bs * per s< l uare inc h> 
and the moment resisting motion is given by : 

M = i *2 P/-^$ inch-lbs. 

where D 0 = 2 r+~, 
z 

and if: 

4 2 7 ° 106 142 213 lbs. per sq. inch, 

/= o*ooi8 0*0013 0*0011 0*0009 0*0007 inches, 

these values also hold very approximately for initial motion. 

The safe working load in pounds is given by Le Guern : 

{D + Kx io} 2 x 14 

When D = diameter of roller in inches. 

K = coefficient (given in the following table): 


Dia. 

K 

Dia. 

K 

Dia. 

K 

1 

4 

0*1 

11 

1 C 

0*625 

*1- 

1*15 

5 

TF 

°‘ I 75 

3 

4 

0*7 

Itc 

1*225 

3 

8 

0*25 

13 

1 6 

0775 

4 

i '3 

7 

TF 

°‘ 3 2 5 

7 

8 

0*85 

1 iV 

i '375 

1 

F 

0*4 

1 5 

TIT 

0*925 

4 

i *45 

9 

TF 

°*475 

I 

1*0 

I TF 

1 *5 2 5 

5 

8 

°’55 

j tV 

i*o 75 

l| 

1*6 


The Stoney sluice is a well-known device. The live roller train reduces 
the total friction either initial or during motion to about 1 per cent, of the water 
and dead load. Sketch No. 272 shows the details of stanching rods and roller 
trains found in modern work. 

The contrast between Fig. 1, which is adapted to a gravel-bearing river, and 
Fig. 3, which shows modern Indian practice in rivers carrying fine sand only, is 
instructive, and should be followed in future designs. 

Class II. (Special Cases).—In all gearing work, worms seems to be preferable 
to toothed wheels. It would appear that the slight sliding motion that occurs 
in a worm and wheel is more effective in preventing rust than the rolling of one 
tooth over another, such as occurs in toothed wheels. 

For securing water-tightness I have been accustomed to rely mainly on 
stanching rods (Sketch No. 272), as used in Stoney gates. A wooden stanching 
rod, weighted with lead or iron at the lower end, fitting roughly into a brickwork 
and wooden groove, will be found very effective, provided the wooden rod is not 
too rigid. 

In cases where stanching rods are not advisable, a metal-to-metal fitting of 



















992 


CONTROL OF WATER 


the sluice gate to a rigid cast iron bearing plate appears to be the best design. 
Spherical seated bearing plates rapidly become useless when submerged. 

Plating .—The joints of plating are not generally exposed to tensile stresses, 
and should be designed according to the rules for boiler work. 

Leakage has been successfully prevented with far less rivet work by packing 
each joint before riveting up with tape, well covered with red lead. The 
practice has been permanently successful in the case of gas holders, where 
the conditions, apart from the pressures sustained, are quite as exacting 
(possibly more so) as in sluice gates. In sluice gates the process is apparently 
new, and one gate thus caulked certainly leaked badly ten years after installa¬ 
tion. The plating of sluice gates may be proportioned either for strength or 
for deflection. 

Plating of Gates .—The following investigation, in so far as it concerns the 
thickness of plating, may be regarded as applicable to such sluice gates as 
occur in irrigation and power canals. These gates are worked under the 
following conditions : 

(a) Should the plating become entirely corroded, temporary repairs can be 
made with wood or cloth packings ; and opportunities for permanent repairs 
occur, at the very worst, at least twice a year. 

{&) The gates can be overhauled and inspected in the dry at least once a 
year. Under circumstances such as occur in sluice gates, closing the draw¬ 
off tunnels of reservoirs, or the filling gates of locks, the question of possible 
failure by corrosion is important, and an ample margin in excess of the 
thickness indicated below must be allowed. 

The plating of a sluice gate may be considered as continuous over two 
spans, between three stiffeners, at least; and as subjected (except in the 
plating close to the water surface) to a uniform load of 0^43 D, lbs. per square 
inch, where D, is the depth in feet below the water surface, measured either 
to the centre or bottom of the interval between the three stiffeners considered. 

Let t, represent the thickness of plating, in inches. 

/, the span of the plate between the stiffeners, or cross girders, in inches. 

The deflection 8 is represented by : 

*2’04/ 4 xo’ 43 D x 12 
EP 


where, E, is the elastic modulus for steel; that is to say, 28 to 30 million pounds 
per square inch. 

Hence, if 8 — ~, we get: • 

n K 

where we have : 

72 = 500 1000 1500 2000 2500 3000 

K = i29 102 89 82 75 71 

Similarly, if the plating is not continuous over two spans, but is fixed at 
each support, we obtain a similar equation : 

where K^i^K 
•K-l 

So also, for strength, we have, if /, be the stress on the plating in pounds 
per square inch, reckoned without deductions for rivet holes :— 

(i) Plating continuous over two spans : 


/V D 
N 






PLATING 


993 


(ii) Plating, not continuous, but fixed at the ends of each span : 

where Nj = T23 N 
N]_ l j 

and the values of N, are : 

/ = ioooo 12500 15000 17500 20000 lbs. per square inch, 

N = 175 196 215 232 248 

As an example, take D = 12 feet, n= 1000, and inches. 

Thus, we get /= L ° j. ^r g inches = ^ 2 - = 14 inches, 

V12 2-29 ^ ’ 

and for this value of /, N = — X l6 ^ 12 = 44-8X3*46= 155, or, 7=8850 lbs. per 
square inch, approximately. 

Allowing for rivet holes, the stress in the plates at the line of rivets over 
the centre girder is probably about 10500 lbs. to 11000 lbs. per square inch. 

62’S 

If we take j— 12500, we get /=— y= 17*5 inches, 

, 17*5 x 16 , , „ . „ / 

and K= —x 2*29= 56 x 2*29= 129, corresponding to a deflection of 

or 0 035 inches. 

For the portion of the plating near the top of the tank, or sluice gate, where 

the variation in water load as the depth increases must be taken into account, 

we have a somewhat different set of equations : 

2 ‘55 /r °'43 D x 12 A ft 2 ow „ 

d = -f 2 / 4 - ■ - and f ~2 — = o" 128 1 2 x 0*43 D 

384 IK 6 

where D is now measured to the centre of the span of plating, the upper end 
of which is assumed to lie at the water surface. 

It will be found that the stiffness entirely fixes the thickness of the plating, 
until : 

y^_T 90 -i 66 _^i 
,l ' Vd “k 

which, even under such abnormal conditions as f— ioooo lbs. per square inch, 
^=500, gives : 

D o.i66 = I75 = I . 35 or d=6'o 8 feet, 

129 

while the more reasonable conditions,/= 12500 lbs. per square inch, ?i= 1000, 


give : 

J30-166_ j or D = 53 feet. 

Also, the thickness of the plating at the water surface should be sufficient 
to sustain shocks from floating bodies and ice-thrust, if these are likely to 
occur. 

Summing up :—It appears advisable to proportion the plating wholly by 
considerations of stiffness, and to make the absolute deflection under the 

/ 

water load about -at the most. 

1000 

Framing of Gates .—The plating which forms the outer skin of sluice gates 
and water tanks is usually supported on stiffeners. In general, these are made 
of I or channel beams, and in hydraulic work are usually best proportioned by 
stiffness. The rules given on page 988 may be followed for sluice gates. In 
tanks or gates provided with stanching rods, less stiffness will usually be found 

63 












994 


CONTROL OF WATER 


sufficient; and the rule M/= 150,000 I will generally give good results, provided 
the strength is sufficient. 

Framed Stiffeners .—The stresses in a trussed frame stiffener can be ascer¬ 
tained by the ordinary rules. The stiffness, however, is important. 

Let 8 , represent the deflection in any given direction, at any point R, 
in inches. 

Let /, be the length of any member of the truss, in inches. 

Let p, be the stress in pounds per square inch existing in this member, 
under the load that produces the deflection at the point R. 

Let 21, be the stress produced in this member by a force of one pound, 
applied at R, and acting in the direction in which 8 is measured. 

Then, we have § = 

E 

where the summation extends to every member of the truss, and the signs of 
p, and u, must be taken into account. That is to say, on the usual convention, 
p, and u , are positive when they represent compressive stresses, and negative 
when they represent tensile stresses. Thus, for example,/, compressive, and 
u , compressive, gives a positive term, and also p, tensile, and u , tensile ; while 
p, tensile, and u , compressive, gives a negative term. 


As a rule, the central deflection does not exceed 


Span 

2000 


in successful 


examples, but the connection between the central deflection and the liability 
to leakage is plainly not so close as in simple beams under uniform load. 

Water Towers.—The use of elevated tanks as service reservoirs is quite 
common. The principles concerning the hydraulic design of these tanks are 
treated under Service Reservoirs (see p. 612). The following notes are con¬ 
cerned solely with the general form of the tank ; and although the actual wording 
refers to steel plate tanks, the stresses found and the principles laid down are 
equally applicable to tanks built of reinforced concrete. 

Sketch No. 273 shows the ordinary forms. The circumferential stress on 
the cylindrical portion is : 

T = o* 43DR lbs. per lineal inch. (Inches.) 
where D is the depth below the top water level, in feet, and R is the 
radius of the tank, in inches. The details concerning the usual stresses, 
minimum thickness of plating, and workmanship in general, have already been 
considered. 

The stresses in the bottom of the tank are, however, somewhat more 
complicated. 

Consider any point P (see Sketch No. 273). Let the tangent to the bottom 
plating at P, make an angle a with the horizontal. Let r, be the distance of P, 
from the central axis of the tank, in inches. Let W, be the total weight of 
water and metal which lies on the farther side (from the supports) of P. 

Then, the total stress per lineal inch in the plating in a radial direction 
(relative to the axis of the tank) is given by : 


<r= - t -lbs. per lineal inch. 

27rrsina r 

In addition, a circumferential stress r exists in the plating. 

Put p for the radius of curvature of the diametral section of the bottom of 
the tank, in inches. 





WATER TOWERS 


995 


Then, +-±—-—= +o’43D 

p r cot a ~ ° 

where D is the depth in feet below top water level. 

In the only two cases which it is proposed to consider we have : 

(a) Tanks with spherical bottoms, p = radius of the. sphere. 

(b) Tanks with conical bottoms. p = infinity. 

The signs require careful consideration. If we denote compression by a 
positive sign, and tension by a negative sign, the sign of o*43D is always the 

same as that of —-—. 

root a 

In Sketch No. 273 the following four cases are shown : 



Sketch No. 273.—Stresses in Water Tower Plating. 


(See Hutte, vol. iii. p. 231. The sign conventions are different, but the various 
cases are solved in detail for a spherical bottom.) 

We have for : 

(a) Tanks with spherical bottoms. p = r cot a. 

(b) Tanks with conical bottoms. ~ = 0, 

Thus, or and r can be obtained. 

The portion of the bottom near the supports also requires consideration. 
This position is exposed to a radially directed load, which produces a 

circumferential compression ' 

p = Wi_cota, ]bs ($ee Fjg _ No 

27T 

-W.cotai —V^cotai , bs (s£e Fig Na ^ 

° r > 277 

according as the supporting ring is at the outer circumference of the tank, or at 
some distance less removed from the axis of the tank. 


















































996 CONTROL OF WATER 

According to Halphen’s investigation (Fojictions Ellifttiques) the ring will 
preserve its form if: 

P, be less than 

/ a 2 

where a = r 1 cot a 1} or, r x cot a 2 , whichever is the greater, f is a factor of safety. 
I is the moment of inertia of the diametral section of the ring in (inches) 4 , and 
E = 30,000,000 lbs. per square inch. 

The entire sufficiency of this last formula is open to doubt. The dimensions 
are usually determined by the fact that the whole ring has to afford sufficient 
bearing area on the masonry for the load W 1} or W 1 + W 2 , and in good 
examples f is usually about 4, although it is improbable that the designer used 
the above formula. 

The principle of supporting a water tower, not at its outer edge, but some¬ 
where about the middle of each radius, is, however, a good one; and Intze’s 
designs, which make the inner portion spherical and the outer portion conical, 
and W x cot a x nearly equal to W 2 cot a 2 , produce a very pretty result. 

The possibility of making o- and r tensions, or compressions, at choice, enables 
other advantages to be secured. For example, Case III. is very well adapted 
to designs in reinforced concrete, while Case IV. is better fitted for tanks 
constructed of thin unstiffened plates. 

Similarly, if a rectangular tank is considered advisable, the supports should 
be fixed by the following condition : 

Central bending moment in the central span of the bottom beam of the 
tank = bending moment in the projecting cantilevers. 

The only possible objection to these principles lies in the fact that the wind 
stresses in the supporting columns may be increased. As a rule, however, no 
difficulty arises from this cause, and wind stresses are usually only of vital 
importance relatively to the statical load stresses in small tanks. 





TABLES 

The following Tables, if used in conjunction with Diagrams Nos. i to io 
and the ordinary tables of powers and areas employed by engineers, will 
be found to give all the information required in hydraulic calculations. 

LIST OF TABLES. 

No. i. —Velocity Head from to z>= 5’o feet per second 

No. 2.—Values of H 1 5 , from H = o*oo to H = 2'oo .... 

No. 3.— Values of H“ 5 , from H =0*40 to H = i*7o 
No. 4.— Auxiliary Values for Solution of Kutter’s Formula 

Nos. 5 and 6.— -Bresse’s Backwater Function and Bresse’s Dropdown 
Function .... ... 

No. 7.—Punjab Watercourses .... • 


PAGE 

998 

999 
1002 
1004 

1006 

ion 


w 


993 


CONTROL OF WATER 


TABLE No. i.—VELOCITY HEAD FOR USE IN 
WEIR CALCULATIONS 

<r/2 

Values of H=—, or Heads due to Velocities 

2 'g* 

from o to 4‘99 Feet per Second. 


Velocity 
in Feet per 
Second. 

Head in Feet. 

Velocity 
in Feet per 
Second. 

4 \ A \ ^ 

Head in Feet. 

0*0 

0*0000 

2*5 

0*0972 

0*1 

0*0002 

2*6 

0:1051 

0*2 

0*0006 

2*7 

0*1133 

0’3 

0*0014 

2*8 

0*1219 

o*4 

0*0025 

2*9 

0*1307 

o*5 

0*0039 



o*6 

0*0056 

3*° 

0*1399 

07 

0*0076 

3* 1 

0*1494 

o*8 

0*0099 

3*2 

0*1592 

°*9 

0*0126 

3*3 

0*1693 



3*4 

0*1797 



3*5 

0*1904 

1*0 

O'O^S 

3‘ 6 

0*2015 

i*i 

0*0188 

3*7 

0*2128 

1*2 

0*0224 

3-8 

0*2245 

i*3 

0*0263 

3*9 

0*2365 

i*4 

°*°3°5 



i*5 

0*0350 

4*o 

0*2487 

i-6 

0*0398 

4*i 

0*2613 

17 

0*0449 

4*2 

0*2742 

i*8 

0*0504 

4*3 

0*2875 

i*9 

0*0561 

4*4 

0*3010 



4*5 

0*3148 



4*6 

0*3290 

2 ‘0 

0*0622 

4*7 

0*3434 

2 ’1 

0*0686 

4*8 

0*3582 

2*2 

0*0752 

4*9 

o*3733 

2*3 

0*0822 



2*4 

0*0895 

5*° 

o* 3 88 5 


This table is based on 2^=64*32 ; and, if the usual 2£-=64'4 be used, the 
fourth place of decimals will be found in error, being about one unit too high 
from v=2’6 to v = y6, two units up to v = 4*4, and three units beyond. 

A more complete table by hundredths of a foot in v is given by Horton 
(Weir Experiments) and others. Reference is made to page 157 of Horton’s 
treatise for a complete bibliography concerning weir tables. 
























i-5 POWERS 


599 


TABLE No. 2.—VALUES OF H 1& 


H 

H 1 ' 6 

H 

H 1 ' 5 

0*00 

0.0000 

0*40 

0*2530 

0*01 

0*0010 

0*41 

0*2625 

0*02 

0*0028 

0*42 

0*2722 

°’°3 

0*0052 

o *43 

0’2820 

0*04 

0*0080 

0*44 

0*29I9 

o-o5 

0*01 12 

°*45 

°*3 oi 9 

o*o6 

0*0147 

0*46 

0*3120 

o’o7 

0*0185 

0*47 

0*3222 

o*o8 

0*0226 

0*48 

°*33 2 5 

0*09 

0*0270 

0*49 

0*343° 

0*10 

0*0316 

°'5° 

°'353 6 

0*11 

°*°3 6 5 

°'5 I 

0*3642 

O ’ I 2 

0*0416 

0*52 

0*375° 

0*13 

0*0469 

°'53 

o *3 8 5 8 

0*14 

0*0524 

°’54 

0*3968 

0-15 

0*0581 

°’55 

0*4079 

0*16 

0*0640 

0*56 

0*4191 

0*17 

0*0701 

°‘57 

0*4303 

0*18 

0*0764 

0*58 

0*4417 

0*19 

0*0828 

o *59 

°*453 2 

0*20 

0*0894 

o*6o 

0*4648 

0'2 I 

0*0962 

o*6i 

0*4764 

0*22 

0.1032 

0*62 

0*4882 

0*23 

0*1 103 

0*63 

0*5000 

0*24 

0.1176 

0*64 

0*5120 

0*25 

0*1250 

0*65 

o* 5 2 4 o 

0*26 

0*1326 

o*66 

0*5362 

0*27 

0*1403 

0*67 

0*5484 

0*28 

0*1482 

o*68 

0*5607 

0*29 

0*1562 

0*69 

o *573 2 

°’3° 

0*1643 

0*70 

o* 5 8 57 

0 '3 1 

0*1726 

0*71 

°'59 8 3 

0-32 

0*1810 

0*72 

0*6109 

°*33 

0*1896 

°’73 

0*6237 

o '34 

0*1983 

0*74 

0*6366 

0*35 

0*2071 

o *75 

0*6495 

0*36 

0*2 160 

0*76 

0*6626 

°'37 

0*2251 

0*77 

0-6757 

0*38 

0*2342 

0 

OO 

0*6889 

0*39 

0*2436 

0*79 

0*7022 






























IOOO 


CONTROL OF WATER 


Table No. 2— continued . 


H 

H 1S 

I 

H 

h 1 : 6 

o*8o 

o'7i55 

1*20 

1 *3 I 45 

o*8i 

0'7290 

I *21 

I *33 I ° 

0*82 

0'7425 

1*22 

i*3475 

0-83 

O756 2 

1*23 

i ‘3 6 4 i 

0*84 

0*7699 

1*24 

1*3808 

’ 0-85 

0*7837 

1*25 

i*3975 

o’86 

07971 

1*26 

1*4144 

0*87 

0*8115 

1*27 

i*43 12 

o-88 

©•8255 

I *28 

1*4482 

0*89 

0*8396 

I ‘29 

1*4652 

0*90 

0*8538 

1*30 

1*4822 

0*91 

0*8681 

1*31 

1*4994 

0*92 

0*8824 

1*32 

1 *5166 

°*93 

0*8969 

i*33 

i*533 8 

0-94 

0*9114 

i*34 

I *55 12 

°*95 

0*9259 

i*35 

1 *5686 

0*96* 

0*9406 

1 *36 

1 *5860 

°’97 

o'9553 

i*37 

1*6035 

0-98 

0*9702 

1*38 

1 *6211 

°*99 

0*9850 

i*39 

1*6388 

I *00 

1 *oooo 

1*40 

1*6565 

1*01 

1*0150 

1*41 

1-6743 

I *02 

1*0302 

1*42 

1*6921 

I *°3 

1*0453 

i*43 

1 *7100 

1*04 

I *0606 

i*44 

1 *7280 

i*°5 

1*0759 

i*45 

1*7460 

1 *06 

1*0913 

1*46 

17641 

1-07 

1*1068 

i*47 

1*7823 

1*08 

1 *1224 

1*48 

1 *8005 

i'o9 

1*1380 

i*49 

1*8188 

1*10 

I * I 537 

i*5° 

1*8371 

i'ii 

1*1695 

i*5i 

1 '8555 

1 ’ 12 

i' i8 53 

1*52 

1*8740 

i'i3 

1*2012 

I *53 

1*8925 

ri4 

1*2172 

r 54 

1*9111 

I'iS 

I*2332 

i*55 

i *9 2 97 

ri6 

1*2494 

1'56 

i*9484 

i*i7 

1*2656 

i*57 

1 *9672 

i'i8 

I *28l8 

i*5 8 

1 *9860 

i*i9 

I *2981 

1 59 

2*0049 

V. 0 

















































i*5 POWERS 


IOOl 


Table No. 2— continued. 


H 

■ 

H 1 5 

! 

H 

\ ) t 

H 1 ' 5 

1 *6o 

; * V,. f 

2*0238 

*.♦•»# . 1 

1 *8o 

2*4150 

i*6i 

2*0429 

1 *81 

2 - 435 1 

1‘62 

2*0619 

1 *82 

2 ’4553 

1*63 

2*0810 

•' 8 3 

2’4756 

1 64 

2*1002 

I*84 

2*4959 

1-65 

2*1195 

1*85 

2 * 5 i6 3 

1 *66 

2T388 

i*86 

2 * 53 6 7 

1*67 

2*1581 

1*87 

2 ’ 557 2 

168 

2*1775 

i*88 

2*5777 

1 ‘69 

2*1970 

1-89 

2*5983 

0 

w 

2-2165 

1 '90 

2*6190 

i * 7 1 

2*2361 

1*91 

2*6397 

172 

2*2558 

1 -92 

2*6604 

173 

2*2755 

I# 93 

2*6812 

1 74 

2*2952 

1*94 

2*7021 

175 

2 , 3 i 5 ° 

i ’95 

1*7230 

176 

2*3349 

1*96 

2*7440 

177 

2*3548 

1*97 

2*7650 

178 

2*3748 

1*98 

2*7861 

179 

2*3949 

i *99 

2*8072 



2*00 

2*8284 


1*5 

The original authority for the tables of H ' is believed to be Francis 
(.Lowell Hydraulic Experiments). The most complete set, covering thousandths 
of a foot from o to 1*49, and hundredths of a foot up to 12 feet, is given by 
Horton (Weir Experiments). No tables which permit quick calculation when 

the head is measured in fractions of an inch are known to me, and conversion 

\ \ * ( 1 

into decimals of a foot on the basis 


Inches . 

1 2 

3 

4 

5 

6 


Peet . 

0*08 0*17 

0*25 

o*33 

0*42 

0*50 




7 

8 

9 

10 

11 



o* 5 8 

0*67 

o *75 

0*83 

0*92 


is usually sufficiently accurate. The American Well Works publish a very 
excellent table of discharges based on Francis’ formula, by sixteenths of an 
inch, but the results are given in U.S. gallons per minute. 















































1002 


CONTROL OF WATER 


TABLE No. 3.— VALUES OF H 2 ' 5 
FOR USE IN CALCULATING DISCHARGE OF 
TRIANGULAR NOTCHES 


H 

H 2 ' 6 

H 

H'25 

0*40 

O'IOI 2 

o*75 

O-487I 

0*41 

CIO76 

0-76 

0-5036 

0*42 

°' II 43 

o*77 

0-5203 

o*43 

0*1213 

0*78 

°'5373 

0-44 

0*1285 

o*79 

o*5547 

o*45 

°‘ I 359 



0*46 

OI 435 

o’8o 

0-5724 

°*47 

0 *I 5 I 4 

o*8i 

°' 59°5 

0*48 

0 'I 596 

0*82 

0*6089 

°'49 

0*1681 

0-83 

0-6276 



0*84 

0*6467 

0*50 

0*1768 

0-85 

0*666l 

°‘ 5 I 

°-i857 

o*86 

0-6859 

0-52 

0 - 195 ° 

0*87 

0*7060 

°’53 

0-2045 

o-88 

0*7264 

o‘54 

0-2143 

0*89 

0-7472 

°*55 

0-2244 



0*56 

0-2347 

0*90 

0-7684 

o*57 

°’ 2 453 

0*91 

0*7900 

0-58 

0*2562 

0-92 

o*8i 18 

°*59 

0-2674 

°*93 

0 - 834 1 



0*94 

0-8567 

o*6o 

0*2789 

o*95 

0*8796 

o‘6i 

0*2906 

0*96 

0*9030 

0*62 

0*3027 

o*97 

0*9266 

0*63 

o'3 I 5° 

0*98 

0-9508 

0*64 

0-3277 

o*99 

o*9752 

0*65 

0-3406 



o*66 

°'3539 

I’OO 

1*0000 

0*67 

0-3674 

1*01 

1*0252 \ 

o-68 

0*3813 

I *02 

1*0508 

0*69 

°*3955 

1-03 

I -0767 

! 


1*04 

I -1030 

070 

0*4100 

r °5 

1*1297 

0-71 

0-4248 

1*06 

i * t 568 

072 

0-4399 

1 07 

1-1843 

°*73 

°’4553 

1*08 

1*2122 

074 

0*471 1 

1*09 

1*2404 












2'5 POWERS 


Table No. 3— continued. 


H 

H 2 ' 5 

no 

1 ‘2691 

i'll 

1*2982 

1*12 

1 *3 2 7 5 

1*13 

1 ‘35 73 

i*i4 

''3875 

i-i5 

1*4182 

i*i6 

1'449 2 

1*17 

1*4807 

i*i8 

i ' 5 I2 6 

1*19 

i'5448 

I ’20 

1 *5 7 74 

1*21 

i ’6io5 

1*22 

1*6440 

1*23 

1*6778 

1*24 

1*7122 

1-25 

1*7469 

I - 26 

1 7821 

I'27 

1*8176 

1*28 

i,8 53 8 

I ’29 

1*8901 

1-3° 

1*9269 

I ’3 I 

1*9642 

1 ’3 2 

2*0019 

1 ‘33 

2*0400 

1 ‘34 

2*0786 

i35 

2*1176 

i*3 6 

2 * i 57° 

i*37 

2*1968 

i*3 8 

2 ' 2 37 I 

i'39 

2*2779 


H 

H 2 6 

I 

1*40 

2 '3 I 9 T 

1 '4 1 

2*3608 

1 '42 

2*4028 

i‘43 

2 *4453 

i*44 

2 ’4 88 3 

i'45 

2 '53 I 7 

1*46 

!*575 6 

i*47 

2*6200 

1*48 

2*6647 

1*49 

2*7 IOO 

i*5° 

2 *7557 

I *5 I 

2*8109 

r 5 2 

2 ’ 8 4 8 5 

!*53 

2*8956 

I *54 

2 *943 I 

i*55 

2*9910 

i*5 6 

3*°395 

I *57 

3* o88 5 

1-58 

3**379 

r 59 

3* i8 77 

i*6o 

3’ 2 3 81 

1*61 

3*2890 

1 *62 

3*3402 

1*63 

3*3920 

1*64 

3*4443 

1*65 

3*4972 

1 *66 

3*5504 

1*67 

3*6040 

i*68 

3’ 6 5 82 

1*69 

3*7129 

1 *70 

3*768i 



















1004 


CONTROL OF WATER 


TABLE No. 4.—AUXILIARY VALUES FOR SOLUTION OF 
RUTTER’S FORMULA. (See p. 472.) 

Kiitter’s formula for the value of C in the equation 

v=C^ rs 


is— 


1*811 


C = - 


n 


. / , , 0*00281 \ 

+( 4 i*6+——) 


1+ 


n / , 0*00281 \ 

A 4v6+ ' s ) 


T c , I*8l I , , , 

If we put - = a, and 41*6 + 


V r 

0*00281 


n 


= b, the formula becomes 


a+b 


, nb 

H—t= 

V f 


Table of a . 


n 

1 

a 

0*010 

181*1 

0*01 I 

164*6 

0*01 2 

1 5 °' 1 

0*01.3 

T 39‘3 

0*014 

129*4 

0*015 

120*7 

0*016 

113*2 

0*017 

106*5 

0*018 

ioo *6 

0*019 

95‘3 

0*020 

90*6 

0*021 

86*2 

0*022 

82*3 

0*0225 

80*5 

0*023 

78*7 

0*024 

75 'S 

0*025 

72*4 

0*026 

69.7 

0*027 

67*1 

°’°275 

6 5’9 

0*028 

64*7 

0*029 

62*4 

0*030 

60*4 

°*° 3 2 5 

557 

°'°35 

5 1 *7 

°’°375 

48-3 

0*040 

45‘3 

























RUTTER'S FORMULA 


1005 


and a depends merely on the value of n selected, while b is a function of the 
slope only. 

The values of a and b are tabulated below. 

In practice it is usually simplest to calculate CyV directly without obtaining 
the value of C. 


We have 

and in this form the calculation requires 


(a+b)r 
A r ~ \f r f nb 


One addition : a + b. 

One multiplication : (a+b)r. 
One multiplication : bn. 


One addition : V r+bn. 

_ (a + b)r . 

One division : C */r— —: . 

V r-\-bn 


Table of b. 


Slope. 

b 

Slope. 

1 

b 

Absolute. 

i in 

Absolute. 

I in 

O'OIOOO 

100 

41*9 

0*00009 

11000 

72*5 

0*00500 

200 

42*2 


12000 

75*3 

0*00250 

400 

42*7 


13000 

78*1 

0*00200 

500 

43 ’° 


14000 

80*9 

0*00100 

1000 

44*4 


15000 

83-8 

0*00067 

1500 

45*8 


16boo 

86*6 

0*00050 

2 000 

47*2 


17000 

89*4 

0*00040 

2500 

48*6 


18000 

92*2 

0*00033 

3000 

50*0 


19000 

95 '° 

0*00029 

35 °° 

5 r 4 


20000 

978 

0*00025 

4000 

52*8 


Beyond this limit the 

0*00022 

4500 

54*2 


formula 

rests on 

1 0*00020 

5 °°° 

55*7 


slender, 

and prob- 

0*00018 

55 °° 

57 *i 


ably erroneous evi- 

0*00017 

6000 

5S’5 


dence. 


0*00015 

6500 

59*9 


22000 

103*4 

0*00014 

7000 

61*3 


24000 

109*0 

0*00013 

7500 

62*7 


26000 

114*7 

0*000125 

8000 

64*1 


28000 

120*3 

O'OOOI 2 

8500 

65*5 


30000 

I2 5’9 

0*0001 I 

9000 

66*9 


Formula is probably 

0*000105 

9500 

68*3 


quite inapplicable 

O’OOOIO 

10000 

69*7 


beyond this limit. 



















































ioo6 


CONTROL OF WATER 


TABLES Nos. 5 and 6.— BACKWATER FUNCTION 
DROPDOWN FUNCTION x {£). (See p. 483.) 

n 1 K > :jf >i. * ». 1 , • / j’) f . i 1 M /'j , . » ! 

As already pointed out, the backwater functions are tabulated under 
the argument The dropdown functions %(x) are tabulated under argu- 

Jv 

ment x. 


I 

x or - 

X 

4 >{x) 

1 

X ( x ) 

O’O 

O’OOOO 

— 0*6046 

0*1 

0*0050 

-0*5046 

0*2 

0*0201 

— 0*4042 

°’ 3 ° 

0*0455 

-0*3025 

°' 3 l 

0*0486 

- 0*2922 

°‘ 3 2 

0*0519 

- 0*2819 

°*33 

o *°553 

-0*2716 

°*34 

0-0587 

— 0*2612 

°*35 

0*0623 

- 0*2508 

0*36 

0*0660 

-0*2403 

°*37 

0*0699 

-0*2298 

0-38 

0*0738 

- 0*2192 

°'39 

0*0779 

- 0*2086 

o’4o 

0*0821 

— 0*1980 

0*41 

0*0865 

— 0*1872 

0-42 

0*0909 

-0*1765 

°‘43 

o*o 955 

— 0*1656 

o *44 

0*1003 

- 0-1547 

o *45 

0*1052 

-0*1438 

0*46 

0*1 102 

-0*1327 

0-47 

0*1154 

- 0*1 2 16 

0*48 

0*1207 

- o*i 104 

o *49 

0*1262 

— 0*0991 

0-50 

0*1318 

— 0*0878 

0-51 

0*1376 

- 0*0763 

0-52 

°‘ I 435 

- 0*0647 

o *53 

0*1497 

-0*0530 

o *54 

0*1560 

- 0*04I2 

o *55 

0*1625 

— 0*0293 

0-56 

0*1692 

-0*0I72 

o *57 

0*1761 

— 0*0050 

0-58 

0*1832 

+ OOO74 

o *59 

0*1905 

+ 0*0199 

..' ~ _ f 















1007 


BA CKIVA TER AA T D DR0PD0 WN 

Tables Nos. 5 and 6 — continued . 


x or i 

X 

<p(x) 

x(*) 

0*60 

0*1980 

0-0325 

o*6i 

0*2058 

0*0454 

0*02 

0*2 138 

0*0584 

O 63 

0*222 I 

0*0716 

0*64 

0*2306 

0*0851 

0-65 

0 2 395 

0*0987 

0*64 

0*2486 

0*1127 

0*67 

0*2580 

0*1268 

0'68 

0*2677 

0*1413 

j 0-69 

co 

N 

b 

0*1560 

070 

0*2883 

0*1711 

071 

0*2991 

0*1864 

072 

°’3 io 4 

0*2022 

°*7 3 

0*3221 

0*2184 

°74 

°’3343 

0*2350 

°*75 

0*3470 

0*2520 

076 

0*3603 

0*2696 

°77 

°’374 I 

0*2877 

078 

0*3886 

0*3064 

079 

0*4039 

°'3 2 5 8 

o*8o 

0*4198 

o‘3459 

o-81 

0-4367 

0*3668 

0*82 

o'4544 

0*3886 

0*83 

0*4733 

0*4144 

0*84 

0*4932 

o*4353 

0-85 

0*5146 

0*4605 

o*86 

o*5374 

0*4872 

0*87 

0*5619 

°*5i5 6 

o-88 

0*5884 

°'S459 

0*89 

0*6173 

°'578S 

0*900 

0*6489 

0*6138 

0*901 

0*6522 

0*6l75 

0*902 

0*6556 

0*6213 

0*903 

0*6590 

0*625l 

0*904 

0*6625 

0*6289 

°'9°5 

0*6660 

0*6327 

0*906 

0*6695 

0*6366 

0*907 

0*6730 

0*6405 

0*908 

0*6766 

0*6445 

0*909 

0*6802 

0*6485 



































,oo8 CONTROL OF WATER 

Tables Nos. 5 and 6 — continued. 


I 

oc or — 

X 

(p{x) 

x(*) 

0*910 

0*6839 

0-6525 

0*911 

0*6876 

0*6566 

0*912 

0*6914 

0*6607 

o'9 T 3 

0*6952 

0*6649 

0*914 

0*6990 

0*6691 

°' 9 l 5 

0*7029 

0*6733 

0*916 

0*7069 

0*6776 

0*917 

0*7109 

0*6820 

0*918 

°‘7 I 49 

0*6864 

°'9 1 9 

0*7190 

0*6908 

0*920 

o'7 2 3 I 

0*6953 

0.921 

0*7273 

0*6999 

0*922 

°'73 T 5 

0-7045 

0*923 

o*735 8 

W ( 

00 

0 

b 

0*924 

0*7401 

°'7 J 3 8 

0*925 

o-7445 

0*7186 

0*926 

0*7490 

07234 

0*927 

o*7535 

0*7283 

0*928 

o'75 Sl 

0*7332 

0*929 

0*7628 

o73 82 

0*930 

0*7675 

o*7433 

°‘93 I 

0*7723 

o-74 8 5 

0*932 

0*7772 

0*7537 

°‘933 

o # 

00 

w 

t-H 

0*7589 

°’934 

O 

00 

*0 

rH 

0*7643 

°’935 

0*7922 

0*7698 

0*936 

0*7974 

0*7753 

°‘937 

0*8026 

0*7809 

0*938 

0*8079 

0*7866 

°*939 

0*8133. 

o-79 2 3 

0*940 

0*8188 

0*7982 

o*94i 

0*8244 

0*8041 

0*942 

0*8301 

0*8102 

o*943 

°* 8 359 

0*8164 

o‘944 

0*8418 

0*8226 

o*945 

0*8478 

0*8289 

0*946 

°* 8 539 

0-8354 

o*947 

0*8602 

0-8430 

0*948 

0*8665 

0*8487 

o*949 

0*8730 

1 

0*8554 

































BACKWATER AND DROPDOWN 


1009 


Tables Nos. 5 and 6— continued. 


I 

x or 

X 

<t>[y) 

xM 

°' 95 ° 

0*8795 

0*8624 

o’ 95 1 

0*8862 

0*8694 

°‘ 95 2 

0-8931 

0*8767 

°'953 

0*9002 

0*8840 

°‘954 

0*9073 

0*8916 

o *955 

0-9147 

0*8992 

0-956 

0*9221 

0*9071 

o *957 

0*9298 

°* 9 T 5 ! 

0-958 

0-9376 

0-9233 

o *959 

o *9457 

0 * 93 ! 7 

0*960 

o '9539 

0*9402 

0-961 

0*9624 

0-9489 

0*962 

0*9709 

0-9580 

0*963 

o *9799 

0-9672 

0*964 

0*9890 

0*9767 

0-965 

0-9985 

0*9865 

0*966 

1 *0080 

0-9965 

0-967 

t-oi8i 

1 -0068 

0*968 

1 *0282 

1-0174 

0-969 

1-0389 

1*0283 

0-970 

1-0497 

1*0396 

°* 97 I 

1*0610 

1-0512 

0-972 

1 -0727 

1*0632 

o '973 

1 *0848 

i*o 757 

o *974 

1-0974 

1 *0886 

o *975 

i* 11 05 

I "1020 

0*976 

1-1241 

I "I l6o 

o *977 

i‘i 3 8 3 

1*1305 

o* 97 8 

1 * 153 ! 

i*i 457 

o *979 

1*1686 

1-1615 

0*980 

! 1*1848 

1*1781 

0*981 

1-2019 

i*i 955 

0*982 

1-2199 

1-2139 

0*983 

1-2390 

1-2323 

0*984 

1-2592 

!* 2 53 8 

0-985 

1-2807 

1-2757 

0*986 

1*3037 

1 2990 

0*987 

1-3284 

i* 3 2 4 ! 

0*988 

i’ 355 T 

I ’ 35 11 

0*989 

I-384I 

i* 3 8 °4 


64 














































IOIO 


CONTROL OF WATER 


Tables Nos. 5 and 6— continued . 


1 

I 

x or - 

X 

<p(x) 

xW 

0*990 

I ‘ 4 I 59 

1*4125 

0*991 

1*4510 

1*4486 

0*992 

1*4902 

1*4876 

°’ 993 ~ 

I- 534 8 

1 ' 53 2 4 

0*994 

1*5861 

i’ 5 8 4 i 

o ’995 

1*6469 

1*6452 

0*996 

1*7213 

1*7206 

0*997 

1 *8172 

1*8162 

0*998 

I * 95 2 3 

I * 95 I 7 

0*999 

1 *ooo 

2*1834 

2*1831 

1 1 O 


Several discrepancies exist between the various published copies of this 
table. A systematic check could not be undertaken, but all values occurring 
in several years’ work have been checked, and any suspicious changes 
examined. It is believed that the third place of decimals is always reliable ; and 
it is known that the fourth place is frequently two, or even three, units in error. 
















PUNJAB WATERCOURSES 

TABLE No. 7.—PUNJAB WATERCOURSES. 

Table of Discharges for Watercourses. 


1 o 1 i 


Bed 

Slope 

\ 1 
300 

1 

500 

1 

750 

1 

1000 

1 

1500 

I 

2200 

1 

2857 

1 

3636 

1 

4400 

1 

55 oo 


Full Supply Depth in 

Feet for i*o Cusec Discharge. 


Bed 











Width. 











Feet. 











I'O 

o'6 

07 

o-8 

o *9 

o *95 

I'O 

i'i 

1 ‘2 

1*25 

i *3 

1*5 

• • • 

... 

• • • 


... 

0-85 

o *95 

I'O 

1-05 

i*i 5 

2 ‘O 

• • • 

• • • 

• • • 

• • • 

• • • 

o *7 

o'8 

0-85 

o'go 

I'O 

2‘5 

• • • 

• • • 

• • • 

% • • 

• • • 


• • • 

o *75 

o'8o 

o'go 

Full Supply Depth in Feet for 1*5 Cusec Discharge. 

I'O 

07 

o-8 

°*9 

I'O 

I 

i'i 

1*2 

i *3 

i *4 

i *5 

1 6 

1 '5 

• • • 

... 

... 

0-85 

0 9 

I'O 

i'i 

I '2 

1 *3 

J *4 

2'0 

• • • 

... 

• • • 

• • • 

... 

0*8 5 

o *95 

I'O 

1 i 

1'2 

2 ’5 

• • • 

... 

• • • 

... 


. . . 

o'8 

o *9 

I'O 

i'i 

3’° 

• • • 

... 

... 



' • • 

• • • 

0-85 

o *95 

1*05 

3*5 

• • • 


... 

... 

... 

... 

• • • 

o'8 

°*9 

1 '0 

4 *o 

• • • 

• • • 

• • . 

• • • 

• • • 

* * * 

• • • 

• • • 

• • • 

o *9 


Full Supply Depth in Feet for 2*0 Cusecs Discharge. 


I'O 

o'8 

°*9 

I 'O 

1 'i 

1 ‘3 

* i*4 

i*6 

i *7 

i*8 

2 ‘0 

!'5 

07 

o *75 

o'8 

°*9 

T *°5 

1*2 

J *3 

i *4 

**5 

i *7 

2'0 

• • • 

. . • 

. . . 

... 

o *9 

I 'O 

i'i 

I '2 

1*3 

i *4 

2’5 

• • • 

• • • 

• . . 

• . • 

... 

°*9 

0 95 

I *°5 

i'i 

1 '2 

3 *° 

• • • 

• • • 

... 

... 

• • 

o-8 

0-85 

o*9 

I'O 

I'I 

3’5 

• • • 

... 

... 

. • • 

• • • 

... 

• • • 


o*9 

I O 

4'° 

• • • 

• • • 

... 

• • ’ 

• • • 

• • • 

... 1 

• • • 

• • • . 

°*9 

% 

Full Supply Depth in Feet for 2-5 Cusecs Discharge. 

I'O 

°‘9 

1 0 

11 

r2 5 

i*4 

1'6 

i*75 

i*9 

2'0 

2'2 

i ‘5 

o'8 

°*9 

I 'O 

i'i 

I '2 

i*35 

i *5 

1 - 6 

i*7 

i*9 

2'0 

o *75 

o'8 

0*85 

o*95 

1*0 

i'i 

1*25 

i*4 

i *5 

i*7 

2-5 

• • • 


• • • 


• • • 

o*95 

1 'i 

1*2 

1 3 

1*5 

3 '° 

• • • 

• • • 

• • • 

... 

• • • 

0*85 

1 'O 

i'i 

1*2 

i *3 

3'5 

• • • 

• • • 

• • • 

• • • 

• • • 

• • • 

• • • 

I'O 

i'i 

1*2 

4 *o 

• • • 

• • • 

... 

• • • 

• • • 

1 

... 


0*9 

I'O 

I'I 


















































































































1012 


CONTROL OF WATER 


Table No. 7 — continued. 


Bed 1 

1 1 

1 

1 

1 

1 

I 

I 

I 

1 

1 

Slope j 

f 300 

500 

75 ° 

1000 

1500 

2200 

2857 

3636 

4400 

55 oo 

Full Supply Depth in Feet for 3'o Cusecs Discharge. 

Bed 











Width. 




1 







Feet. 











1*0 

1*0 

i*i 

1*25 

i *4 

i*6 

i*8 

i *9 

2*0 

2'1 

2'2 

i *5 

0*9 

j o *95 

1*05 

1 "2 

i *4 

i*6 

i *7 

i *9 

2*0 

2 'I 

2*0 

o-8 

0-85 

o ’9 

1*0 

I *2 

i *4 

i *5 

1'6 

i *7 

i*8 

2 '5 

07 

075 

o*8 

°*9 

1*0 

1*2 

I *3 

i *4 

i *5 

1'6 


• • • 

• • • 

. . . 

o-8 

1 0*9 

I'O 

i'i 

I'2 

i *3 

i *4 

3*5 

• • • 

... 

• • • 

• • • 

! 0-8 

i o*9 

I'O 

I'I 

1 '2 

1 *3 

4 ‘° 

• • • 


• • • 

• • • 

I ... 

o - 8 

o '9 

I'O 

I - I 

1*2 

Full Supply Depth in Feet for 3*5 Cusecs Discharge. 

1*0 

n 

1*2 

i *4 

i *5 

i *7 

i *9 

2*0 

2 ' I 

2*3 

2*5 

1 '5 

o *95 

1*05 

1*2 

i *3 

i *5 

i *7 

i-8 

i *9 

2 "O 

2 "2 

2*0 

o-8 

°*9 

ro 

i'i 

i *3 

i *5 

1 '6 

I- 7 

i*8 

2'0 

2 '5 

... 

o-8 

o *9 

1 *o 

ri 

*i *3 

i *4 

!*5 

1 '6 

I'8 

3 '° 

... 

• • • 

o-8 

o ‘9 

1 *o 

11 

I '2 

!*3 

i *4 

i'6 

3*5 

... 

• • • 

... 

o-8 

o ‘9 

I 'O 

I'I 

I '2 

!*3 

i *45 

4-0 

• • • 

• • • 

• • • 

• • • 

o-8 

o '9 

I 'O 

I'I 

I '2 

!*3 

Full Supply Depth in Feet for 4-0 Cusecs Discharge. 

1 *o 

1*2 

r 35 

!*5 

T *7 

i *9 

2 * 1 

2 ‘ 2 

2*3 

2-5 

2*7 

1 *5 

1*0 

1*15 

!*3 

1*45 

1 *6 

i-8 

i'9 

2*05 

2*2 

2‘45 

2*0 

°*9 

1*0 

I 'I 

1*2 

1 ’4 

i *5 

1 '6 

i*8 

2 'O 

2'2 

2 ‘5 

• • • 

o '9 

1*0 

1*1 

1*2 

i *3 

i *4 

1 '6 

i'8 

2*0 

3 *° 

« • • 


o *9 

I'O 

I'I 

1 2 

T *3 

i *4 

1'6 

i'8 

3*5 

• • • 


o-8 

o ’9 

I *o 

i'i 

I '2 

!*3 

T *45 

i*6 

4 *o 

• • • 

; 

• • • 

0*85 

o ’9 

I 'O 

i'i 

1*2 

i *3 

i *5 

Full Supply Depth in Feet for 4*5 Cusecs Discharge. 

I ’0 

!*3 

i *5 

i *7 

i *9 

2*1 

2*3 

2'4 

2*5 

27 

2'9 

i *5 

I'I 

T *3 

i *5 

1’6 

i*8 

2*0 

2'I 

2*2 

2*4 

2*6 

2*0 

1*0 

i*i 

T *3 

i *4 

1 '6 

T *7 

i*8 

i *9 

2 ' 1 

2*35 

2 *5 

0-9 

1 *o 

1 • 1 

I ‘2 

i *4 

r *5 

1*6 

i *7 

1'9 

2 • 1 

3 ’° 

o*8 

°*9 

1*0 

I *1 

I '2 

i *3 

i *4 

i *5 

i *7 

1 *9 

3*5 

... 

o*8 

o *9 

1*0 

I *1 

I '2 

1 *3 

i ’4 

i *55 

i *7 

4 *o 

• • • 

• • • 

o'8 

o ’9 

I'O 

I'I 

1*2 

!*3 

i *4 

1 *6 








































































































ioi 3 


PUNJAB WATERCOURSES 


Table No. 7 — continued . 


Bed 1 

1 

I 

1 

I 

I 

1 

1 

1 

1 

1 

Slope J 

300 

500 

75 o 

IOOO 

1500 

2200 

2857 

3 6 36 

4400 

55 oo 

Full Supply Depth in Feet for 5*0 Cusecs Discharge. 

Bed 











Width. 











Feet. 











1 *o 

i '4 

1 -6 

i*8 

2*0 

2*2 

2*4 

2*5 

2*65 

2*8 

3*0 

r *5 

1*2 

i *4 

i*6 

1*7 

1*9 

2*1 

2*2 

2*35 

2*5 

2*7 

2 '0 

1*1 

1*2 

i *4 

i *5 

1 *6 

i*8 

i *9 

2*1 

2*2 

2*45 

2 ’5 

I *0 

I *1 

1 *2 

!*3 

i *4 

i*6 

i *7 

1*9 

2*0 

2*2 

3 '° 

0*9 

I *o 

i*i 

1*2 

!*3 

1*4 

i *5 

1*7 

i*8 

2*0 

3'5 

• • • 

0*9 

1*0 

i*i 

1*2 

i *3 

i *4 

i *5 

1 *6 

1*8 

4 *o 

• • • 

o*S 

0*9 

1*0 

i’i 

1 2 

ir 3 

i *4 

i *5 

1*65 


Full Supply Depth in Feet for 5*5 Cusecs Discharge. 


I ’O 

i *5 

,7 

1*9 

2*1 

2*3 

2*5 

2*7 

2*8 

2*9 

3 * 1 

r 5 

1-3 


i *7 

i*8 

2*0 

2*2 

2*4 

2*5 

2*6 

2*8 

2*0 

I ’2 

i *3 

!*5 

1*6 

i *7 

1*9 

2*1 

2*2 

2*3 

2*6 

2'5 

I *1 

1*2 

i *3 

!*4 

i *5 

1*7 

1*9 

2*0 

2*1 

2*3 

3 *° 

I *0 

1*1 

1*2 

1*3 

i *4 

i *5 

!*7 

1*8 

1*9 

2*1 

3*5 

o *9 

1*0 

1*1 

1*2 

i *3 

i *4 

i *5 

i*6 

1*7 

1*9 

4-0 

... 

0*9 

1*0 

1*1 

1 *2 

i *3 

i *4 

i *5 

i*6 

1 1 


These tables are based on the assumption that the side slopes of the 
excavation and banking are dressed to 1:1; and that 05=6 fieeboaid 
above full supply water level is given to the banks. i he figures are the result 
of experience, rather than of definite calculation, and produce a very practical 
set of channels. Given the ordinary maintenance, breaches, or deficiencies 
in supply, rarely occur ; and, if tested by calculation, it will be found that the 
larger channels, which receive more careful attention, aie, relatively to the 
smaller channels, proportioned on this basis. Thus, no unduly excessive 
factor of safety is employed. Where labour is dearer, or less efficient than in 
India, I have been accustomed to employ these tables, but provide a greater 
freeboard than 6 inches. 






























































GRAPHIC DIAGRAMS 

These diagrams are prepared according to the principles laid down by 
M. d’Ocagne ( Traite de Nomographie ). 

The present applications are believed to be original, although at least one 
hydraulic diagram based on these methods has been published (Hiilte, vol. 3, 
p. 245). 

Since the principle is a powerful aid in graphing nearly every hydraulic 
formula of general application, the following details may prove of utility. 

Consider the line joining the points A(—jjq) and B (x 2 ,y 2 )‘ 

The equation of this line is : 

x+x 1 = y-y\ 

■*■*+*1 y*-yi 

Putting x — o, we find that the intercept OC on the axis of y is given by, 

. which determines the distance OC. 

x 1 +x 2< 

Thus, any formula of the type : 

* ai + a 2 ’ 

can be reduced to a graph, once the ds and ds are properly plotted. 

The typical hydraulic formula is usually : 

Q = E l n h n \ 

or, taking logarithms, 

log Q —log E = /z log l+m log h ; 
and n and m are generally constants. 

Thus, if we plot logarithmic scales of h and /, and insert a properly divided 
logarithmic scale (usually with a different unit for base) at the proper 
intermediate distance between the scales of log h and log /, the readings on 
this intermediate scale will represent log Q — log E, and the scale can therefore 
be graduated so as to read Q directly. 

The real difficulties in preparing workable diagrams arise merely from the 
necessity of avoiding unduly acute intersections of the line AB which joins the 
points representing the given values of / and h , with the scale of log Q —log E 
on which the corresponding value of Q is read off. 

Thus, in employing the following diagrams, we merely select the points 
corresponding to the two known quantities typified by l and h on the 
appropriate scales, and lay a straight edge across the diagram to join these 
points ; the value corresponding to the graduation at which the line of the 
straight edge crosses the third scale will be found to represent the third 
(unknown) quantity typified by Q. 


IOI4 






GRAPHIC DIAGRAMS 


1015 

The diagrams have all been tested, not only by careful arithmetical 
checking, but by a period (in some cases, three or four years) of office use. 
Ihey are drawn and reproduced on a scale which permits an accuracy of 
1 per cent, to be obtained. This is amply, in fact over, accurate for all 
practical purposes except the comparison of the more refined observations that 
are rarely undertaken save under laboratory conditions. 

It should, however, be noted that if these drawings are enlarged to more 
than double the size, arithmetical checking will disclose errors, which, in No. 1 
amount to as much as o*6 per cent. 


LIST OF DIAGRAMS. 

PAGE 

No. 1. — Discharge of Sharp-Edged Weirs .... 1016 

No. 2.—Discharge of Generalised Weir ..... 1018 

No. ? i 

No* 4 j Tables (Graphic), No. i and No. 2 .... 1020 

No. 5.—Discharge of Orifices with C = 0-625 .... 1022 

No. 6.—Velocity of Water in Channels of Bazin’s Class I. ; 7 = 0-109. 1024 

No. 7. —Velocity of Water in Channels of Bazin’s Class II. ; 7 = 0*290 1026 

No. 8 .—Velocity of Water in Channels of Bazin’s Class IIa; 7 = 0-55 1028 

No. 9.—Velocity of Water in Channels of Bazin’s Class III. : 7 = 0*833 1030 

No. 10.—Velocity of Water in Channels of Bazin’s Class IV. ; 7=1*54. 1032 

No. 11.—Velocity of Water in Channels of Bazin’s Class V. ; 7 = 2*35 . 1034 

No. 12.—Velocity of Water in Channels of Bazin’s Class VI. ; 7 = 3*17 . 1036 


I 



io 16 


CONTROL OR WATER 


20 . 0 — 

/SO - 


70.0 A 


9.0 A 

X 

8.0 




7.0 - 

\ 



s.o — 

* 

- 


5.0 A 


1 


4.0 A 


— 

V 

- 


3.0 — 

s 





— 

XI 


2.0 — 

Z50 - 

/o- 

Diagram No, 


400.0 

300.0 

200.0 


700.0 A 

% 








<0 

50.0 — 


40.0— 



X 



30.0— 

< 

20.0— 



<o 



— 

\ 

/ 0.0 


— 


_ 

$ 


x: 

_ 


— 

.b 

5.0 

§ 

4.0 — 


3.0 — 


2.0 — 


7.0 -A 


0.70 



i.—D ischarge of 


3.0 


H 

-I 

-I 

J 

I 

1 

1 

-i 

4 


1 

_i 

l 

“I 

2.0— j 

-I 




I 

i 


X 

* 

* 

ts 

I 


750- 


fO — 
0.30- 

0.80- 
0.70-A 

0.60 - 


0.50 


0.40 — 


Sharp-Edged Weirs. 





























GRAPHIC DIAGRAMS 


1017 


DISCHARGE OF SHARP-EDGED WEIRS. 

The diagram on the opposite page represents the Discharge of Water over 
Sharp-Edged Weirs, as detailed on p. 112. 

Head over o’4o feet : 

Q = 3 'iio L 1 H 14G ° ; with L less than 4 feet. 

Q = 3 122 L 1 010 H 1 475 ; with L between 4 and 10 feet. 

Q = 3 i48 L 1 ,1u H 1 485 ; with L greater than 10 feet. 

77 2 

Where, H = D+i*4// = D +1*4— 

2g. 


«S c o/e of Co-efficien ts. 


1018 


CONTROL OF WATER 


4.0 



• i t 


♦ , 


4.0 -q 

3.5 ^ 
3.0— 

2.5 - 


40.0 - 
30.0 - 

20.0 — 


/O.O- 




>■' 'j ■ i m . i 


5.0 — 
4.0 — 

3.0 - 

2.0 —j 


/.O —rr 


% 

I 

<o 

* 

* 

<0 




& 

f 

■$ 

• 5 ? 




o 

<0 


3.0 


2.0 


' 

. u 


(,>' 

/.50 


LO¬ 


OM — 


0.80 


0.70 — 


0.60 


Diagram No. 2.—Discharge of Generalised Weir. 


Sca/e of fJecrc/ over Notch /n Fee/. 













GRAPHIC DIAGRAMS 


1019 


DISCHARGE OF GENERALISED WEIR. 

The diagram on the opposite page represents the general formula : 

Q = CLH 1 5 

which has been found to be more or less applicable to all weirs, whatever 
their section may be. 

1 he table on page 1020 shows the sections of all weirs for which it is 
known that 

the value of C is constant, 

and gives the range of H over which C remains constant. 

Similarly, the table on page 1021 shows the sections of all weirs for which 
the expression 

C=a+6H 

holds : and the upper and lower limits of H between which this expression 
holds good. 

In every case, slight variations in C, not exceeding 1 per cent, either way, 
from the constant value or the straight line law have been disregarded. 

The experiments on which these tables are founded are mainly those 
of Bazin ; but, for their conversion into English measure, and for a series 
of graphic plots of C, which have materially helped me in arriving at the 
tables, I am indebted to Horton {Weir Experiments). 

Following Horton, in cases where the accuracy of the observation requires 
it, I generally put 

ip 

h=d+^=d+- 

I may state that these tables have been in steady practical use for some five 
years, and that resort has been made to every accessible published observation in 
order to check them. It is believed that no result obtained by their use is likely 
to be more, than 3 per cent, in error, so far as the value of C affects the result {i.e. 
errors in observing H are neglected). In most cases, the observed errors are 
less than 2 per cent., and this statement applies also to some 80 small scale 
experiments specially undertaken for the purpose of checking the tables. 


1020 


CONTROL OF WATER 


Value of 
C 

Section of 
Weir 

Valueof 

P 

H exceeds 

Rutho- 

-rity 

Valueof 

C 

Section of 
Weir 

Vatueof 

P 

Hexceeds 

Rutho- 

-rity 

5-87 


1-64 

0-75 

3 

3-39 

\ 

4-90 

1-8 

c 

5-85 

■H- 

2-46 

0-3 

3 

5-55 

Francis 

Sharp -t 

DQed . 

tteif 

3-85 


y/fl 

* 

1 


i-64 

0-70 

3 

5-52 

->-48*- 

11-25 

0-8 

G 

3-74 

kTs £ 

K/.3 

il-25 

2-4 

0 

C 

5-5! 

|*— /-65—' ► 

11-25 

2-6 

G - 

3-74 

jf' 1 


4-9 

2-0 

C 

3-51 

- 95* 

II-25 

1-6 

G 

5-72 

w. v 

v 

l -64 

0-55 

3 

3-30 


11-25 

2-5 

• r * 

G 

5-70 


1 

dr 

4-90 

i-8 

C 

5-22 

——4£_-04 - 7-&S! 0 \ 

7-75 

0-6 

C 

3-68 


i-64 

0-55 

3 

-r-L 

5-21 

f^^^ 5 . 25 ruk 

as above but mitt) sou 

W6 7-75 
wth plan, 

c" 

C 

5-66 

K— Wb—ktb 

J 


10 > 

7-9 

0-2 

C 

3-22 


75 4-55 

1-8 

c 

5-62 

-1-9 ~8v5 

as above but wire c 

7-9 

kith on c. 

0-2 

xst 

c 

3-/5 

as C= 3-21 but roi 

7-75 
<oh slope 

0-8 

V wire dot, 

c 

on 

3-58 

ir*< 

1-64 

0-5 

3 

3-14 

Ip— 

2-46 

0-95 

iciest 

3 

5-58 


r 

67 

49 

2-0 

C 

5-09 

Theoretical value 

r orbroads 

tying cres 

drveir 

5-52 

vV~~^iCc J 

< 


i-64 

0-5 

3 

2-95 


2-46 

0-70 

3 

3-50 

ir* 


2-46 

0-25 

3 

2-8! 

r—6 -S &—*j 

n-ssmO. I 

4-56 

J-0 

C 

5-49 

-^ 

I 67 

49 

J-7 

C 

2-64 

Flat Tot) 12-21 wide 

11-25 

1-8 

G 

5-45 

0 1 

tAjLTL- 
- ^'1 

< 

49 

2-0 

C 

C 

2-64 

Do. 5-88 wide 

11-25 

TO 

G 

3-42 

1-5 ft—^ 
JpC 

1 


4-65 

2-5 

2-65 

Do. 16-50 wide 

11-25 

t-0 

G 

3-41 

_ 

!-64 

0-75 

3 

2-62 

Do. 898 wide 

11-25 

J-0 

G 


Diagram No. 3 .—Weirs with Constant Coefficients. 



















































































































GRAPHIC DIAGRAMS 


102 I 


Section of Weir 

Value of C 

UpperLimit 
of H 

Section of Weir 

Value of C 

UpperLimit 
of H 

hff-i W--0328 

I 4. P - 2-46 

2-76 * 780(H-0-/5) 

0-55F.D 

m * 4 

2-82 * 0-52(0-0-6) 

75 F.S. 

W*0-656 P--2-46 

2-8/ *705(0-0-45) 

705 0 

m=6 

2-80 *0-27(0-0-5) 

7 5 F.S. 

W--73/5 [0--2-46 

2-64 *0-51(0-0-6) 

755F.S 


5-11 *0-54(0-045) 

75 Dl 

yj: pop P-2-46 
n ™ P-4-56 

2-53 *0-H(H~0-5) 

2-77 *0-175(0-2-0) 

!-4 F.S. 
5-3 F.S. 

4 1=/ 

3-06*0-67(0-0-5) ' 

7-377 

ij.ccc P'-246 
h/‘6-56 p z4 . 57 

2-52 *0-H(H-0-5) 

2-40 *0-05(0-2-0) 

75 F.S. 
5-2 F.S. 


2-78 *0-01(0-0-4) 

7/577 

.J..*-— 

W=0-48 p=//-25 

2-50 * 1-40 (H-0-2) 

0-80 

Ups/ream Face Vertical 

2-55 *0-06(0-0-25) 

I-ID 

W = 0-95 p=/725 

2-57 * 0-62(H-0-3) 

74D 

M-yjr^ 5-28 

4X\Fod Widlti=5' 

3-25 * 0-/0 (0-0-8) 

4-9 F 

rv= i-65 0--H-25 

2-52 * 0-42(0-0-6) 

2-40 


»- 16 ^13^/0 h- 

5-60-0-16(0-0-4) 

2-5F 

W=2-I7 p=1725 

2-64 *0-/7 (H-/-5) 

5-0 F 

JU^ p- li-25 

6 W\ 1-0-75 

3-40 * ‘05(H-0-7') 

5-2F 

M-2-62 0=2-46 
[ | p-4-57 

2-03 *0-U (0 -0-4) 

2-84 *0-17(0-1-0) 

735£5. 

5-2 F.S. 

P-1725 1=75 

3 - 52 * 0 - 13 ( 0 - 1 - 0 ) 

2-7 D 

L. 

N = 6-56 p= 2-46 

2-85 *0-15(0-0-6) 

755F.O 

P = 1725 1=2-86 

3-50 *O-2O(0-7O) 

_ - 

WF 

--L 

Ofr*. n -‘ , 

2-72 *0-Q6(H-0-2) 

72 0 

P-/725 t* 0-75 
One end contraction 

3-24 * -09 (0-0-6) 

4-2/7 

% 

n -2 

2-60* 0-85(0-0-2) 

7/50 

p=/725 1-75 

One end contraction 

3-37 *0-/2 (0-0-8) 

4-7/7 

■n=5 

2-60*0-70(0-0-1) 

/-2D 

/J 


3-35 * -07 (Hr 7/) 

3-8 F 

<n =4 

5-04 *0 -40(0-0-65) 

75D 


_ 

5-/7 * 0-/8(H-0-2) 

2-8F 

n=5 

2-75 *0-54(0-0-2) 

7/60 

, 

—- 204 -ffSAT 

3-07*0-1/(0-75) 

4-/F 

.. . , 

2-80 * 0-47 (H-0-6) 

75F.S. 

, -t’65 


< 


Diagram No. 4 .—Weirs with Linear Coefficients. 




















































1022 

2 . 0 - 


CONTROL OF WATER 


fO— 
0.90- 

0.80- 

070 

;\*\ ; 

0.80-\ 
0.50- 

0.40—\ 


030- 


0 . 20 — 


0 / 0 - 


* 

v. 

<0 

<0 


o 

<0 


mo— 


50.0— 


/ao- 


5.0- 
4.0 

30 - 

i i t 

2.0 - 


/.o 


0.50 


0 

°D 

* 

* 

'Q 

a 


<0 

C 

o 

.<0 

§ 

<5 

o 

<0 


200.0 


/ 00 . 0 — 


500- 


/OO- 


5.0 

4.0 

3.0 

2.0 


LO —= 


0.50 


Diagram No. 5. —Discharge of Orifices. 


Sca/e of Heads in Feef. 






















r — 


GRAPHIC DIAGRAMS 


1023 


DISCHARGE OF ORIFICES. 

The diagram on the opposite page represents the usual formula for orifice 
discharge : 

Q = CAV 2 gh 

The value of C selected is o'62 5, so that the formula shown in the graph is : 

1 * 

Q = 5‘oiA V h 

Corrections for special values of C are easily made by remembering that, a 
change of 0-025 in C produces a variation of 4 per cent, in Q. 

Thus : 


c 

Discharge. 

0*575 

0-92 Q 

o*6oo 

0-96 Q 

0-625 

1 -oo Q 

0-650 

1-04 Q 

0-675 

1 "08 Q 

0*700 

1*12 Q 

0-725 

ri6Q 

0-750 

1*20 Q 

0775 

1-24 Q 

o*8oo 

1-28 Q 


For values of A and h outside the limits of the diagram it suffices to 
remember that : 

(i) If A be doubled or halved, Q is doubled or halved ; and if A be 

multiplied by 10, Q is multiplied by 10. 

(ii) If h be multiplied or divided by 4, Q is doubled or halved. 

If h be multiplied by 100, Q is multiplied by 10. 




* 













T 024 


CONTROL OF WATER 


WO 


200 —- 


300 - 


400 - 


J- 50.0 
■ 40.0 


30.0 


--- 20.0 


I 

X 

! 

I 


500 

600 

700 

800 

$00 

1000 


1-/O.O 


2000 - 


3000 — 


4000 — 


5000 —_ 

6000 
7000 
8000 — 
3000 - 


70000 - 


$ 

V, 

5.0 ^ 

\ 

4 - 0 v 
3.0 


2.0 


- fO 


0.50 


00.0-3 

50 . 0 -j 
40 . 0 — 


30.0 — 


20.0 — 


W.O— 

5.0 -E 
4.0 - 

3.0 





0 . 50 —_ 
0 . 40 - 

0 . 30 - 

0 . 20 - 


//.O-i 
W.O - 
9.0 — 

8 . 0 - 
7.0 - 
6 . 0 - 

5.0 - 
4.0 - 


3.0 


2.0 - 

/.50 - 

/.o 

0 . 50 - 

0 . 40 - 

0 . 30 - 

0.20 ~ 


O./O- 


0 . 05-1 


Diagram No. 6 .—Velocity of Water in Channels of Bazin’s 

Class I.; 7=0*109. 


//yc/rac///c A/fecr/i*/?ac//us //? feef 















GRAPHIC DIAGRAMS 


102 


VELOCITY OF WATER IN CHANNELS OF BAZIN’S 

CLASS I. ; y = o'io9. 

The diagram on the opposite page, together with the five succeeding diagrams, 
represent the formulas: 

v=C V rs ; 

with, c = r5z^_. 

as laid down by Bazin in 1897 (see p. 474)- The present diagram corresponds 
to Class I., y=o'io9 : and Bazin assigns channels of smoothed cement and 
planed wood to this class. 

In practical commercial engineering I am inclined to believe that very few 
channels are sufficiently carefully constructed to fall within this class. 

I have succeeded in constructing a planed wooden flume which was smooth 
enough to give y=o'ioo, but did not feel sufficiently certain of it remaining in 
this smooth state to design the flume on this assumption, and therefore based 
my calculations on y = o’i3. 


65 


io 



1026 


CONTROL OF WATER 


wo- 


-50.0 
40.0 


200 - 


300 — 


400 


I 

•• 

s 

i 

oo 

X 

<o 


500 

600 

700 

800 

800 

/ooo 


30.0 


200 


-/o.o 


*s 


-E ^ 


50 ^. 




2000 - 


40 


3.0 


60.0 
500 

40.0 
30.0 

20.0 A 


/O.O- 


5.0 
4.0 

3.0 

2.0A 



1 - 

0.40- 


— 2.0 : 


3000- ^ 

: /o- 

0.30- 

4000A 

— 

- 

5000A 

• - 

- 1.0 1 

0.20- 

6000- 

7000- 

- 0.50- 

r 0 . 40 — _ 

— 

. . 

- 0.30- 

-0.50 025- 

O./O- 


% 

l 




$ 

<3 


/4.0 

/0.0 


50 

4.0 

3.0 

20 - 
/.SO 

/O- 


050- 


Diagram No. 7.—VELOCITY OF Water IN Channels OF Bazin’s 

Class II.; 7=0*290. 


//yc7rau//c Me a/? /fac//us i /7 feef 












GRAPHIC DIAGRAMS 


1027 



VELOCITY OF WATER IN CHANNELS OF BAZIN’S 

CLASS II. ; 7=0*290. 

The diagram on the opposite page corresponds to Class II. ; or y =0*290. 

Bazin assigns all channels of planks, bricks, and cut stone to this class. 

The remarks on pages 474 and 475 should, however, be consulted. 

I do not usually design channels of this class in practical work. 

The requisite smoothness of surface is easily obtained ; but, under normal 
conditions, the extra cost of the more careful workmanship required usually 
exceeds the saving produced by the smaller dimensions of the channel. The 
exceptions generally prove to be large channels, with r exceeding say 3 feet. 




S/ope - / /n_ 


1028 


CONTROL OF WATER 


100 —1 


t -50.0 
40.0 


30.0 


200 - 


300- 

400- 

500- 

600 - 
700 
800- 

900- 
/ 000 


2000 - 


20.0 


/ 0.0 % 


4.0^ 


1-3.0 


2.0 


1 . 

. * 


\#*>- 


: 1 


40.0~ 
30.0- 

20.0 -3 


/ 0.0 


5.0- 
4.0- 

3.0 -3 
2.0 


1 


1 . 0 - 


>5 

o 

<0 

* 

* 

* 

$ 

* 

< 5 > 


i5 


3000— 

I _ 

- • ‘ • t * - 

4000-_ 

_ ‘ ‘ ‘3 

; 0.50-i 

5000-_ 

- 7.0 0 

6000- 

— 


- 0.30-. 

7000- 

_ • 

8000- 

— I 

9000- 

“ 0.20- 

/0,000- 

-0.50 


Diagram No. 8. 


-Velocity of Water in Channels of 
Class IIa. ; y=0-55. 


90 ~ 

« 

5.^-; 
_ \ 

4.0- 

3.0- 

2 . 0 - 
7.50 ~ 

AO- 

0.50~ 

0.40- 

0.30- 

0 . 20 - 

0 / 0 - 

Bazin’s 


ff vc/rau//c Mean fiad/us />7 Feef 



















GRAPHIC DIAGRAMS 


1029 




VELOCITY OF WATER IN CHANNELS OF BAZIN’S 

CLASS IIa. ; y = 0*55* 

The diagram on the opposite page corresponds to a class determined by 
Bazin’s 7=0*55. 

This class was not specified by Bazin. 

In practice, it is probably that most frequently used in the design of 
artificially lined channels. All slime encrusted channels, such as occur in 
sewerage and other works dealing with polluted water, rapidly pass into this 
class as they age, whether the original channel was smoother or rougher than 
is indicated by 7=0*55. The only exceptions appear to be those channels 
which are initially rougher to the eye than rough cast plaster work or brick¬ 
work enclosure walls,— i.e . relatively speaking, carelessly laid masonry or 
brickwork. Ordinary unrendered concrete which has not been deposited with 
excessive care also agrees very fairly with 7 = 0*50 ; and all slimed concrete 
rapidly reaches the state where 7=55. 


1030 


CONTROL OF WATER 


700 — 


1—30.0 


200 - 


I 

I 

I 

<8 


300 -t 

400 

300—_ 

600- 

700- 

800- 
$ 00 - 
7000- 


2000 - 


3000 —: 


4000 


5000 

6000 

7000 — 
8000— 
$000 
70,000- 


500 

40.0 


— 20.0 


> / * 

( > 

-/o.o 

■ I 

' fe 

-5.0 
4.0 ^ 


—3.0 


2.0 


-.— 70 


0.50 


40.0— 
30.0—z 

20 . 0 —: 


/O.O 


5.0—_ 
4.0 

3.0 - 

2.0 - 


o 

■ , 

* 

$ 


7.0 — 

0.50—_ 
0.40—_ 

0.30— 

0 . 20 — 



70.0 — 

SO — 
40 — 

3.0 — 

2.0 — 

7.50 - 

7.0 — 


0.50— 

0.40— 

0.30— 

0 . 20 — 

(JR 

0.75 J 


Diagram No. 9. Velocity of Water in Channels of Bazin’s 

Class III. ; 7=0*833. 


/7yc/rau//c Mean Acre//us /r? fee 7 

















GRAPHIC DIAGRAMS 


I ° 3 I 


VELOCITY OF WATER IN CHANNELS OF BAZIN’S 

CLASS III. ; 7 = 0-833. 

The diagram on the opposite page corresponds to Bazin’s Class III. ; or 
7 = 0*833, which Bazin specifies for rubble masonry. 

In practice, I consider that it is advisable to provide for some extra work in 
roughly dressing the faces of the stones, and filling hollows with mortar, in 
order to secure a smoothness corresponding to 7 = 0-55. The cost, except in 
small channels, does not exceed the advantages secured. 

If, however, either concrete, masonry, or brickwork facings are laid on newly 
excavated earth slopes, and especially on artificial banks of earth, the adoption 
of 7 = 0*833 is advisable, since bad settlement will produce a state of affairs 
corresponding to this class. 

By careful maintenance it is also possible to change a channel of this 
character from 7 = 0*833, to 7 = 0*60, or 0*65 approximately ; and in many cases 
considerable increases in discharge may be secured without heavy capital 
expenditure. 


I0 3 2 


CONTROL OF WATER 


ZOO 


200 — 


300 


400—- 


I 

s 

$ 

N 

I 

'S 

°0 


500 

600- 

700- 

800- 

900- 

/OOO- 


500 

40.0 

30.0 


20.0 


—ZO.O 




\ 


- ^ 

' ^ 
~-5.0 \ 

X 

-4.0 


-—3.0 


2000 — 


3000— 

4000 — 

5000 — 

6000 
7000- 


8000 — 
9000—- 
10 . 000 - 


20 


Z.O 


0.50 


300 — 


20.0 


ZO.O — 


50- 
4.0 - 

3.0 — 

2 . 0 - 




/O 


0.50- 
0.40- 

0.30— 

0 . 20 — 


K 

o 






\ 


0./5 —* 

Diagram No. io.-Velocity of Water in Channels of 

Class IV.; y = 1*54. 


ZO.O— 

5 . 0 - 

40— 

3.0— 

2 . 0 — 

Z.50- 

/.O— 

■ 

0.50 — 
_ > 

0.40— 

030— 

0 . 20 — 

Bazin’s 


fY yc/rav/zc Mean fiaaZ/us /r? Wee7 



















GRAPHIC DIAGRAMS 


io 33 


VELOCITY OF WATER IN CHANNELS OF BAZIN’S 

CLASS IV. ; y— 1*54. 

The diagram on the opposite page corresponds to Bazin’s Class IV. ; or 
7=1-54. 

Bazin specifies this for earth channels of very regular surface, or reveted 
with stone. 

In actual practice I have found that only very carefully maintained channels 
in earth fall under this class. The presence of fine silt permits of y = 1-54 being 
attained fairly rapidly, provided that the maintenance is intelligently directed. 
Likewise, coarse sandy silt is unfavourable, and such channels should not be 
designed with y much under 2*00. My experience of stone revetments is not 
very extensive ; but, so far as it goes, in cases where pains are taken to 
secure a smooth surface, any carefully constructed revetment is smoother than 
y=i*54, and corresponds more nearly to 7=1*20 to 1*30. A rough revetment 
of loose stone of large size is usually rougher than 7=1*54, at any rate in small 
channels. 


1034 


CONTROL OF WATER 



30.0 —: 

20 . 0 —_ 

w.o — 


5.0 - 
4.0- 

3.0 — 


2.0 


3 


/0 — 


0.50 L 
0.40- 

0.30—- 

0 . 20 - 
0./5 H 


§ 

x 


$ 

t 


/o.o — 

5.0 — 
4.0 — 

3.0 — 

• __ 

2.0 — 

/.SO - 



0.50— 

040— 

0.30— 

0.25- 


Diagram No. u.—V elocity of Water in Channels of Bazin's 

Class V.; 7=2-35. 


Mye/s'cruZ/c Mean fiac//us //? fecf 

















GRAPHIC DIAGRAMS 


io35 


VELOCITY OF WATER IN CHANNELS OF BAZIN’S 

CLASS V. ; y=2*35. 

The diagram on the opposite page corresponds to Bazin’s Class V. ; or 
7 = 2*35. 

Bazin specifies this for ordinary earth channels. 

I believe that designs for artificial channels should only be based on this 
value when the channel is markedly crooked in plan, or when maintenance is 
not well attended to ; but no advanced hydraulic engineer will allow an im¬ 
portant channel to remain in such a state for a lengthy period. 

Silt and scour are, of course, unfavourable conditions, and when present, the 
value 7 = 2-35 may temporarily prove too low. 


V| . gV"' j V > - 1 ■' * ’■ 


i 



r 


1036 


CONTROL OF WATER 



/ 0 . 0 — 


20 . 0 — 



5.0 
4.0 — 






* 


5.0 - 
4.0 — 


50- 


2.0 - 


1.50 - 





0.50—_ 
0.40— 



0.30 


0.50- 


0.20 

0./5 


0.40- 

0.30- 


Diagram No. 12.—Velocity of Water in Channels of Bazin’s 

Class VI.; 7=3*17. 


H yc/rav/ic Mean /Pc/c//c/s //? Feef 











GRAPHIC DIAGRAMS 


1037 


VELOCITY OF WATER IN CHANNELS OF BAZIN’S 

CLASS VI.; 7 = 3-17. 

The diagram on the opposite page corresponds to Bazin’s Class VI. ; or 

7 = 3 * 17 - 

Bazin specifies this for exceptionally rough earthen channels (bed covered 
with boulders), or weed-grown sides. 

Judging by my own experience, such values of 7 usually occur only in flood 
gaugings. 

I have employed 7 = 3*17, in the design of a channel which was likely to be 
largely obstructed by weed growth, and in which it was undesirable to cut or 
destroy the weeds more frequently than once a year. 




'■ '■ • ' V' \ ■ 




















■ 










'■ : ‘ '■ t 1< 1 1. .!•) ; :■■■! • ;> V'l ! . .. . / | r j 

m»'£ fJ.1V \?./, K \ ) 

■ • 

' , \ 

■ ’ ■ ■ 

.8 .-'ii-ur 

‘ 













































INDEX 


Aboukir, Lake, reclamation, 745. 
Absorbent areas, floods, 281. 

Absorption, 631, 637, 638, 643, 738, 741. 
distributaries, 733. 
fields, 647. 

losses by agriculturists, 649. 

Acre foot, 5. 

Aeration, colour, 588. 
deferrisation, 585. 
ddgroisseurs, 544. 
odours and tastes, 589. 

Afflux, 657, 694. 

Ageing, 454. 
pipes, 436. 
steel pipes, 457. 
table, 443. 

Tutton formula, 442. 

Weston-Darcy formula, 442. 
Aggregate, concrete, 959, 960, 973. 
Agricultural drainage, run-off, 223. 
Agricultural machinery, 732. 
duty, 645. 

Agricultural operation, irrigation, 625, 
Agriculturists, 730. 
alkaline soils, 746. 
waterings, 641. 

Aichel, oblique weirs, 118. 

Air, accumulation in syphons, 829. 
chamber, hydraulic ram, 844. 
compressed. See Compressed Air. 
entrainment in syphons, 826. 
lift pumps, 831. 
mixture with water, 839. 
pipes in filters, 581, 583. 
skin friction with water, 833. 

“ snifter,” 844. 
velocity of bubbles, 827, 839. 
volume of chamber, 852. 
water ratio, 827, 829, 832. 

“Air slaking,” cement, 958. 

Air valve, 611. 

Alfalfa. See Lucern. 

Alkali, removal, 745. 

Alkaline soils, 742. 

Alkalinity, 556. 

coagulation, 561. See also Softening. 
Allowance of water, subsoil water, 747. 
Alluvial deposits, percolation in, 26. 
Alluvial underflow, 256. 

Alpine areas, rainfall loss, 209. 

Altitude, rainfall, 181. 

Aluminium sulphate, “ basic alum,” 562. 
sedimentation basins, 564. 
solution, 563. 

American weirs, 673. 


Anderson process, colour, 588. 

Andrd, experiments, 798. 

Angus Smith, 437, 438, 

pipe coating, discharge, 428. 

Anicut. See Weirs, 
discharge, 133. 

Aprons, Assouan, 343. • 

regulation, 697. 
talus, under-sluices, 692. 
weir, 134, 680, 683. 

Aqueducts, 625, 706. 
rapid, 720. 
timber, 718. 

Arch dams, 358, 403. 

Arch, deflection, 405. 
puddle loaded, 337. 
stresses, 338. 

Arch and buttress dam, 410. 

Area of irrigation plots, 644. 

Artesian wells, discharge, 151. 
mineral content, 271. 
Queensland, 272. 
temperature of water, 272, 273. 
theory, 271. 
thickness of strata, 272. 
velocity of flow, 274. 
yield, 273. 

Asphalte, 340, 396, 619. 

coated pipe discharge, 428, 432. 

core walls, 317. 

dam fissures, 378. 

filters, 535. 

specification, 460. 

steel, 354. 

Assouan dam, 399. 
repairs, 343. 

Assouan. See also Barrage. 

Atcherley dams, 374. 
weirs, 673. 

Atmospheric pressure, 6. 

Automatic cut-off valves, 611, 612. 

Automatic diaphragm, valves, 594. 

Austin dam, 392, 652. 

Australian absorption, 741. 

Average, 172. 

Backwater functions, 1006. 

Bacteria, America, 371. 
coagulation, 561, 576. 
mechanical filters, 572, 374, C77. 
sedimentation, 533. 
slow sand filters, 532. 
softening, 591. 
storage, 534. 

Balanced gate, 32 7 . 

1C39 




INDEX 


1040 

Balancing depth, 726. 

Ball bearings, 776, 990. 

Band shoes for wood pipes, 464. 

Banks, distributaries, 727. 

Bar, 656, 684. 

Bara, 686. 

Jhelum, 678. 

Sidhnai, 657. 

Tajewala, 662. 

Bar and Bet, 637. 

Bara, bar, 686. 

Bari Doab, discharge, 738. 
distributaries, 726. 

Kennedy’s observations, 753. 

Lower, 639. 
silt, 766. 

Barley, duty ratio, 640. 

Barrage, 683. 
failure, 701. 
grouting, 981. 
springs, 690. 

See also Esneh, Assouan, Menufiah. 

Bars, velocity in rivers, 92. 

Base, duty, 631. 

Basin, irrigation, 626. 

Batter, dams, 364. 

dam thickness, 367. 

Bazin, drowned weirs, 124, 
end contraction of weirs, 114. 
flat-topped weirs, 128. 
formula for channels, 474. See also Bazin’s y. 
Francis weirs, 113. 

graphic velocity diagrams, 1025-1037. 
inclined weirs, 119. 
notch and dam face, 401. 
pit, 103. 

weir description, 109. 
weir formula, 109. 

Bazin’s y, 474. 
brick conduit, 435. 
floods, 91. 

graphic determination, 87, 476. 

Kiitter’s n, 474. 
limits, 477. 
rod floats, 59. 
silt, 477. 

surface velocity, 64. 

B. coli, 571. 

Bear trap dams, 772, 777, 779. 
river regulation, 772. 
stiffness of leaves, 782. 

Bear Valley Dam, 408. 

Bearings, 776. 

Bed silt, 750, 752. 

Bellasis, Hydraulics , 2. 

Kennedy’s rule, 754. 

Bellmouth orifice, 147. 

Bellmouth resonance, 818. 

Bell’s dykes, 667, 668. 

maintenance, 653. 

Bends, 611. 
anchoring pipes, 463. 
table of resistance, 31. 

Bending moment in reinforced concrete, 413. 
Bending stress, iron pins, 402. 

Bengal, rice watering, 643. 

Bengal gates, 694, 711. 

Bernouilli’s equation, 13. 

Bernouilli’s variable flow, 480. 


Bet, 637. 

Bidone, orifice, 151. 

Binnie, rainfall, 178. 
run-off and rainfall, 242, 243. 

Bitumen, 437, 619. 
brickwork, 621. 
filters, 535. 

sheeting, 321, 340. See also Asphalte. 

Black alkali, 743. 

Bohemia, evaporation, 192. 

Boilers, coagulation processes, 568. 

Borda, orifice, 78, 151. 

Borda’s formula, 793. 

Bournes, 211. 

Bouzey dam, 390. 

Brass pipes, discharge, 432. 

Brick conduit, discharge, 428. 
friction, 435. 

Brick drains, 530. 

Brick filter, 543. 

Brickwork, Bazin’s y, 475. 
bitumen, 621. 
face batters, 420. 
specification, 339. 
springs, 689. 
temperature, 619. 
well curbs, 984. 

Bridges, 711. 

Brightmore, experiments, 791. 

British rainfall intensity, 277. 

Brunei, retaining walls, 418, 421. 

Brushing, pipes, 438. 

Buoyancy dams, 775. 
shutters, 775. 

Burma, non-silting velocity, 768. 

Calibration, 38. 
irregularities, 39. 

Pitot tube, 69. 

California, alkaline soils, 748. 

Californian absorption, 740. 

Californian irrigation, 628, 748. 

Californian run-off, 251. 

Canal head gates, 664. 

Canal heads, alignment, 752. 
discharge, 165. 
silt, 751. 

Canal irrigation, 927. 
duty, 645. 

Canal regulators. See Regulators. 

Canal sections, 728. 

Canals, alteration in cross-section, 707, 712. 
closure, 660. 
grading, 713. 

Capillary elevation, 23. 

Carbon, porous, 588. 

Casing, dam, 330. 

Cast-iron pipe discharge, 428, 432. 
pipe thickness, 445, 446. 
tensile stress, 445. 

Young’s modulus, 811. 

Cast-iron pipes, specification, 450. 

Catchment area, 171. 
critical period, 282. 
drainage, 256. 
flood discharge, 280. 
leakage, 205. 
peat colour, 587. 
secondary, 254. 





INDEX 


1041 


Catchment galleries, 257. 
formulae, 262. 

Caulking, 449, 451, 452, 459. 

Cement. See Chapter Heading, p, 957. 
dams, 377. 

| hydraulic lime in dams, 395. 
lined pipe discharge, 428. 
rendering, 619. 

Centre of gravity. See Mass Centre. 

Centrifugal pumps, 869, 937. 
skin friction, 857. 

Chalk, rain-fall loss, 189. 
water softening, 592. 
wells, 258, 268. 

Channel in bank, maintenance, 654. 

Channel of approach, 98. 
waves, 102. 

Channels, open. See Chap. IX. p. 469. 

Charcoal. See Carbon. 

Chases, 340. 

concrete, 317, 323. 
puddle, 324. 

Chemical “filtration,” climate, 596. 

Chemical gauging, 33, 73. 
accuracy, 74. 
table, 76. 
weirs, 77. 

Chenab canal, silt, 754. 

Upper, 638. 

Chenab, Lower. See Khanki. 

Circular orifices, pipes, 790, 799. 

Clark’s process. See Softening. 

Clay, hydraulic fill dam, 349. 
permeability, 348. 
precipitation, 562, 573. 
removal from sand, 542. 
specification, 311. 

See also Puddle. 

Clay precipitate, deferrisation, 586. 

Cleaning filters, 531. 
ferrous sulphate, 569. 
mechanical, 569, 576. 
slow sand, 530. 

Clearance, skin friction, 859. 

Climate, 175. 
droughts, 196, 
duty, 634. 
filtration, 596. 
dashboards, 401. 
hydraulic fill dam, 350. 
pipe incrustations, 441. 
rainfall, 179. 
second type, 239. 
third type, 249. 
types, 196. 

Clouds, evaporation, 191. 

Cippoletti notch, 126. 

Circular orifices, 139. 
tables, 142-144. 
workmanship, 145* 

Coagulation, alkalinity, 561. 
bacteria, 561. 
colour, 562. 
mechanical filters, 575* 
motion, 562. 
pipes, 563. 

sedimentation, 563, 567. 
slow sand filters, 564, 57 °* 
solution, 563. 

66 


Coagulation, sulphur process, 569. 
turbidity, 561. 
washing filters, 577. 

Coating pipes, 428, 459. 

Cock, loss of head, 789. 

Coefficient of contraction, 137. 

Coefficient of discharge, capillarity, 139. 
high heads, 788. 
normal 144. 
orifices, 137. 
regulators, 730. 
screen, 85. 
waste weir, 288. 
watercourse outlets, 735. 

Coefficient of expansion, 398. 
humidity, 399. 

Coefficient of velocity, 137, 145. 

Coke filter, 543. 

Coker, Venturi meter, 80. 

Cole’s Pitometer, 71. 

Collars, 461. 
cast-iron pipes, 452. 

Colleroon weir, 672, 

Colloids, 586. 

Colour in water, 586. 
alkalinity, 562. 
aluminium sulphate, 569. 
clay precipitation, 562. 
discharge by, 434. 
ferrous sulphate, 569. 

Command, 725, 728, 729. 

Complete suppression, 158. 

Compressed air, 838, 840. 
filters, 580, 583. 

Compressor, air. See Hydraulic Air Com 
pressor. 

Concrete. See Chapter Heading, p. 957. 
core wall, 313, 318. 
creeping flange, 341. 
dams, 395. 
deposition, 535. 
expansion, 398. 
filters, 535. 
lias lime, 397. 
plums, 404. 

Poisson’s ratio, 405. 

reinforced. See Reinforced Concrete. 

sand washing, 542. 

shearing strength, 371. 

shuttering, 976. 

slab specification, 331. 

specification for junctions, 316. 

springs, 689. 

strength of dry and wet, 396. 
temperature, 619. 

Condensation, 206. 

Coned valves, 594. 

Cones, divergence loss, 797. 
skin friction, 797. 

Conical orifice, 148. 

Constricted channel, river weirs, 668. 

Constriction, Venturi meter, 82* 

Consumption of water, Australia, 603. 
China, 605. 
daily variation, 600. 
day and night rates, 608, 609. 
domestic, 603. 

England, 601. 

Europe, 603, 605. 








1042 


INDEX 


Consumption of water, France, 604. 
Germany, 602. 
hourly variations, 598. 

India, 605. 

Japan, 606. 

London, 603, 604, 

S. Africa, 606. 
trade, 603. 

Continental climates, rain-fall, 179. 

Contour drains, 256. 
lines, 725. 

Contracted weirs, m. 

Contraction, end, 104. 
end, Francis, 107. 
loss of head, 790. 
pipes, 790. 

suppressed, 104, 117. 
steel pipes, 455. 

Conversion tables, 2. 

Copper sulphate, 589. 

Core wall, 305. 
permeability, 348. 
pressure, 319, 
rubble, 352. 
steel, 354. 
timber, 353. 

Core wall and trench, drainage, 317, 319. 

See also the Various materials. 

Corrected head. See Head, Weirs. 

Corrosion, 458, 463. 

Cotton, duty, 630. 

Crack. See Fissure. 

Crayfish, 684. 

Creeping flanges, 341. 
puddle, 335. 

Critical head, 142. 
obstructions, 791. 

Critical period, 279, 282. 
floods, 277. 

Critical velocity, 20. 

Bilton and Thrupp, 22. 

Venturi meter, 82. 
weirs and orifices, 22. 

Crops, alkaline soils, 746. 
duty, 641. 
duty ratios, 640. 

Cross sections of rivers. See River, Cross 
Sections. 

Croton, mass curve, 230. 

Culvert, 334, 335. 
puddle load, 337. 
slip joint, 336. 
tunnel, 336. 

Current meter, 33. 
change of velocity, 40. 
description, 47. 
errors in flood, 51. 
errors of discharge, 51. 
irregularity, 37. , 1 . } 

laboratory, 48. 
local velocities, 17. 
manufacturer’s rating, 50. 
oblique currents, 47. 

Pitot tube, 67. 
rating, 48. 
rating errors, 49. 
rating in current, 49. 
rating, irregularities, 50. 
silt, 50. 


Current, swinging, 41. * 
time of run, 37. 
vibratory motion, 48. 
waves, 49. 
weir, 40. 

weir discharge, 56. 
weir error, 41. 

Curtain wall, 696. See also Cut Off. 

Curve resistance, 28. 
large pipes, 30. 
reverse curve, 30. 
table, 31. 

Weisbach’s formulas, 31. 

Curved dams, 403. 

triangular section, 408. 

Curves, pipes, 16. 

Cusec, 5. 
gallons, s, 

gallons per hour, 612. 

Cut off, weirs, 683. 

wells 690. See also Curtain Wall. 

Cycle, hydraulic ram, 845, 851. 

Cylindrical orifice, 149, 151. 

Dale Dyke dam, 330. 

Dam, hydraulic fill. See Hydraulic Fill Dam. 
masonry. See Chap. VIII. (Section B), p. 
356 . 

sluice design, 343. 
stockramming fissures, 691. 

Damping waves, 102. 

Darcy, pipe formula, 444. 

Darcy tube. See Pitot Tube. 

Debris dam, 719. 

Deferrisation, 584. 
colour, 589. 
pipe mains, 438. 
vegetable colour, 586. 

Deflection, arch, 405. 
cantilever, 782. 
steel pipes, 458. 
temperature in dams, 398. 

Deflection resistance, Weisbach’s formulae, 
3 T * 

D^groisseur, 544. 
climate, 596. 
deferrisation, 585. 

Delta barrage. See Barrage. 

Density, water, 1. 

Depletion, mass curve, 232. 
maximum, 222. 
run-off, 220. 

Deposits, pipes, 437, 438. 

Derived silt, 750. 

Derwent filters, 530. 

Desarenador, 344. 

Desert, run-off, 195. 

Deviation, rain-fall, 177. 

Dew ponds, 207. 

Diagrams, graphic, 1014-1037. 

Diaphragm, loss of head, 790. 

Differential gauge, 68. 
silt, 72. 

water tower, 954. : 

Discharge, artesian well, 273. 

Bazin’s formula, 474. 
central surface, 64. ' ' 

central vertical, 63. 
colour, 434. 





INDEX 


*°43 


Discharge, contour, 44. 

Darcy’s formula, 444. 
drain formulae, 283. 
duty, 632. 
elementary, 43. 
elimination period, 44. 
faults, 205. 
flood, 280. 
formula, 34, 45. 
fountain, 151. 
glaciers, 208. 
ice-covered rivers, 54. 

Kistna weir, 133. 

Kiitter's formula, 471. 
large pipes, 434. 
launder, 131. 
limits of formulae, 477. 

Manning’s formula, 472. 
mean velocity over vertical, 44. 
mid depth, 55. 
mountain streams, 208. 
o’6 depth, 54. 
o’8-f o'2 depth, 54. 
open channels, 470. 
percentage of rainfall, 277, 282. 
pipes, 427. 
pipes, errors in, 429. 
scraping pipes, 440, 442. 
sluices, 164. 

steel pipes, 453, 455, 457. 

summation, 55. 

surface, 55, 63. 

three point, 55. 

total, 43. 

waterfall, 131. 

waves, X02. 

weir formulae, 112. 

Discharge curve, 85. . 

errors, 51. 

shifting beds, 93, 95. 
slope, 89, 92. 
tributary, 91. 

Disk, friction, 856. 

Displacers, concrete, 975. 

Distortion, steel pipes, 458. 

Distributary, 625. 
absorption, 737. 
bank, 727. 
design, 733. 
falls and rapid, 723. 
location, 725. 
plans, 735. 
regulation, 742. 
silt, 723. 

Distribution of velocities, 15. 
losses, 800. 

Venturi meter, 83. 

Divergence, skin friction, 797. 

Diversion channel, 254. 

Dome valve, 333. 

Domed dam, 409. 

Domestic consumption meters, 609. 

Dowlaisheram weir, 675. 

Draft tubes, turbines, 901. 

Drain capacity, 276, 279. 
dam, 306. 

discharge formulae, 283. 
spacing, 745, 746. 

Drainage, alkaline soils, 743. 


Drainage, arch spandrels, 620. 
dam, 306, 319. 
filters, 530. 

hydraulic fill dam, 351. 

Indian dams, 322. 
irrigation, 625, 748. 
masonry dams, 380. 
mechanical filters, 577. 
peat colour, 587. 
run-off, 223. 
slips, 325. 
springs, 690. 

Driest year, equalising reservoir, 232. 
Drift, moveable dams, 776. 

Dropdown functions, 1006. 

Drought, 194. 

Drowned weirs, 121. 
errors, 123. 
flat-topped, 133. 

Dry weather flow, 199. 

Dry years, depletion, 189, 
rain-fall, 178. 
run-off, 213. 

Dune sand water supplies, 257. 

Durance, canal head, 765. 

Duty, 629. 

Bari Doab, 631, 640. 
base, 631. 
cotton, 630. 
depth of water, 631. 

Egypt. 6 3o. 650. 

estimation, 641. 

Ganges, 632. 

Indian floods, 650. 

Kharif, 637. 
maturing crops, 633. 

Mesopotamia, 636. 
plot area, 643, 647. 
ploughing, 630. 

Punjab, 629. 

Rabi, 638. 
rain-fall, 634. 
rate of flow, 647. 
ratios, 640. 
rice, 631. 

Sirhind, 640. 
soil, 633, 639. 
temperature, 635. 
utilised, 649. 
variations, 639. 
wheat, 633. 

Earth, density, 419. 
pressure, 417. 
pressure on pipes, 446. 
puddle, 312. 

Earthdams, permeability, 348. 
Earthwork, consolidation, 309, 324. 
humps, 310. 
subsidence, 308. 

Eckart, experiments, 935, 

Effective size of sand, 25, 

Efficiency, air lift, 833, 835. 
hydraulic compressor, 840. 
hydraulic ram, 849, 853. 

Effluent waste, bacteria, 573, 576. 

mechanical filters, 574, 575, 376, 584. 
Egypt, alkaline soils, 748. 
canal headworks, 752. 







1044 


INDEX 


Egypt, depths of floods, 650. 
non-silting velocity, 768. 
silt, 757. 

See also Nile. 

Egyptian absorption, 740. 
irrigation, 627. 

Ejector, 820. 
efficiency, 538. 
proportions, 537. 
ratio sand and water, 539. 
sand washers, 536. 

Elbe, run-off, 193. 

Elbow, resistance of, 29, 31. 

Embankment, specification, 307. 

Emulsion, 831, 832, 834. 

End contractions, Bazin, 114. 

End suppressed contraction weir, 112. 

Energy, mooring vanes and pipes, 861. 

Enlargement, loss of head, 793, 796. 

Enteisenung. See Deferrisation. 

Equalising reservoir, 226, 235. 
driest year, 233. 
flood, 284. 

Erosion, falls and rapids, 720. 
soft bricks, 714. 

Escape troughs, 582. 

Escapes, 625, 664, 702. 
capacity, 704, 705. 
channel training, 721. 

Faizabad, 694. 
oblique weirs, 126. 

Qushesha, 699. 
silt, 764. 

Esneh piles, 690. 

Evaporation, 173, 740. 
clouds, 191. 
free water, 207. 
mass curve, 229. 
monthly, 192. 
run-off, 190. 
temperature, 191. 

Vermeule, 219. 

Expansion. See Coefficient of Expansion, 
joints, concrete, 978. 
joints in pipes, 456. 
timber, 467. 

Experimental dam, 349, 

Fall, 713. 
aqueduct, 708. 
erosion, 720. 
intensifier, 925. 

Madras, 718. 
maintenance, 651. 
notched, 721. 
ogee, 653. 
training, 655. 
turbine, 714. 

See also Notch and Needle, Falls and 
Rapids. 

Falls and rapids, 713. 
distributary, 723. 
erosion, 720. 

Fault, leakage, 737. 

Ferrous sulphate, coagulation reactions, 565. 
colour, 562. 
dosing, 568. 
steam, 567. 

“ Fetch,” 331. 


Field absorption, 739. 
division, 731. 
irrigation, 730. 

Filter, area, 531. 
drains, 592. 

mechanical. See Mechanical Filters, 
reversed. See Reversed Filters, 
washing, 542. 

Filtration rate. See Rate of Filtration. 

Fissure, Bouzey dam, 392. 
dams, 309. 
earthwork, 310. 
masonry dams, 383. 
puddle, 311, 312, 317. 
reinforced concrete. 416. 
retaining walls, 421. 
stockramming, 691. 
strain, 387. 
undersluices, 693. 
weak dam, 385. 
weir, 676. 

Finkle, velocity diagrams, 932. 

Fissured rock, dams, 353. 
fires, 618. 
insurance, 616. 
mains, 613. 
nozzles, 791, 792. 

Fissures, canals, 740. 

Flashboards, 401, 417, 773, 774. 

Flat areas, rainfall loss, 208. 

“ Flats ” discharge, 280. 

Flat-topped weirs, 128, 130, 132. 
drowned, 133. 

Floats. See Rod, Surface or Turn-floats. 

Flood irrigation, 626, 649. 
duty, 650. 

Floods. See Chap. VI. (Section B), p. 275. 
Bazin’s y, 91. 
dam, 308. 
damage, 91. 

Kutter’s n, 91. 
maxima, 281. 

overtopping dams, 329, 332. 
permeable strata, 204. 
preliminary formuke, 281. 
silt rejection, 345. 
subsidiary gauge, 91. 

Flow irrigation, 626. 

Fluid, definition, 6. 

Flynn and Dyer, Cippoletti notch, 116. 

Forage, duty ratios, 640. 

Forcheimer, well formula:, 264. 

Foundation, dams, 378. 
reinforced concrete, 416. 

Fountain, discharge, 151. 
failure, 697, 701. 

Fractures, resonance, 817. 

Francis, Bazin weirs, 113. 
drowned weirs, 122. 
end contractions, 107. 
rod float correction formula, 58. 
turbines. See Turbines, 
weir description, 106. 
weir formulae, 105. 

Freeze, weir formula, 1x8. 

French absorption, 738. 

Friction, air and water, 833. 
boards, 854. 
cones, 800. 




INDEX 


I 




Friction, cylindrical orifice, 149. 
dams, 369, 374, 394. 
losses, 13. 

turbines and pumps, 857. 

Frizell, experiments, 838. 

Frost, filter cleaning, 543. 

Froude, experiments, 855. 

Fteley & Stearns, round-edged weirs, 121. 

Galleries, See Catchment Galleries. 
Gallons, imperial, cube feet, 2. 
cusec, s, 612. 

United States, 2. 

Galvanised pipes, discharge, 432. 
Ganguillet, 471. 

Gardens, duty ratio, 640. 

Garland, 314. 

Gauge, hook, 101, 108. 
location of, 426. 

wheel, 101. See also Rain Gauge. 
Gauge-discharge. See Discharge Curve, 
pit, Bazin, 101. 

Punjab, 103. 
theory, 102. 

Gauging. See Chapter Heading. 

silted water, 146. 

Gelpke, accurate method, 914. 
guide vanes, 864. 
turbines, 884, 896, 909. 

Geology, artesian wells, 274. 

German absorption, 741. 

German reservoir capacity, 228. 

Gibson and Ryan, experiments, 857. 
Glaciers, run-off, 207. 

Glaisher gauge, 182. 

Glass, pipes discharge, 432. 

Godaveri weir, 676. 

Gorge, dam, 308. 

Governors, resonance, 817. 

Graeff, orifices, 168. 

Granite Reef weir, 673, 

Graphic diagrams, 1014-1037. 

Grashof, pipe thickness, 444. 

Grass, specification, 331. 

Gravel, mechanical filters, 573, 579. 
percolation, 26. 
roughing filter, 571. 
shutter dams, 773. 
thickness in filters, 529. 
trap, 765. 

Gravel-bearing rivers, working, 662. 
Gravimetric gauging, 33. 

methods, 77. 

Gravity dams, 358. 

Ground storage, 189. 

Indian, 245. 
permeable strata, 193, 

Ground water, 187. 

chemical determination, 194. 
depletion, 220, 222. 
drought, 195. 
equalising reservoir, 235. 
replenishment, 266. 
run-off and rain-fall, 218. 

Grouting, 391, 680, 688, 690, 
cement, 980. 
fissured rock, 319. 
springs, 690. 

Groynes, 682, 684. 


Groynes silt, 750. 

Guide vanes, turbines, 881, 897, 904, 923 

Gulp gauging, 77. 

Gypsum, alkaline soils, 743. 

H 1 ' 5 values, 999. 

H 2 ’ 5 values, 1002. 

Habra dam, 653. 

Hamilton Smith, circular orifices, 143. 
square orifices, 154. 

Plat leather packing, 595. 

Hawksley, cast-iron pipes, 445. 
reservoir capacity, 226. 
waste weirs, 286. 

Head, 6. 
critical, 142, 
critical in orifices, 588. 
divergence loss, 797. 
entrance, 424. 
error in measurement, 100. 
friction and shock, 8. 
load on valves, 805. 
mains, 612. 
measurement, 100. 
strainers, 582. 
velocity, 7. 
weirs, 98. 

Head reach, double, 665, 766. 

Head works, 625. 

Egyptian, 752. 
inundation canal, 670. 

Lombardy, 664. 
maintenance, 666. 
silt, 751. 

Tajewala, 664. 

Height, dam, 305. 

Herschell, drowned weir, 123. 

Venturi meter, 80. 

High dams, 371. 

Hilly areas, rainfall loss, 209. 

Hindan headworks, 751. 

Hook gauge, iox. 

Horizontal orifices, 145. 

Horton, Weir Experiments, 3. 

House fittings, 609. 

House-to-house inspection, 607. 

Humidity, concrete, 399. 

Humps, earthwork, 3x0. 

Hydraulic air compressor, 836. 

Hydraulic fill dam, 305, 349. 

Hydraulic gradient, 471. 

Hydraulic lime, dams, 377, 395. 
strength of mortar, 396. 

Hydraulic mean radius, 471. 

Hydraulic rams, 843. 
indicator diagram, 849. 
practical rules, 852. 
valves, 807. 

Ibrahimiya canal, 696. 
discharge, 739. 
silt, 750. 

Ice, thrust of, 394. 

Impact losses, Pelton wheels, 866. 
tube, 67, 72. 
water, 861, 864. 

Impermeability, puddle, 312, 

Impermeable stratum, culvert, 337 See 
Permeable Strata. 




INDEX 


1046 

Incrustation, calcium carbonate, 437, 441, 
444 - 

limpet. See “ Limpets.” 
slime. See Slime, 
steel pipes, 457. 
tropical climates, 441. 

Venturi meter, 82. 

Incrusted pipes. See Pipes, Incrustations. 
Indian absorption, 738, 741. 
dam, 321. 
irrigation, 627. 
run-off, 245. 

Indicator diagram 848. 

Inspection, house-to-house, 607. 

Insular climates, rain-fall, 179. 

Inundation canals, 695. 
head works, 752. 
maintenance, 670. 
silt, 763. 
working, 669. 

Inundation irrigation, 649. 
duty, 650. 

Invisible storage, 194. 

Iron, deposits in pipes, 438. 
ultimate bending stress, 402. 

See also Anderson process and Deferrisa- 
tion. 

Irregularities in stream bed, 51. 

Irregularity. See Motion, Irregular; also 
Rod Floats and other instruments. 
Irrigated area, 636. 

Irrigation, fall and rapid, 714. 
lining channels, 725, 740, 748. 
methods, 730. 
seepage, 194. 

See also Chap. XII., p. 623. 

Irrigation canals, emergency supply, 638. 
Irrigation, depth of water, 629. 

See also Duty. 

Iso-hyetals, 181. 

Italian irrigation, 627. 

Jack arches, dams, 396. 

Jaipur dam, 327. 

Jamrao canal, 696. 

regulator, 699, 700. 

Jet, capillarity, 139. 
coalescence, 588. 
cross sections, 137. 
fountain, 151. 
impact tube, 72. 
viscosity, 139. 

Jet pump, 820. 

Jets, Pelton wheels, 928. 

Jhelum bar, 678. 
regulator, 697. 
silt, 754. 

under-sluices, 695. 
weir, 680, 682. 

Johnstown flood, 287. 

Joint rings. See Collars. 

Joints, cast-iron pipes, 447. 
sliding, 595. 
wood staves, 465. 

Jumna. See Tajewala. 

Kali Nadi aqueduct, 707. 
flood, 284. 

Kaplan types of turbines, 896, 909. 


Keller, rainfall loss, 208. 

Kennedy, channels and silt traps, 757. 
effect of silt grade, 756, 758. 
Hydraulic Diagrams , 3. 
observations, 753. 
physical basis, 767. 
rule, 754. 

silt in watercourses, 756. 
velocity, 733, 734. 

Kennedy channels, 729. 

silt carried forward, 769. 

Khanki, 754. 
regulator, 696. 
training works, 669. 
under-sluices, 693, 696. 
weir, 676, 685. 

Kharif, 636. 

Kiari, 644, 731. 

Kila, 731. 

Kistna weir, 133, 674. 

Knee, resistance of, 29. 

Koshesha. See Qushesha. 

Kuichling, 787. 

Kutter's n, 471. 
auxiliary values, 1004. 

Bazin’s y, 474. 
bottom velocities, 65. 
brick conduit, 435. 
floods, 91. 
limits, 477. 
rod floats, 59. 
silt, 473, 477. 
surface velocity, 64. 
variations, 476. 

Labyrinth packing, 795. 

Laguna weir, 673, 679. 

“ Laitance,” 980. 

Lakes and swamps, run-off, 207. 

Lang dams, 777, 782. 

Large orifice, 163. 

Large weirs, 131. 

Launder discharge, 131. 

Lead, pipes discharge, 432. 

Leakage, Baroda dam, 329. 
bear trap dams, 781. 
canals, 628, 738, 739. 
catchment areas, 205. 
ground surface, 307. 
lining canals, 740. 
puddle trench, 317. 
reservoirs, 741. 
town water, 599. 
town water catchment area, 210. 
wood pipes, 466. 

See also Absorption and Waste. 
Level crossings, 711. 

Levelling, ridge lines and errors, 737. 
Lime, milk of, 592. 

See also Milk of Lime. 

Limestone filters, 438. 

Lime water. See Milk of Lime. 
Limpets, 437, 439, 441, 444. 

Lias lime concrete, 397. 

Lift irrigation, 626. 

Lining channels, 740, 748. 

Locking bar pipe, 461, 462. 

Loffel wheels, 927, 931. 

Logarithmic pipe formula, 431.. 












INDEX 


1047 


Logarithmic plotting, 87. 

Lombardy headworks, 664. 

winter meadows, 647. 

London filters, 535. 

filter sand specification, 530. 

Low dams, 332. 

Lucern, duty ratio, 640. 

Madhuptir headworks, 663, 

Madhupur regulator, 699. 

Magnesia, 591. 

Clark’s process, 593. 
coagulation, 561. 
ferrous sulphate, 566. 

Magnesia water, treatment, 593. 

Mahanadi weir, 672. 

Mains, branched, 614. 
fires, 613. 

incrusted and clean, 613, 
leakage, 608, 610. 
pressure, minimum, 616. 
river crossings, 613. 

See also Pipes. 

Maintenance, 651. 
distributaries, 728. 
falls, 717. 

falls and rapids, 721. 
headworks, 666. 
inundation canals, 670. 
weir, type (B), 673, 675. 

Maize, 643. 

Malaria, 647. 

Manganese. See Deferrisation. 

Manganese deposit in pipes, 438. 

Manning, discharge formula, 472, 478. 
Manure, duty, 641. 

Marcite, 647. 

Masonry, face batters, 420. 

specific gravity, 362. 

Masonry core walls, 317, 318, 319, 323. 
Cyclopean, 380. 
depth to resist pressure, 709. 
expansion, 399. 
service reservoir, 618. 
specification, 339. 

Masonry dams. See Chap. VIII. (Section 
B). P- 356 . 

Mass centre, buttresses, 414. 

Mass curve, 229. 

Mean value, 172. 

Measuring apparatus, permanent, 33. 
Mechanical filters, 572. 
area, 577. 
cleaning, 569, 576. 
dams, 772, 777. 
disinfection, 584. 
effluent waste, 574, 575, 576. 
filter bed, 579. 
filtration rate, 579. 
head lost, 577. 
irregular working, 574, 576. 
pipes, 563. 
rate of filtration, 573. 
strainers, 578, 581. 

Melbourne run-off, 201. 

Menufiah regulator, 701, 702. 

Meters. See Water Meters. 

Metric equivalents, 2. 

Middle third rule, 361, 374, 379. , 


Middleton, reservoir capacity. See Rolfe. 
Milk of lime, 570. 

Mineral waters, artesian well, 273. 

Mixed areas, rainfall loss, 209. 

Mixing machines, concrete, 974. 

Mixture, air and water, 839. 

conditions, 73, 820, 831. 

Module, 730, 736. 

Modulus, bulk, 8x1. 

Young’s, 81 x. 

Moldau, run-off, 193. 

Monsoon, run-off, 218. 

Month, monsoon and snow, 218. 

Monthly run-off, Vermaule, 221. 

Mortar, impermeable, 983. 

Motion, of water, character, 798. 
irregular, 36, 41. 
periodic unsteady, 11. 
steady, 9. 
stream line, 17. 
turbulent, 17, 424. 
uniform, 10. 

Mountain streams, run-off, 208. 

Movable dams, 771, 778. 

Nagpur rainfall and run-off, 244. 

Nappe, 98. 
adhering, 127. 

Bazin’s boundaries, 400. 
drowned, 127. 
pressure, 23, 124. 
springs free, 121. 
standing wave, 127. 
types, no. 
wavy, 127. 

Narora under-sluices, 693. 

Narora weir, 671, 685. 

Needle falls, 715. 

Needles, 657, 712, 715, 772, 775, 776. 

Nile, Ibrahimiah canal, 750. 
river banks, 727. 

Nile slope, 753, 757. See also under Egypt. 
Nipher shield, 182. 

Non-silting velocity. See Kennedy. 

Notch, 98. 

calculation in canals, 724. 
fall, 716, 721. 
width in canals, 724. 

See also Chapter Heading, IV. 

Oblique weirs, 1x8. 

Obstructions, Kiitter’s n, 473. 

loss of head, 786. 

Odours in water, 589. 

Ogee fall, 652, 653, 715. 

Okla weir, 672, 683, 697. 

Old pipes. See Ageing. 

Orifices. See Chapter Heading No. V. p. 
135 - 

aeration, 588. 
critical velocity, 22. 
graphic diagrams, 1023. 

Outlet, balanced gate, 326. 
capacity, 342. 
head wall, 342. 
pipes, 333. 
tunnel, 336. 

See also Reservoir Outlets. 

Overfall dam, 364. 








1048 


INDEX 


Overflow dam, form of face, 399. 
maintenance, 652. 
silt, 346. 
vacuum, 415. 
weirs, 129, 131. 

Overhang, 366. 
dams, 370. 

Packing-, hat leather, 595. 
labyrinth, 795. 

Panicum crus galli, 744, 746. 

Parabolic dam, 365. 

Parker dams, 777, 779. 

Partial suppression, 158, 

Partially suppressed orifice, 147. 

Partially suppressed rectangular orifice, 158. 

Pearsall Ram, 849. 

Pearson dams, 374, 375, 

Peat, drainage and colour, 587. 

Pelton wheels, 864, 866, 927, 929. 

efficiency, 933. * 

impact tube, 72. 
velocity equation, 862. 

Pendulum valves, 850. 

Percolation, 173. 
alluvial deposits, 26. 
dam, 321. 
dirty sand, 26. 
failure, 389. 
gravel, 26. 
puddle, 312. 
puddle wall, 323. 
sand, 25. 
slips, 322. 

sodium carbonate, 743. 
table, 27. 
velocity, 25. 

See also Leakage. 

Perennial irrigation, 626. 

Permanent hardness, ferrous sulphate, 568. 

Permeability, 258. 
artesian wells, 273. 
clay puddle, 348. 
earth dams, 348. 
equations, 260, 262. 
table, 269. 

Permeable strata, floods, 204. 
ground storage, 188, 193, 245. 

Puentes dam, 389. 
rain-fall loss, 211. 

Peuch-Chabal, 544. 

Piers, under-sluices, 693. 

Piles, dam, 389. 

Esneh, 690. 
grouting, 690, 691. 
wells, 691. 

Piling, cast-iron, 319. 
open spaces, 701. 
steel, 319. 
timber, 339. 
weirs, 679. 

Pipe bands, 465. 

Pipe bends, anchoring, 463. 

Pipe coating, specification, 437. 

Pipe discharge, gallons per minute, 428. 

Pipe joints, 448, 449, 450, 451, 452, 456, 461. 

Pipe laying, 429, 448. 
specification, 450. 

Pipe mains, calculation, 612. 


Pipes. See Chap. VIII. p. 422. 
air in filters, 581. 
capillary motion, 24. 
circular, 789. 
coagulating solution, 563. 
conical, 797. 
contractions, 792. 
creeping flange, 341. 
curve losses, 15, 16. 
discharge of large, 434. 
distribution of velocities, 19. 
enlargements, 792. 
enlargements or contractions, 796. 
entry into, 863. 
incrustations, 592. 
inlet to service reservoir, 6x8. 
Kiitter's n, 473. 

Levy’s formula, 3. 

loss of head at contraction, 790. 

loss of head at diaphragms, 793. 

loss of head at enlargements, 793. 

loss of head at obstructions, 786. 

losses of head, 796. 

motion of body in, 855. 

motion of water, 861. 

old. See Ageing. 

orifices, 841. 

Pitot tube, 69. 

pressure by water hammer, 810, 812. 

pressure diagrams, 811. 

pressure orifice, 68. 

proportions of ram, 852. 

resistance, 855. 

resistance of bends, 31. 

resistance to stream line motion, 19. 

resistance to turbulent motion, 20. 

resonance, 816. 

resonance fractures, 817. 

shock at entry, 863, 864. 

“ specials,” 611. 
stiffness, 783. 
stream lines, 18. 
tapered in air lifts, 836. 
transport of sand, 539. 
turbulent motion, 18. 

Tutton’s formula, 612. 
velocity, 430. 

Venturi meter, 82. 
water hammer, 809. 

Piping failure, 701. 

Piston flow, 832, 834. 

Pitching, 330. 
aqueducts, 707. 
bridges, 711. 
escapes, 704. 
falls, 718, 721. 
falls and rapids, 719. 
roughened, 707, 720. 
specification, 331. 
syphons, 709. 

Pitometer, Cole and Gregory, 71. 

Pitot tube, 33. 
current meter, 67. 
description, 65. 
error, 42. 
formula, 67. 
irregularities, 39. 
pipes, 69. 

pressure orifice, 67. 






INDEX 


1049 


Pitot rating, 42. 
still and running water, 39. 
weir, 42. 

Plaster, dams, 395. 

Plating, sluice gates, 992. 

water tanks, 993. 

Plot division, 732, 745. 

Ploughing watering. See Duty. 

Plug chases, 340. 
culvert, 335. 
specification, 339. 

“ Plums," concrete, 975. 

Pointing dams, 396. 

Poisseuille’s ratio, 24. 

Pole and plug valve, 333. 

Pollution wells, 265. 

Population, 621. 

Portland cement. See Cement. 
Precipitation, 203, 206. 

Precipitation, clay. See Clay Precipita¬ 
tion. 

hydrates, 589. 

Prefilters, washing, 543. 

Pressure, absolute, 6. 
dams, 359, 371, 374. 
dynamic. See Head Velocity, 
earth, 417. 
gauge, 6. 

maximum in dams, 372. 

mooring vanes and pipes, 862. 

orifice, 67, 68. 

tons per square foot, 405. 

unit, 5. 

weir, 671. 

working on sand, etc., 632 . 

Pressure gauge, capillary, 23. 

Venturi meter, 84. 

Private water supplies, 607. 

Prolonged orifice, 159. 

Puddle, base of wall, 323. 
creeping flange, 341. 
dam fissures, 378. 
filters, 534. 

Indian, 322. 

Indian trench, 323. 
service reservoir, 618. 
settlement, 335. 
specification, 310. 
tenacity, 312. 
thickness, 312. 
trench filling, 315. 
trench garland, 314. 
trench leakage, 317. 

See also Clay. 

Puentes dam, 389. 

Pump, shock at closure, 803. 

Pump valve, 794, 802. 

Pumps, air lift, 831. 
centrifugal. See Centrifugal Pumps, 
jet, 820. 

Pumping, service reservoirs, 615. 

Punjab, alkaline soils, 748. 
canal silt, 757, 760. 

Kennedy’s observations, 753. 

ploughing duty, 646. 

ploughing watering, 643. 

river silt, 760. 

slope of rivers, 753, 757. 

watercourses, Table of Discharges, ion. 


Qushesha, 699. 
escape, 699. 

Rabi, 636. 

Radial exit, turbines, 883. 

Rails, dam, 308. 

Rain-fall, 173. 
altitude, 181. 
condensation, 206. 
cycle, 177. 

discharge percentage, 277, 282. 

diversion channel, 255. 

drought, 194. 

duty, 634, 646. 

errors, 200. 

ground storage, 187. 

intensity, 275. 

long period, 177. 

mean annual, 178. 

ratio, 178. 

seasonal, 183, 203. 

space relationship, 178. 

variability in space, 180. 

variability in time, 176, 177, 236. 

vegetation period, 235. 

wet and dry seasons, 196. 

yearly ratios, 237. 

Rain-fall and run-off. See Run-off. 
Rain-fall loss, 173. 

British table, 237-9. 

European, 241. 
first type, 197. 

German, 208. 
individual years, 199, 211. 
limestone, 211. 
maximum British, 203, 239. 
probable error, 210. 
summer and winter, 198. 
temperature, 186, 193, 219. 
tropical, 249. 

United States, 240, 254. 
very wet areas, 214. 

Victorian, 252. 

Raingauge, autographic, 278. 
location, 200. 
run-off, 202. 
spacing, 181. 
surroundings, 182. 

Rainstorm, irrigation, 705. 
mass curve, 230. 
motion, 282. 

third type of climate, 197. 

See also Thunderstorm. 

Raised sill, 699. 
falls and rapids, 722. 

Madhupur, 663, 664. 
ogee falls, 653. 
shutters, 701. 

Sirhind, 659, 660. 

Rakes, mechanical filters, 580. 

Ralli weir, 675. 

Ramming, 309. 

Rams, hydraulic. See Hydraulic Rams. 
Rapids, 713. 

maintenance, 651. 
slopes, 719. 
width, 719. 

See also Falls. 

Rate of filtration, cleaning, 531. 



1050 


INDEX 


Rate of filtration, deferrisation, 585. 

mechanical filters, 573, 574, 579. 

Rate of flow, duty, 647. 

Rating. See Calibration. 

Ravi, 661, 665. 

Raw sand, 537. 

Reclamation, alkaline soils, 742, 744. 
Rectangular orifice, 155, 159. 

Reducing valve, 609, 617. 

Reflux valve, 611. 

Rdgime, 655. 

Regulating apparatus, filtration, 593. 
Regulator, 656, 695. 
apron, 697. 

bellmouth sluices, 766. 
branch canal, 711. 
capacity, 698, 700, 730. 
clay foundations, 666. 
discharge, 165. 
erosion, 702. 
fall and rapid, 714. 
floor thickness, 697. 
gravel streams, 699. 
irrigation canals, 741. 

Jamrao, 699, 700. 

Madhupur, 663. 

Menufiah, 701, 702. 
raised sill. See Raised Sill, 
silt, 761. 

Tajewala, 663. 

Trebeni, 698. 

Regulators, branch canals, 711. 
failures, 701. 

Reinforced concrete, culvert, 338. 
dams, 410. 
fissures, 416. 
stress, 412. 
syphons, 710. 
temperature, 620. 

Remodelling, 735. 

Rendering, concrete, 977. 

Repairs, falls, 717. 
house fittings, 609. 

Narora, 671. 

Replenishing period, 184, 234. 

Reservoir capacity, 226, 228, 248. 

Reservoirs, absorption, 737. 
escape, 706. 
evaporation, 740. 
flood equalisation, 284. 
ground water, 347. 
irrigation, 627. 
maximum capacity, 236. 
outlet, 326, 342. See also Outlets and 
Valve Tower, 
seepage, 740. 
silting, 344. 
stripping, 587. 

terminal. See Service Reservoirs, 
three dry years, 226. 

Residual irregularities, 172. 

Resonance, pipes, 816. 

Retaining walls, 417. 

Retrogression of levels, 656. 

Reversed filter, 322, 327, 686, 689. 
toe wall, 325. 
weir, 672, 682. 
wells, 268. 

Reynold’s critical velocities, 19. 


Rice, 643. 
duty, 631. 

Ring banks, 689. 

River banks, 727. 

River cross sections, aspect, 90. 
discharge, 86. 
survey, 89. 

River discharge, duty, 639. 

River regulation, movable dams, 772. 

River working, 658-670. 
under-sluices, 692, 695. 

Rivers, Bazin’s y, 475. 
deeps and shallows, 92. 

Kiitter’s n, 473. 
shifting beds, 92. 

Riveted pipes, discharge, 428, 432. 

Riveting, 460, 462. 
stresses, 990. 

Rivets, obstruction, 455, 457. 
specification, 459, 461. 
turbines, 903. 1 

Rock fill dam, 351. 

Rock, fissured, 3x9. 
working stresses, 404. 

Rocky catchment areas, 250, 256. 

Rod floats, 33. 

correction formula, 58, 60. 
description, 60. 
error, 42, 58, 59. 
fair runs, 41. 
immersed length, 57. 
irregularity, 37. 
number, 37. 
weirs, 59. 

Rolfe, reservoir capacity, 227. 

Roller bearings, 776, 990. 

Rollers, 308, 323. 

Roofing service reservoirs, 620. 

Rotating discs, 856. 

Roughened pitching, 720, 721. 

Roughing filters, 544, 571. 

Round edged weirs, 121. 

Rubble core walls, 352. 

Rugosity, co-efficient of. See Kutter's n. 

Run-off, 173. 

agricultural drainage, 223. 

American, 214. 

British, 213. 
diversion channel, 255. 
equivalents, 3. 
error in rainfall, 200. 
evaporation, 185, 190, 192. 
glaciers, 207. 
ground water, 187. 
monthly, 225. 
mountain streams, 208. 
rainfall, 184. 
rain-gauge, 202. 
seasonal, 203, 215. 
statistics, 174. 

Sudbury, 217. 

Thames, 216. 
topographical, 187. 
topography, 193, 204. 
vegetation, 185. 

Run-off and rain-fall, ground water, 218. 
hill and valley, 240. 

Indian ratios, 247. 
monsoon, 242, 243. 





INDEX 


1051 


Run-off and rainfall, proportional, 218. 
records, 218. 
subtractive, 217. 
third type of climate, 249. 

Vermeule, 219. 

Rupar. See Sirhind. 

Salt land. See Alkaline Soils. 

Sand, Bouzey dam, 393. 

cleaning and effective size, 532. 
effective size, 25. 

Egypt, 679. 
in concrete, 960, 969. 

Madras, 672, 679. 
mean diameter, 26. 
mechanical filters, 573, 579. 
percolation, 25. 
percolation in dirty, 26. 
piping, 683, 697. 
pockets in concrete, 317. 
puddle, 312. 

Punjab, 679. 
ripe, 529. 

roughing filter, 571. 
sifted, 540. 

size of grains and permeability, 269. 

sizes, 679. 

specification, 530. 

suspension, 580, 582. 

thickness in filters, 529. 

transport in pipes, 539. 

uniformity coefficient, 25. 

voids, 25. 

washing, 579. 

working pressure, 682. 

Sand bearing rivers, 659. 

Sand dam, 327. 

Sand filters, climate, 596. 

Sand sizing, wells, 267. 

Sand traps, 664, 666, 764. 

Sand washing, 535, 541. 

Sand waves, slope of river, 93. 
velocity, 92. 

Saph and Schroder, pipe discharge, 433, 
434 - 

Saturated solution, 73. 

Saturation plane, slope, 348. 

Savannah, rain-fall intensity, 275. 
Schmutzdecke, formation, 529. 

mechanical filters, 573. 

Scour, bed, 721. 

Bell dyke, 667. 
gallery, 344. 

Kennedy’s rules, 703. 
river working, 658. 
sluice capacity, 344. 
valves, 611. 
velocity, 751. 

Scouring sluices. See Under-sluices. 
Scraper, filter, 543. 

hatch, 441. 

Scraping pipes, 439. 

Screen, coefficient of discharge, 85. 
gauging, 33, 84. 
mechanical filters, 579. 

Second foot. See Cusec. 

Secondary catchment areas, 254. 
Sedimentation, 571. 

Clark’s process, 593. 


Sedimentation, climate, 596. 
coagulation process, 567. 
deferrisation, 586. 
duty, 646. 
seepage, 194, 740. 
slow sand filters, 564. 
softening, 592. 
turbidity, 533. 

See also Absorption. 

Service reservoirs, 615. 
capacity, 616. 
construction, 618. 
puddle, 618. 

Sextant, 36. 

Sharp-edged orifice, 141. 

Sharp-edged weir or notch, 104. 

Sharp-edged weir, graphic diagram, 1016. 

Shear, dams, 359, 371, 375. 
reinforced concrete, 413. 
stone and concrete, 372. 

Shearing strength, dams, 397. 

Sheffield, mass curve, 231. 

Shock, vanes and pipes, 863, 864. 
losses, 14. 

Shoot, discharge, 159. 

Shrinkage, earthwork, 309, 324. 
hydraulic fill, 351. 

Shutter dams, 772, 773, 774. 
boulders, 773. 

“Shuttering,” concrete, 976. 

Shutters, raised sill, 701. 
river crossings, 711. 

Side suppressed contraction weir, 112. 

Sidhnai Bar, 657. 

Silt, 749. 

adjustment, 763. 

Bazin’s y, 477. 

bear trap dams, 779, 781. 

bed, 755. 

berm, 729. 

bottom velocity, 65. 

classifier, 759. 

clearance, 626, 696, 728, 755. 
coarse, 757. 

constricted channel, 668. 
deposits, 723. 
differential gauge, 72. 
distributary banks, 728. 
diversion channel, 255. 
double head reach, 766. 
escape channel, 705. 
escapes, 763. 
falls and rapids, 723. 
fertilising, 756. 
grade, 659, 756, 758. 
ground water, 347. 
head reach deposits, 761. 

Kennedy channels, 769. 

Kiitter’s n, 473, 477. 
maintenance, 654. 
modules, 736. 
motion, 755, 761, 762. 
needles and stop planks, 712. 
non-silting velocities, 769. 
notches, 116. 
outlet, 342. 
profiles, 655. 

Punjab, 727, 760. 
reservoirs, 344. 




1052 


INDEX 


Silt, river working, 658. 
sand trap, 764. 

Sirhind deposits, 659, 661. 
skin friction, 703. 
slope, 93, 757. 
spacing of traps, 765. 
stanching, 691. 
suspended, 759. 
syphons, 708. 
tanks, 324. 

trap, 660, 666, 692, 761. 
traps and channels, 757. 
turbidity, 763. 
warping, 749. 
watercourses, 756. 
weight of, 767, 

See also Kennedy. 

Sind, non-silting velocity, 768. 

Sirhind canal, 704. 
discharge, 738. 
escapes, 705. 
head works, 659, 751. 
regulator, 699. 
silt, 762. 

under-sluices, 694. 

Skin friction, ageing pipes, 443. 

Bernouilli’s equation, 480. 

brickwork and concrete syphons, 426. 

clearance, 859. 

conical pipe, 797. 

jet pumps, 823. 

locking bar pipe, 462. 

pipes, 427. 

sand and water, 540. 

silt, 703. 

steel pipes, 453. 

temperature, 857. 

turbines, 857. 

Sliding joint, 595. 

Slinae, 437. 

Slip-joint, culvert, 336. 

Slips, 310, 322. 
drainage, 325. 

Slope, discharge curve, 89, 92. 

Indian dam, 325. 

Rutter's ?i, 472. 
silt, 93. 

Slow sand filters, 529. 
applicability, 532. 
colour, 588. 

odours and tastes, 589. See also Chapter 
Heading, p. 8. 

Sluice, framing, 993. 
loss of head, 788. 
movable dams, 773, 775. 
plating, 992. 
repairs, 343. 

Smooth pipes, discharge, 433. 

Smooth-topped weirs, 129. 

Snow, rain-fall conversion, 182. 

run-off, 218, 220. 

Snowdon gauge, 182. 

Sods, 331. 

Softening, 437, 590. 

Soil fertility, alkaline soils, 749. 

Soils, duty, 642. 

Sone weir, 672. 

Sound velocity, Sir. 

Soundings, 34, 51. 


Soundings, hemp cord, 35. 
piano wire, 35. 
pole, 35. 
rapid river, 35. 
sextant, 36. 
sinker, 35. 
small stream, 35. 

Special crops, duty, 649. 

Specification, asphalte, 460. 
brickwork, 339. 
cast-iron pipes, 446, 450. 
caulking, 451, 459. 
concrete surfaces, 316. 
culvert plug, 339. 
dam casing, 330. 
dam site, 306. 
embankment, 307. 
grass, 331. 

hydraulic qualities, pipes, 427. 

London filter sand, 530. 

masonry, 339. 

pipe coating, 437, 438, 460. 

puddle, 310. 

rivets, 459, 461. 

steel, 461. 

steel pipes, 459. 

wood pipes, 464. 

Spillway. See Waste Weir. 

Spillway dam. See Overflow Dam. 

Sponge filter, 543. 

Spoon wheels, 927, 931. 

Springs, 688. 
closure, 689. 
collection, 257. 
faults, 205. 
hydraulic rams, 850. 
load on, 807. 
sealing, 689. 
temperature, 690. 

Spur dykes, 92. 
maintenance, 654. 

Square, 731. 

Square orifice, 153. 

Stanching, canals, 740. 
rods, 991. 

Standard weirs, 105. 

Standing wave, weir, 688. 

“ Starters ” syphons, 829. 

Steel, minimum plate thickness, 463. 
specification, 461. 
stresses, 460. 

Young’s modulus, 811. 

Steel core walls, 354. 

Steel pipes, 453. 
specification, 459. 
syphons, 709, 710. 

Steel rings, cast-iron pipes, 448, 449, 

Stilling well. See Gauge Pit. 

Stockramming, 691. 

Stone, shearing strength, 371. 

Stoney gates, 693, 698. 
bearings, 989. 

Stop-cocks, 607. 

Stop planks, 712. 

Storage depletion, 220, 222: 
maximum reservoir, 236 

Storage period, 184, 234. 

Stored water, 188. 

Strain, fissures, 387. 



INDEX 


Strainers, 578, 582. 

Stream, flood discharge, 280. 

Stream flow, geology (faults), 205. 

Stream line motion, 17. 

Stress, cast-iron tensile, 445. 
compressive, on rock, 404. 
crushing, timber, 466. 
expansion, timber, 467. 
fissures, 387. 
pipe bands, 467. 
rivetting, 990. 
steel, 460. 

water hammer, 463. 
working, reinforced concrete, 412. 
Stripping, specification, 307. 

Structures, stresses and strengths, 987. 
Submerged orifice, 146, 162, 163, 168. 
Subsoil water, irrigation quota, 747. 

Sud, evaporation, 207. 

Sugar-cane, duty ratio, 640. 

Sulphur coagulation, 569. 

Summer floods, 279. 

Suppressed contraction. See Contraction. 
Suppressed square orifice, 157. 
Suppression, 158. 

Suresnes trestles, 776. 

Surface floats, 33. 

discharge formula, 61. • 
error, 42. 
fair runs, 42. 
flood and freshet, 62. 

Harlacher’s method, 61. 

Surface friction, 855. 

Surface irregularity, 37. 
number, 42. 

Survey, discharge curve, 89. 

irrigation, 736. 

Suspended silt, 749, 752. 

Sutlej, 659. 
silt, 761. 

Swamps, run-off, 207. 

Sylvester’s process, 984. 

Syphons, 625, 708, 823. 
entrance head, 426. 
outlets, 335. 

reinforced concrete, 710. 


1053 

Temperature, reinforced concrete, 416, 620. 
skin friction, 857. 
springs, 690. 
vapour pressure, 186. 

Venturi meter, 83. 

yearly variation in masonry, 399. 

Terminal reservoir, 6x8. 

Thames, evaporation, 192, 

Thomson, triangular notch, 114. 

Throttle valve, 789, 

Thunderstorms, 181. 

See also Rainstorm. 

Timber, aqueduct, 718. 
core wall, 353. 
crushing stress, 466. 
durability, 468. 
expansion, 467. 

Kiitter’s n, 473. 
piling, 319. 
specification, 464. 
weir, 684. 

Timbering, 452, 454 
trench width, 3x2. 
walings and runner, 313. 

Tobacco, duty ratio, 640. 

Toe wall, 325. 

Torpedo sinker, 35. 

Torquay, rain-fall loss, 197. 

Town water areas, rain-fall loss, 210. 

Town water supply. See Chap. XI. p. 
597 - 

Trade supplies, 606, 609. 

Training banks, 665, 667, 668, 669. 

Bell’s, 653. 
escapes, 721. 
falls and rapids, 721. 

Training dykes, maintenance, 655. 

Trebeni regulator, 698. 

Trench, width, 312. 

Trestle dams, 772, 775. 

Triangular notch, 114. 
duty, 642. 

H 2 * 5 values, 1002. 
probable error, 115. 

Triangular orifice, 162. 

Triangular weir, 130. 

Tributary, discharge curve, 91. 
floods, 91. 

Tropics, rainfall intensity, 279. 

Trough sand washers, 536. 

Trussed frames, 994. 

Tube gauge, 183. 

Tunnel outlet, 336. 

Turbidity, bacterial size, 575. 
coagulation, 561. 
ferrous sulphate, 569. 
mechanical filters, 572. 
silt, 763. 

slow sand filters, 533. 

Turbine, energy equation, 863. 
resonance, 817. 
skin friction, 857. 

Turbines, 869. 

design, 881, 885, 920. 
efficiency, 898. 
exit angle, 912. 

Francis. 872, 889. 
governing, 942. 
guide passages, 903. 


Tail thickening, dams, 382, 
Tajewala, 662, 663, 664. 

regulator, 699. 

Talus, repairs, 688. 
weir, 680. 

Tank, irrigation, 627. 

See also Reservoir. 

Tarred pipe, discharge, 428. 
Tastes in water, 589. 

Tawi syphon, 710. 

Tees, 611. 

Tension, dams, 377. 
Temperature, artesian well, 273. 
brickwork, 619. 
concrete, 619. 
dams, 398. 
duty, 635, 645. 
evaporation, 191. 
inundation irrigation, 649. 
orifices, 145. 
pipes, 459. 

rain-fall loss, 186, 193, 219. 





io 54 


INDEX 


Turbines, horse power, 894. 
regulation, 923. 

Type II., 891. 
vanes, 863. 
wheel entry, 905. 
wheel vanes, 915. 

Turbulent motion, 21, 798. 

Ktitter’s n , 473. 

Turf, 306, 331. 

Turned joints, 450. 

Tutton’s formula, 427, 612. 
steel pipe, 457. 
table, 478. 

Twin floats, 54. 

Two angle survey, 36. 

Typhoid, 534. 

Underflow, 205, 257. 
climates of second type, 248. 

Under-sluices, 692. 

Bengal gates, 695. 
capacity, 661, 665, 694. 
discharge, 165. 
floor thickness, 693. 

Jhelum, 695. 
reservoir, 333. 

Tajewala, 662. 

Uniformity coefficient, 25. 

United States, absorption, 741. 
rain-fall intensity, 278. 
rain-fall losses, 254. 
reservoir capacity, 228. 

Units, conversion, 3. 
length, time, etc., 5. 

Unwin, cast-iron pipe thickness, 445, 447. 
experiments, 856. 
pipe formula, 432. 
weir formula, 130. 

V 0 . See Kennedy. 

Vacuum, dam face, 400. 
syphons, 824. 

Valve tower, 333, 335, 341. 

Valves, 611. 

automatic diaphragm, 594. 
balanced, resonance, 817. 
closure, 810, 812. 
closure velocity, 803, 804, 805. 
cone and diaphragm, 594. 
dome, 333. 

head lost, 787, 805, 845. 

hydraulic rams, 844, 850. 

loading, 805. 

motion in pumps, 802. 

pendulum, 850. 

pipes, 785. 

pole and plug, 333. 

pump, 794. 

reducing, 609. 

rubber beat, 844. 

seats, 847. 

shock, 812. 

sounding, 804. 

spring, 850. 

throttle, 789. 

water hammer, 804, 809. 

Vane, motion over, 862. 

Vanes, impact, 863. 
turbines, 897. 

Vapour pressure, temperature, 186. 


Variable flow, 480. 
escapes, 703. 
mains, 612. 

Vegetables, duty ratio, 640. 
Vegetation, growth, 184, 234. 

water consumption, 234. 

Velocity, 9. 
aqueducts, 708. 
artesian wells, 274. 
bottom, 65. 
central surface, 64. 
central vertical, 63. 
critical. See Critical Velocity, 
curve of vertical, 52. 
differences of local, 11. 
distribution of observations, 52. 
energy of, 15. 
erosion, 714. 
head, 7. 
irregularity, 12. 
local, 17. 

local distribution, 15. 
maximum, 63. 

maximum and minimum, 74. 
mean, 9. 
mean local, 11. 
mean over a vertical, 51. 
non-silting, 753, 768. 
number of points, 52. 
resultant, 9. 

silt and scour, 751, 752. 
surface, 63. 
syphons, 708. 

Velocity of approach, 98. 

Velocity, corrections, 113. 

orifices, 139, 145. 

Ventavon, canal head, 765. 

Venturi meter, 33, 79. 
formula, 80. 
minimum velocity, 83. 
pipes, 82. 

pressure gauge, 84. 
proportions, 83. 
temperature, 83. 

Vermeule run-off, 219. 
tables, 224. 

Victorian rainfall and run-off, 251. 
Virgin soil, irrigation, 633. 

Viscosity, 8. 

Volume, masonry dam, 368. 
Volumetric chemical methods, 74. 
Volumetric gauging, 33. 

error, 33. 

Vortex, 28, 651. 

Vyrnwy, 254, 398. 

Walings, 313. 

Warping, 749. 

Washing, volume of water, 583. 
waste after. See Effluent Waste, 
water pressure, 581. 

Waste of water, 607, 629, 640. 
hourly variation, 598. 
reduction, 609. 

See also Absorption and Leakage. 
Waste weir, 287. 
breadth, 305. 

Hawksley formula, 286. 
silt, 347. 





INDEX 


io 55 


Water allowance, Punjab, 733. 

Water barometer, 6, 150. 

Water, bulk modulus, 811. 
consumption by vegetation, 234. 
density, 1. 

Watercourses, 732. 
capacity, 733. 
distributary level, 730. 
irrigation, 625. 
outlets, 735. 

table of discharges, ion. 

Water cushion, 675, 715. 
depth, 716. 

Water face toe, dams, 378. 

Waterfall, discharge, 131. 
water cushion, 717. 

Water hammer, 44 c, 809. 
stresses, 463. 

Waterings, abnormal, 642. 
number, 641. 
ploughing, 645. 
virgin soil, 635. 

Waterlogging, 748. 

Water meters, 607, 610. 
sale by, 608. 

Water rates, 607. 

Water softening. See Softening and Clark’s 
Process. 

Water tanks, plating, 993. 

Water-tightness, dams, 395. 
dusting, 402. 
reinforced concrete, 413. 

Water tower, 615, 944, 994. 
differential, 955. 

Water year, 183. 

Waves, damping, 102. 

Waves, height, 331. 
silt, 478. 
velocity, 810. 

Webber, experiments, 838. 

Weep holes, 421. 

Weir coefficient, falls and rapids, 722. 

Weir gauging, 33. 

Weirs. See Chapter IV. p. 96. 

American, 673. 
apron, 683. 

apron and talus width, 680. 
apron thickness, 681. 
chemical gauging, 77. 
circular, 151. 

Colleroon, 672. 
concrete apron, 675. 
constricted channel, 668. 
critical velocity, 22. 
current meter, 40. 
current meter discharge, 56. 
curtain wall, 679. 
cut-off, 683. 
dam or core wall, 681. 
deep foundations, 672. 
description, 678. 

Dowlaisheram, 675. 
failures, 685. 
fountain, 151. 

Godaveri, 675. 

Granite Reef, 673. 
graphic diagrams, 1016. 
groynes, 682, 684. 
irrigation, 625. 


Weirs, Khanki, 676, 685. 

Kistna, 674. 

Laguna, 673, 679. 

Lower Jhelum, 681, 682. 

Mahanadi, 672. 
maintenance, 673, 678, 688. 

Narora, 671, 685. 
ogee, 675. 

Okla, 672. 
percolation, 677. 
piling, 679. 
piping, 683. 

Pitot tube, 42. 
pressure under, 671. 
puddle apron, 676, 677. 

Ralli, 675. 

reversed filter, 672, 682. 
rod float, 59. 
rubble aprons, 675. 
rubble foundation, 676. 
shutters, 681. 

side contractions, Bazin, 114. 

Sone, 672. 
springs, 672. 
standing wave, 688. 
timber, 684. 
types, 671. 

velocity head figures, 998. 
water cushion, 675. 
width, 679. 

working pressures., 682. 

Weisbach, experiments, 785. 

Well irrigation, 644, 645. 
canal irrigation, 636. 
duty, 645. 

Well curbs, 984. 

plugs, 268. 

Wells, 205. 

artesian. See Artesian Wells, 
blowing, 264, 265. 
chalk, 258. 

curtain or core walls, 690. 
deserts, 250. 
formulae, 260. 
mota or clay, 269. 
permeable strata, 258. 
piles, 691. 

pumpings contours, 263. 
rain-fall, 268. 
reversed filter, 268. 
yield, 264, 267. 

Wet areas, rainfall loss, 209, 210. 

Wheat, duty, 633. 

duty ratio, 640. 

Wheel gauge, 101. 

Wheel vanes, turbines, 897, 915, 919. 
Width, dajn, 332. 

Winter, floods, 279. 

rain-fall intensity, 278. 

Wood pipes, coating, 468. 
discharge, 428, 432. 
specification, 464. 

Workmanship, coefficient of discharge, 145. 

core walls, 319. 

Worm gearing, 991. 

Yearly mass curve, 232. 

Young’s modulus, 811. 

Yuba debris dam, 719. 








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Culley, J. L. Theory of Arches. (Science Series No. 87.).i6mo, 050 

Dadourian, H. M. Analytical Mechanics.i2mo, *3 00 

Danby, A. Natural Rock Asphalts and Bitumens.8vo, *2 50 

Davenport, C. The Book. (Westminster Series.).8vo, *2 00 

Davies, D. C. Metalliferous Minerals and Mining.8vo, 5 00 

-Earthy Minerals and Mining.8vo, 5 00 

Davies, E. H. Machinery for Metalliferous Mines.8vo, 8 00 

Davies, F. H. Electric Power and Traction.8vo, *2 00 

-Foundations and Machinery Fixing. (Installation Manual Series.) 

i6mo, *1 00 

Dawson, P. Electric Traction on Railways.8vo, *9 00 

Day, C. The Indicator and Its Diagrams.i2mo, *2 00 

Deerr, N. Sugar and the Sugar Cane.8vo, *8 00 

Deite, C. Manual of Soapmaking. Trans, by S. T. King.4to, *5 00 

De la Coux, H. The Industrial Uses of Water. Trans, by A. Morris. 8vo, *4 50 

Del Mar, W. A. Electric Power Conductors.8vo, *2 00 

Denny, G. A. Deep-level Mines of the Rand.4to, *10 00 

-Diamond Drilling for Gold. *5 00 

De Roos, J. D. C. Linkages. (Science Series No. 47.).i6mo, o 50 

Derr, W. L. Block Signal Operation.Oblong nmo, *1 50 

-Maintenance-of-Way Engineering. (In Preparation.) 

Desaint, A. Three Hundred Shades and How to Mix Them.8vo, *10 00 

De Varona, A. Sewer Gases. (Science Series No. 55.).i6mo, o 50 

Devey, R. G. Mill and Factory Wiring. (Installation Manuals Series.) 

i2mo, *1 00 

Dibdin, W. J. Public Lighting by Gas and Electricity.8vt, *8 00 

-Purification of Sewage and Water.8vo, 6 50 

Dichmann, Carl. Basic Open-Hearth Steel Process.i2mo, *350 

Dieterich, K. Analysis of Resins, Balsams, and Gum Resins.8vo, *3 00 

Dinger, Lieut. H. C. Care and Operation of Naval Machinery . . . nmo, *2 00 
Dixon, D. B. Machinist’s and Steam Engineer’s Practical Calculator. 

i6mo, morocco, 1 25 

Doble, W. A. Power Plant Construction on the Pacific Coast (In Press.) 
Dommett, W. E. Motor Car Mechanism.i2mo, *1 25 

Dorr, B. F. The Surveyor’s Guide and Pocket Table-book. 

i6mo, morocco, 2 00 

Down, P. B. Handy Copper Wire Table.i6mo, *1 00 






































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Draper, C. H. Elementary Text-book of Light, Heat and Sound . . i2mo, i oo 

-Heat and the Principles of Thermo-dynamics.i2mo, *2 00 

Dubbel, H. High Power Gas Engines. (In Press.) 

Duckwall, E. W. Canning and Preserving of Food Products.8vo, *5 oo 

Dumesny, P., and Noyer, J. Wood Products, Distillates, and Extracts. 

8vo, *4 50 

Duncan, W. G., and Penman, D. The Electrical Equipment of Collieries. 

8vo, *4 00 

Dunstan, A. E., and Thole, F. B. T. Textbook of Practical Chemistry. 

i2mo, *1 40 

Duthie, A. L. Decorative Glass Processes. (Westminster Series.) .8vo, *2 00 


Dwight, H. B. Transmission Line Formulas.8vo, *2 00 

Dyson, S. S. Practical Testing of Raw Materials.8vo, *5 00 

Dyson, S. S., and Clarkson, S. S. Chemical Works.8vo, *7 50 


Eccles, R. G., and Duckwall, E. W. Food Preservatives . . . 8vo, paper, o 50 


Eck, J. Light, Radiation and Illumination. Trans, by Paul Hogner, 

8vo, *2 50 

Eddy, H. T. Maximum Stresses under Concentrated Loads.8vo, x 50 

Edelman, P. Inventions and Patents.nmo. (In Press.) 

Edgcumbe, K. Industrial Electrical Measuring Instruments.8vo, *2 50 

Edler, R. Switches and Switchgear. Trans, by Ph. Laubach. . .8vo, *4 00 

Eissler, M. The Metallurgy of Gold.8vo, 7 50 

-The Hydrometallurgy of Copper.8vo, *4 50 

-The Metallurgy of Silver.8vo, 4 00 

-The Metallurgy of Argentiferous Lead.8vo, 5 00 

-A Handbook on Modern Explosives.8vo, 5 00 

Ekin, T. C. Water Pipe and Sewage Discharge Diagrams.folio, *3 00 

Eliot, C. W., and Storer, F. H. Compendious Manual of Qualitative 

Chemical Analysis.12mo, *1 25 

Ellis, C. Hydrogenation of Oils.8vo. (In Press.) 

Ellis, G. Modern Technical Drawing.8vo, *2 00 

Ennis, Wm. D. Linseed Oil and Other Seed Oils.8vo, *4 00 

-Applied Thermodynamics.8vo, *4 50 

-Flying Machines To-day.nmo, *4 50 

-Vapors for Heat Engines.i2mo, *1 00 

Erfurt, J. Dyeing of Paper Pulp. Trans, by J. Hubner.8vo, *750 

Ermen, W. F. A. Materials Used in Sizing.8vo, *2 00 

Evans, C. A. Macadamized Roads. (In Press.) 

Ewing, A. J. Magnetic Induction in Iron.8vo, *400 

Fairie, J. Notes on Lead Ores.i2mo, *1 oo 

-Notes on Pottery Clays.i2mo, *1 50 

Fairley, W., and Andre, Geo. J. Ventilation of Coal Mines. (Science 

Series No. 58.).i6mo, o 50 

Fairweather, W. C. Foreign and Colonial Patent Laws.8vo, *300 

Fanning, J. T. Hydraulic and Water-supply Engineering.8vo, *5 00 


Fauth, P. The Moon in Modern Astronomy. Trans, by J. McCabe. 

8vo, *2 00 








































10 


D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Fay, I. W. The Coal-tar Colors.8vo, 

Fernbach, R. L. Glue and Gelatine.8vo, 

-Chemical Aspects of Silk Manufacture.i2mo, 

Fischer, E. The Preparation of Organic Compounds. Trans, by R. V. 

Stanford.i2mo, 

Fish, J. C. L. Lettering of Working Drawings.Oblong 8vo, 


Fisher, H. K. C., and Darby, W. C. Submarine Cable Testing . .. .8vo, 
Fleischmann, W. The Book of the Dairy. Trans, by C. M. Aikman. 

8vo, 

Fleming, J. A. The Alternate-current Transformer. Two Volumes. 8vo. 


Vol. I. The Induction of Electric Currents. 

Vol. II. The Utilization of Induced Currents. 

Fleming, J. A. Propagation of Electric Currents.8vo, 

-Centenary of the Electrical Current.8vo, 

-Electric Lamps and Electric Lighting.8vo, 

-Electrical Laboratory Notes and Forms.4to, 

-A Handbook for the Electrical Laboratory and Testing Room. Two 

Volumes...8vo, each, 

Fleury, P. Preparation and Uses of White Zinc Paints.8vo, 

Fleury, H. The Calculus Without Limits or Infinitesimals. Trans, by 

C. O. Mailloux. (In Press.) 

Flynn, P. J. Flow of Water. (Science Series No. 84.).i2mo, 

-Hydraulic Tables. (Science Series No. 66.).i6mo, 


Foley, N. British and American Customary and Metric Measures. .folio, 
Forgie, J. Shield Tunneling.8vo. (In Press.) 


Foster, H. A. Electrical Engineers’ Pocket-book. (Seventh Edition.) 

i2mo, leather, 

-Engineering Valuation of Public Utilities and Factories.8vo, 

-Handbook of Electrical Cost Data.8vo (In Press.) 

Foster, Gen. J. G. Submarine Blasting in Boston (Mass.) Harbor 4to, 

Fowle, F. F. Overhead Transmission Line Crossings.i2mo, 

-The Solution of Alternating Current Problems.8vo (In Press.) 

Fox, W. G. Transition Curves. (Science Series No. no.).i6mo, 

Fox, W., and Thomas, C. W. Practical Course in Mechanical Draw¬ 
ing .i2mo, 

Foye, J. C. Chemical Problems. (Science Series No. 69.).i6mo, 

-Handbook of Mineralogy. (Science Series No. 86.).. i6mo, 

Francis, J. B. Lowell Hydraulic Experiments.4to, 

Franzen, H. Exercises in Gas Analysis.12010, 

Freudemacher, P. W. Electrical Mining Installations. (Installation 

Manuals Series.).i2mo, 

Frith, J. Alternating Current Design.8vo, 

Fritsch, J. Manufacture of Chemical Manures. Trans, by D. Grant. 

8vo, 

Frye, A. I. Civil Engineers’ Pocket-book.i2mo, leather, 

Fuller, G. W. Investigations into the Purification of the Ohio River. 

4 *o, 

Fumell, J. Paints, Colors, Oils, and Varnishes.8vo. 


*4 00 
*3 00 
*1 00 

*1 25 
1 00 
*3 50 

4 00 

*5 00 

*5 °° 
*3 00 
*0 50 
*3 00 
*5 00 

*5 00 
*2 50 


o 50 
o 50 
*3 00 


5 00 
*3 00 

3 50 
*1 50 

o 50 

1 25 
o 50 
o 50 
15 00 
*1 00 

*1 00 
*2 00 

*4 00 
*5 00 

*10 00 
*1 00 


Gairdner, J. W. I. Earthwork 


8vo (In Press.) 










































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


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Gant, L. W. Elements of Electric Traction.8vo, *2 50 

Garcia, A. J. R. V. Spanish-English Railway Terms.8vo, *4 50 

Garforth, W. E. Rules for Recovering Coal Mines after Explosions and 

Fires.i2mo, leather, 1 50 

Gaudard, J. Foundations. (Science Series No. 34.).i6mo, 0 50 

Gear, H. B., and Williams, P. F. Electric Central Station Distribution 

Systems.8vo, *3 00 

Geerligs, H. C. P. Cane Sugar and Its Manufacture.8vo, *3 00 

-World’s Cane Sugar Industry. 8vo, *5 00 

Geikie, J. Structural and Field Geology. 8vo, *4 00 

-Mountains. Their Growth, Origin and Decay.8vo, *4 00 

-The Antiquity of Man in Europe.....8vo. (In Press.) 

Gerber, N. Analysis of Milk,Condensed Milk,and Infants’Milk-Food. 8vo, 1 25 

Gerhard, W. P. Sanitation, Watersupply and Sewage Disposal of Country 

Houses.i2mo, *2 00 

-Gas Lighting (Science Series No. hi.) .i6mo, o 50 

-Household Wastes. (Science Series No. 97.).i6mo, o 5a 

-House Drainage. (Science Series No. 63.).i6mo, o 30 

Gerhard, W. P. Sanitary Drainage of Buildings. (Science Series No. 93.) 

i6mo, o 50 

Gerhardi, C. W. H. Electricity Meters.8vo, *4 00 

Geschwind, L. Manufacture of Alum and Sulphates. Trans, by C. 

Salter.8vo, *5 00 

Gibbs, W. E. Lighting by Acetylene.i2mo, *2 50 

-Physics of Solids and Fluids. (Carnegie Technical School’s Text¬ 
books.). *1 50 

Gibson, A. H. Hydraulics and Its Application.8vo, *5 00 

-Water Hammer in Hydraulic Pipe Lines.i2mo, *2 00 

Gilbreth, F. B. Motion Study.i2mo, *2 00 

-Primer of Scientific Management.i2mo, *1 00 

Gillmore, Gen. Q. A. Limes, Hydraulic Cements and Mortars.8vo, 4 00 

-Roads, Streets, and Pavements.i2.mo, 2 00 

Golding, H. A. The Theta-Phi Diagram.i2mo, *1 25 

Goldschmidt, R. Alternating Current Commutator Motor.8vo, *300 

Goodchild, W. Precious Stones. (Westminster Series.).8vo, *200 

Goodeve, T. M. Textbook on the Steam-engine.12mo, 2 00 

Gore, G. Electrolytic Separation of Metals.8vo, *350 

Gould, E. S. Arithmetic of the Steam-engine.i2mo, 100 

-Calculus. (Science Series No. 112.).i6mo, 050 

-High Masonry Dams. (Science Series No. 22.).i6mo, 0 50 

__practical Hydrostatics and Hydrostatic Formulas. (Scieice Series 

No. 117.).o 50 

Gratacap, L. P. A Popular Guide to Minerals.8vo, *3 00 

Gray, J. Electrical Influence Machines.i2mo, 200 

——Marine Boiler Design.i2mo, *1 2 5 

Greenhill, G. Dynamics of Mechanical Flight. 8 vo, *250 

Greenwood, E. Classified Guide to Technical and Commercial Books. 8vo, *3 00 

Gregorius, R. Mineral Waxes. Trans, by C. Salter.iamo, *3 00 

Griffiths, A. B. A Treatise on Manures.i2mo, 3 00 

-Dental Metallurgy.. • 8vo > *3 5 <> 




















































12 


D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Gross, E. Hops. 8 vo, *450 

Grossman, J. Ammonia and Its Compounds.i2mo, *1 25 

Groth, L. A. Welding and Cutting Metals by Gases or Electricity. 

(Westminster Series).8vo, *2 00 

Grover, F. Modern Gas and Oil Engines.8vo, *2 00 

Gruner, A. Power-loom Weaving.8vo, *3 00 

GUldner, Hugo. Internal Combustion Engines. Trans, by H. Diederichs. 

4to, *10 00 

Gunther, C. 0 . Integration.nmo, *1 25 

Gurden, R. L. Traverse Tables.folio, half morocco, *7 50 

Guy, A. E. Experiments on the Flexure of Beams.8vo, *1 25 

Haeder, H. Handbook on the Steam-engine. Trans, by H. H. P. 

Powles.12 mo, 3 00 

Hainbach, R. Pottery Decoration. Trans, by C. Salter.i2mo, *3 00 

Haenig, A. Emery and Emery Industry.8vo, *2 50 

Hale, W. J. Calculations of General Chemistry.12010, *1 00 

Hall, C. H. Chemistry of Paints and Paint Vehicles.12100, *2 00 

Hall, G. L. Elementary Theory of Alternate Current Working. .. .8vo, *1 50 

Hall, R. H. Governors and Governing Mechanism.i2mo, *2 00 

Hall, W. S. Elements of the Differential and Integral Calculus.8vo, *2 25 

-Descriptive Geometry.8vo volume and a 4to atlas, *3 50 

Haller, G. F., and Cunningham, E. T. The Tesla Coil.i2mo, *1 25 

Halsey, F. A. Siide Valve Gears.nmo, 1 50 

-The Use of the Slide Rule. (Science Series No. 114.).i6mo, o 50 

•-Worm and Spiral Gearing. (Science Series No. 116.)...i6mo, 0 50 

Hamilton, W. G. Useful Information for Railway Men.i6mo, 1 00 

Hammer, W. J. Radium and Other Radio-active Substances.8vo, *1 00 

Hancock, H. Textbook of Mechanics and Hydrostatics.8vo, 1 50 

Hardy, E. Elementary Principles of Graphic Statics.12010, *1 50 

Harris, S. M. Practical Topographical Surveying. (In Press.) 

Harrison, W. B. The Mechanics’Tool-book.nmo, 1 50 

Hart, J. W. External Plumbing Work.8vo, *300 

-Hints to Plumbers on Joint Wiping.8vo, *3 00 

-Principles of Hot Water Supply.8vo, *3 00 

-Sanitary Plumbing and Drainage.8vo, *3 00 

Haskins, C. H. The Galvanometer and Its Uses.i6mo, 1 50 

Hatt, J. A. H. The Colorist.square i2mo, *1 50 

Hausbrand, E. Drying by Means of Air and Steam. Trans, by A. C. 

Wright.i2mo, *2 00 

—— Evaporating, Condensing and Cooling Apparatus. Trans, by A. C. 

Wright.8vo, *5 00 

Hausner, A. Manufacture of Preserved Foods and Sweetmeats. Trans. 

by A. Morris and H. Robson.8vo, *3 00 

Hawke, W. H. Premier Cipher Telegraphic Code.4to, *5 00 

-100,000 Words Supplement to the Premier Cpde.4to, *5 00 

Hawkesworth, J. Graphical Handbook for Reinforced Concrete Design. 

4to, *2 50 

Hay, A. Alternating Currents. 8vo, *2 50 

-Electrical Distributing Networks and Distributing Lines.8vo, *3 50 

-Continuous Current Engineering.8vo, *2 50 
















































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Hayes, H. V. Public Utilities, Their Cost New and Depreciation.. .8vo, *2 00 


Heap, Major D. P. Electrical Appliances.8vo, 2 00 

Heather, H. J. S. Electrical Engineering.8vo, *3 50 

Heaviside, O. Electromagnetic Theory. Vols. I and II. .. .8vo, each, *5 00 

Vol. Ill.8vo, *7 50 

Heck, R. C. H. The Steam Engine and Turbine.8vo, *5 00 

-Steam-Engine and Other Steam Motors. Two Volumes. 

Vol. I. Thermodynamics and the Mechanics.8vo, *3 50 

Vol. II. Form, Construction, and Working.8vo, *5 00 

-Notes on Elementary Kinematics.8vo, boards, *1 oo 

-Graphics of Machine Forces.8vo, boards, *1 00 

Hedges, K. Modern Lightning Conductors.8vo, 3 00 

Heermann, P. Dyers’ Materials. Trans, by A. C. Wright.nrao, *2 50 

Hellot, Macquer and D’Apligny. Art of Dyeing Wool, Silk and Cotton. 8vo, *2 00 

Henrici, O. Skeleton Structures.8vo, 1 50 

Hering, D. W. Essentials of Physics for College Students.8vo, *1 75 

Hering-Shaw, A. Domestic Sanitation and Plumbing. Two Vols.. .8vo, *5 00 

Hering-Shaw, A. Elementary Science.8vo, *2 00 

Herrmann, G. The Graphical Statics of Mechanism. Trans, by A. P. 

Smith.i2mo, 2 oo 

Herzfeld, J. Testing of Yarns and Textile Fabrics.8vo, *3 50 

Hildebrandt, A. Airships, Past and Present.8vo, *3 50 

Hildenbrand, B. W. Cable-Making. (Science Series No. 32.). .. . i6mo, o 50 

Hilditch, T. P. A Concise History of Chemistry.i2mo, *1 25 

Hill, J. W. The Purification of Public Water Supplies. New Edition. 

(In Press.) 

-Interpretation of Water Analysis. (In Press.) 

Hill, M. J. M. The Theory of Proportion.8vo, *2 50 

Hiroi, I. Plate Girder Construction. (Science Series No. 95.). .. i6mo, o 50 

-Statically-Indeterminate Stresses.i2mo, *200 

Hirshfeld, C. F. Engineering Thermodynamics. (Science Series No. 45.) 

i6mo, o 50 

Hobart, H. M. Heavy Electrical Engineering.8vo, *4 50 

-Design of Static Transformers.i2mo, *2 00 

-Electricity.:. 8v0 > * 2 oo 

-Electric Trains.8vo, *2 50 

Hobart, H. M. Electric Propulsion of Ships.8vo, *2 00 

Hobart, J. F. Hard Soldering, Soft Soldering and Brazing.i2mo, *1 00 

Hobbs, W. R. P. The Arithmetic of Electrical Measurements-i2mo, o 50 

Hofr, J. N. Paint and Varnish Facts and Formulas.izmo, *1 50 

Hole, W. The Distribution of Gas.8vo, *7 50 

Holley, A. L. Railway Practice.folio, 12 00 

Holmes, A. B. The Electric Light Popularly Explained. ..12010, paper, o 50 

Hopkins, N. M. Experimental Electrochemistry.8vo, *3 00 

_Model Engines and Small Boats.i2mo, 1 25 

Hopkinson, J., Shoolbred, J. N , and Day, R. E. Dynamic Electricity. 

(Science Series No. 71.). i6mo, o 50 

Horner, J. Metal Turning. I2m0 > 1 5 ° 

_.Modern Ironfounding. i2mo, *2 50 

_Plating and Boiler Making... 8v0 > 

Houghton, C. E. The Elements of Mechanics of Materials.12010, *2 00 














































14 


D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Houllevigue, L. The Evolution of the Sciences.8vo, 

Houstoun, R. A. Studies in Light Production.r2mo, 

Eowe, G. Mathematics for the Practical Man.*....nmo, 

Howorth, J. Repairing and Riveting Glass, China and Earthenware. 

8vo, paper, 

Hubbard, E. The Utilization of Wood-waste.....8vo, 

Hiibner, J. Bleaching and Dyeing of Vegetable and Fibrous Materials. 

(Outlines of Industrial Chemistry.).8vo, 

Hudson, 0 . F. Iron and Steel. (Outlines of Industrial Chemistry.).8vo, 

Humper, W. Calculation of Strains in Girders.i2mo, 

Humphreys, A. C. The Business Features of Engineering Practice..8vo, 

Hunter, A. Bridge Work.8vo. (In Press.) 

Hurst, G. H. Handbook of the Theory of Color.— ..8vo, 

-Dictionary of Chemicals and Raw Products. 8vo, 

-Lubricating Oils, Fats and Greases. 8vo, 

-Soaps.8vo, 

Hurst, G. H., and Simmons, W. H. Textile Soaps and Oils.8vo, 

Hurst, H. E., and Lattey, R. T. Text-book of Physics.8vo, 

-Also published in three parts. 

Part I. Dynamics and Heat. 

Part II. Sound and Light. 

Part III. Magnetism and Electricity. 

Hutchinson, R. W., Jr. Long Distance Electric Power Transmission. 

i2mo, 

Hutchinson, R. W., Jr., and Thomas, W. A. Electricity in Mining. i2mo, 

(In Press.) 

Hutchinson, W. B. Patents and How to Make Money Out of Them. 


i2mo, 

Hutton, W. S. Steam-boiler Construction..8vo, 

-Practical Engineer’s Handbook. 8vo, 

-The Works’ Manager’s Handbook. 8vo, 

Hyde, E. W. Skew Arches. (Science Series No. 15.).i6mo, 

Hyde, F. S. Solvents, Oils, Gums, Waxes....8vo, 

Induction Coils. (Science Series No. 53.).i6mo, 

Ingham, A. E. Gearing. A practical treatise. (In Press.) 

Ingle, H. Manual of Agricultural Chemistry...8vo, 

Inness, C. H. Problems in Machine Design.i2mo, 

-Air Compressors and Blowing Engines.nmo, 

-Centrifugal Pumps.nmo, 

-The Fan.i2mo, 

Isherwood, B. F. Engineering Precedents for Steam Machinery.. .8vo, 
Ivatts, E. B. Railway Management at Stations.8vo, 

Jacob, A., and Gould, E. S. On the Designing and Construction of 

Storage Reservoirs. (Science Series No. 6).i6mo, 

Jannettaz, E. Guide to the Determination of Rocks. Trans, by G. W. 

Plympton.nmo, 

Jehl, F. Manufacture of Carbons.8vo, 


Jennings, A. S. Commercial Paints and Painting. (Westminster Series.) 

8vo, 


*2 00 
2 00 
25 

*0 50 
*2 50 

*5 00 
*2 00 
2 50 
*1 25 

*2 50 
*3 00 
*4 00 
*5 00 
*2 50 

*3 OD 

*1 25 
*1 25 
*r 50 

*3 02 


1 25 

6 00 

7 co 
6 00 
o 50 

*2 00 

o 53 

*3 00 
*2 00 
*2 00 
*2 00 
*2 00 

2 50 
*2 50 


O 5® 

1 50 
*4 00 

*2 00 










































D. VAN NOSTRAND CO/S SHORT TITLE CATALOG 


Jennison, F. H. The Manufacture of Lake Pigments.8vo, 

Jepson, G. Cams and the Principles of their Construction.8vo, 

Mechanical Drawing.8vo {In Preparation.) 

Jockin, W. Arithmetic of the Gold and Silversmith.nmo, 

Johnson, T. H. Arc Lamps and Accessory Apparatus. (Installation 

Manuals Series.).. . . . i2mo, 

Johnson, T. M. Ship Wiring and Fitting. (Installation Manuals Series.) 

i2mo, 

Johnson, W. H. The Cultivation and Preparation of Pa~a Rubber. .8vo, 

Johnson, W. McA. The Metallurgy of Nickel. {In Preparation.) 

Johnston, J. F. W., and Cameron, C. Elements of Agricultural Chemistry 


and Geology ..nmo, 

Joly, J. Radioactivity and Geology.i2mo, 

Jones, H. C. Electrical Nature of Matter and Radioactivity.i2mo, 

-New Era in Chemistry.i2mo, 


Jones, M. W. Testing Raw Materials Used in Paint.i2mo, 

Jones, L., and Scard, F. I. Manufacture of Cane Sugar.8vo, 

Jordan, L. C. Practical Railway Spiral.nmo, leather, 

Joynson, F. H. Designing and Construction of Machine Gearing . .8vo, 
Jiiptner, H. F. V. Siderology: The Science of Iron.8vo, 


Kansas City Bridge.4to, 

Kapp, G. Alternate Current Machinery. (Science Series No. 96.).i6mo, 

Keim, A. W. Prevention of Dampness in Buildings.8vo, 

Keller, S. S. Mathematics for Engineering Students. i2mo, half leather. 


Algebra and Trigonometry, with a Chapter on Vectors. 

Spe ial Algebra Edition. 

Plane and Solid Geometry. 

Analytical Geometry and Calculus. 

Kelsey, W. R. Continuous-current Dynamos and Motors.8vo, 

Kemble, W. T., and Underhill, C. R. The Periodic Law and the Hydrogen 

Spectrum.8vo, paper, 

Kemp, J. F. Handbook of Rocks.8vo, 

Kendall, E. Twelve Figure Cipher Code.4to, 

Kennedy, A. B. W., and Thurston, R. H. Kinematics of Machinery. 

(Science Series No. 54.).i6mo, 

Kennedy, A. B. W., Unwin, V/. C., and Idell, F. E. Compressed Air. 

(Science Series No. 106.).i6mo, 

Kennedy, R. Modern Engines and Power Generators. Six Volumes. 4to, 

Single Volumes.each, 

-Electrical Installations. Five Volumes.4to, 

Single Volumes.each, 

-Flying Machines; Practice and Design.i2mo, 

-Principles of Aeroplane Construction.8vo, 

Kenneliy, A. E. Electro-dynamic Machinery.8vo, 

Kent, W. Strength of Materials. (Science Series No. 41.).i6mo, 

Kershaw, J. B. C. Fuel, Water and Gas Analysis.8vo, 

-Electrometallurgy. (Westminster Series.).8vo, 

-The Electric Furnace in Iron and Steel Production.nmo, 


Electro-Thermal Methods of Iron and Steel Production-8vo, 


15 

*3 00 

*1 50 

*1 00 

*0 75 

*0 75 
*3 00 


2 60 
~\3 0 ° 
*2 00 
*2 00 

*2 00 
*5 00 

*1 50 

2 00 
*5 00 

6 00 
o 50 
*2 00 

*1 75 
*1.00 
*1.25 
*2 00 
*2 50 

*0 50 

*1 50 

*12 50 

o 50 

o 50 
15 00 

3 00 
15 00 

3 50 
*2 00 

*1 50 
1 50 
o 50 
*2 50 
*2 00 

*1 50 

*3 00 













































lO D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Kinzbrunner, C. Alternate Current Windings.8vo, *i 50 

■-Continuous Current Armatures.8vo, *1 50 

-Testing of Alternating Current Machines.8vo, *2 00 

Kirkaldy, W. G. David Kirkaldy’s System cf Mechanical TezLng. .410, 10 00 

Kirkbride, J. Engraving for Illustration.8vo, *1 50 

Kirkwood, J. P. Filtration of River Waters.4to, 7 50 

Kirschke, A. Gas and Oil Engines.i2mo, *1 25 

Klein, J. F. Design of a High-speed Steam-engine.8vo, *5 00 

-Physical Significance of Entropy.8vo, *1 50 

Kleinhans, F. B. Boiler Construction.8vo, 3 00 

Knight, R.-Adm. A. M. Modern Seamanship.8vo, *7 50 

Half morocco. *9 00 

Knox, J. Physico-Chemical Calculations.i2mo, *1 00 

—•—Fixation of Atmospheric Nitrogen. (Chemical Monographs, 

No. 4.)...i2mo. (In Press.) 

Knox, W. F. Logarithm Tables. (In Preparation.) 

Knott, C. G., and Mackay, J. S. Practical Mathematics.8vo, 2 00 

Koester, F. Steam-Electric Power Plants.4to, *5 00 

-Hydroelectric Developments and Engineering.4to, *5 00 

Roller, T. The Utilization of Waste Products.8vo, *3 50 

-Cosmetics.8vo, *2 50 

Kremann, R. Application of the Physico-Chemical Theory to Tech¬ 
nical Processes and Manufacturing Methods. Trans, by H. 

E. Potts.8vo, *3 00 

Kretchmar, K. Yarn and Warp Sizing.8vo, *4 00 

Lallier, E. V. Elementary Manual of the Steam Engine.i2mo, *2 00 

Lambert, T. Lead and Its Compounds.8vo, *3 50 

-Bone Products and Manures. 8vo, *3 00 

Lamborn, L. L. Cottonseed Products.8vo, *3 00 

-Modern Soaps, Candles, and Glycerin.8vo, *7 50 

Lamprecht, R. Recovery Work After Pit Fires. Trans, by C. Salter 8vo, *4 00 
Lancaster, M. Electric Heating, Cooking, Cleaning. .i2mo. (In Press.) 

Lanchester, F. W. Aerial Flight. Two Volumes. 8vo. 

Vol. I. Aerodynamics... *6 00 

-Aerial Flight. Vol. II. Aerodonetics. *6.00 

Larner, E. T. Principles of Alternating Currents.i2mo. *1 25 

Larrabee, C. S. Cipher and Secret Letter and Telegraphic Code. i6mo, o 60 

La Rue, B. F. Swing Bridges. (Science Series No. 107.).i6mo, o 50 

Lassar-Cohn. Dr. Modern Scientific Chemistry. Trans, by M. M. 

Pattison Muir.i2mo, *2 00 

Latimer, L. H., Field, C. J., and Howell, J. W. Incandescent Electric 

Lighting. (Science Series No. 57.) .i6mo, 050 

Latta, M. N. Handbook of American Gas-Engineering Practice . . . 8vo, *4 50 

-American Producer Gas Practice..4to, *6 00 

Lawson, W. R. British Railways. A Financial and Commercial 

Survey.8vo, 2 00 

Leask, A. R. Breakdowns at Sea.i2mo, 2 00 

-Refrigerating Machinery.i2mo, 2 00 

Lecky, S. T. S. “ Wrinkles ” in Practical Navigation.8vo, *8 00 














































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


17 


Le Doux, M. Ice-Making Machines. (Science Series No. 46.). .i6mo, o 50 

Leeds, C. C. Mechanical Drawing for Trade Schools.oblong 4to, 

High School Edition. *1 25 

Machinery Trades Edition. *2 00 

Lefevre, L. Architectural Pottery. Trans, by H. K. Bird and W. M. 

. Binns.4to, *y 

Lehner, S. Ink Manufacture. Trans, by A. Morris and H. Robson. 8vo, *2 50 

Lemstrom, S. Electricity in Agriculture and Horticulture.8vo, *1 50 

Letts, E. A. Fundamental Problems in Chemistry.8vo, *2 00 

Le Van, W. B. Steam-Engine Indicator. (Science Series No. 78.)i6mo, o 50 
Lewes, V. B. Liquid and Gaseous Fuels. (Westminster Series.). .8vo, *2 00 

-Carbonization of Coal.8vo, *3 00 

Lewis, L. P. Railway Signal Engineering.8vo, *3 50 

Lieber, B. F. Lieber’s Standard Telegraphic Code.8vo, *10 00 

-Code. German Edition.8vo, *10 00 

-Spanish Edition.8vo, *10 00 

-French Edition.8vo, *10 00 

-Terminal Index.8vo, *2 50 

-Lieber’s Appendix.-.folio, *15 co 

-Handy Tables.4to, *250 

-Bankers and Stockbrokers’ Code and Merchants and Shippers’ 

Blank Tables.8vo, *15 00 

-100,000,000 Combination Code.8vo, *10 00 

-Engineering Code.8vo, *12 50 

Livermore, V. P., and Williams, J. How to Become a Competent Motor- 

man.i2mo, *1 oo 

Liversedge, A. J. Commercial Engineering.8vo, *3 00 

Livingstone, R. Design and Construction of Commutators.8vo, *2 25 

-Mechanical Design and Construction of Generators.8vo. (In Press.) 

> / 

Lobben, P. Machinists’and Draftsmen’s Handbook.8vo, 2 50 

Lockwood, T. D. Electricity, Magnetism, and Electro-telegraph. . . 8vo, 2 50 

Lockwood, T. D. Electrical Measurement and the Galvanometer. 

i2mo, o 75 


Lodge, O. J. Elementary Mechanics.i2mo, 1 50 

—— Signalling Across Space without Wires.8vo, *2 co 

Loewenstein, L. C., and Crissey, C. P. Centrifugal Pumps. *4 50 

Lord, R. T. Decorative and Fancy Fabrics.8vo, *3 50 

Loring, A. E. A Handbook of the Electromagnetic Telegraph .... iomo o 50 

-Handbook. (Science Series No. 39.).i6mo, o 50 

Low, D. A. Applied Mechanics (Elementary).i6mo, o 80 

Lubschez, B. J. Perspective.i2mo, *1 50 

Lucke, C. E. Gas Engine Design.8vo, *3 00 


-Power Plants: Design, Efficiency, and Power Costs. 2 vols. 

(In Preparation.) 

Lunge, G. Coal-tar and Ammonia. Two Volumes.8vo, *15 oo 

-Manufacture of Sulphuric Acid and Alkali. Four Volumes. . . .8vo, 

Vol. I. Sulphuric Acid. In three parts.*18 00 

Vol. H. Salt Cake, Hydrochloric Acid and Leblanc Soda. In two 

parts.*15.00 

















































l8 D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Lunge, G. Manufacture of Sulphuric Acid and Alkali. 

Vol. III. Ammonia Soda. *1000 

Vol. IV. Electrolytic Methods. (In Press.) 

-Technical Chemists’ Handbook... i2mo, leather, *3 50 

-Technical Methods of Chemical Analysis. Trans, by C. A. Keane 

in collaboration with the corps of specialists. 

Vol. I. In two parts.8vo, *15 00 

Vol. II. In two parts.•...8vo, *18 00 

Vol. Ill. (In Preparation.) 

Lupton, A., Parr, G. D. A., and Perkin, H. Electricity as Applied to 

Mining..8vo, *4 50 

Luquer, L. M. Minerals in Rock Sections.8vo, *1 50 


M acewen, H. A. Food Inspection.8vo, *2 50 

Mackenzie, N. F. Notes on Irrigation Works. 3 vo, *2 50 

Mackie, J. How to Make a Woolen Mill Pay.8vo, *2 00 


Mackrow, C. Naval Architect’s and Shipbuilder’s Pocket-book. 

i6mo, leather, 5 00 

Maguire, Wm. R. Domestic Sanitary Drainage and Plumbing . . . .8vo, 4 00 

Mallet, A. Compound Engines. Trans, by R. R. Buel. (Science Series 

No. 10.). ..i6mo, 

Mansfield, A. N. Electro-magnets. (Science Series No. 64.) ...i6mo, o 50 

Marks, E. C. R. Construction of Cranes and Lifting Machinery .nmo, *1 50 

-Construction and Working of Pumps.i2mo, *1 50 

-Manufacture of Iron and Steel Tubes.12010, *2 00 

--Mechanical Engineering Materials.12010, *1 00 

. Marks, G. C. Hydraulic Power Engineering.8vo, 3 50 

•-Inventions, Patents and Designs.i2mo, *1 00 

Marlow, T. G. Drying Machinery and Practice.8vo, *5 00 

Marsh, C. F. Concise Treatise on Reinforced Concrete.8vo, *2 50 

-Reinforced Concrete Compression Member Diagram. Mounted on 

Cloth Boards.. *1.50 

Marsh, C. F., and Dunn, V/. Manual of Reinforced Concrete and Con¬ 
crete Block Construction.16mo, morocco., *2 50 

Marshall, W. J., and Sankey, H. R. Gas Engines. (Westminster Series.) 

8vo, *2 00 

Martin, G. Triumphs and Wonders of Modern Chemistry. ..8vo, *2 00 

Martin, N. Properties and Design of Reinforced Concrete.i2mo, *2 50 

Massie, W. W., and Underhill, C. R. Wireless Telegraphy and Telephony. 

i2mo, *1 00 

Matheson,D. Australian Saw-Miller’s Log and Timber Ready Reckoner. 

i2ino, leather, 1 50 


J Mathot, R. E. Internal Combustion Engines.8vo, *6 00 

Maurice, W. Electric Blasting Apparatus and Explosives.8vo, *3 50 

--Shot Firer’s Guide.8vo, *1 50 

Maxwell, J. C. Matter and Motion. (Science Series No. 36.). 

i6mo, o 50 

Maxwell, W. H., and Brown, J. T. Encyclopedia of Muncipal and Sani¬ 
tary Engineering. . 4to, *10 00 

Mayer, A. M. Lecture Notes on Physics. 8vo, 2 00 

& McCullough, R. S. Mechanical Theory of Heat.8vo, 3 50 

































D. VAN NOSTRAND CO/S SHORT TITLE CATALOG 


McIntosh, J. G. Technology of Sugar.8vo, 

-Industrial Alcohol.8vo, 


Manufacture of Varnishes and Kindred Industries. Three Volumes. 
8 vo. 


Vol. I. Oil Crushing, Refining and Boiling. 

Vol. II. Varnish Materials and Oil Varnish Making. 

Vol. III. Spirit Varnishes and Materials. 

McKnight, J. D., and Brown, A. W. Marine Multitubular Boilers. 

McMaster, J. B. Bridge and Tunnel Centres. (Science Series No. 20.) 

i6mo, 

McMechen, F. L. Tests for Ores, Minerals and Metals.i2mo, 

McPherson, J. A. Water-works Distribution.8vo, 

Melick, C. W. Dairy Laboratory Guide.i2mo, 

Merck, E. Chemical Reagents; Their Purity and Tests. Trans, by 

H. E. Schenck..8vo, 

Merivale, J. H. Notes and Formulae for Mining Students.i2mo, 

Merritt, Wm. H. Field Testing for Gold and Silver.i6mo, leather, 

Messer, W. A. Railway Permanent Way.8vo (In Press.) 

Meyer, J. G. A., and Pecker, C. G. Mechanical Drawing and Machine 

Design. 4to, 

Michell, S. Mine Drainage. 8vo, 

Mierzinski, S. Waterproofing of Fabrics. Trans, by A. Morris and H. 

Robson. 8vo, 

Miller, G. A. Determinants. (Science Series No 105.).i6mo, 

Milroy, M. E. W. Home Lace-making.i2mo, 

Minifie, W. Mechanical Drawing.8vo, 

Mitchell, C. A. Mineral and Aerated Waters.8vo, 

Mitchell, C. A., and Prideaux, R. M. Fibres Used in Textile and Allied 

Industries.8vo, 

Mitchell, C. F., and G. A. Building Construction and Drawing. i2mo. 

Elementary Course. 

Advanced Course..*.;. 


Monckton, C. C. F. Radiotelegraphy. (Westminster Series.).8vo, 

Ivlonteverde, R. D. Vest Pocket Glossary of English-Spanish, Spanish- 


English Technical Terms.641110, leather, 

Montgomery, J. H. Electric Wiring Specifications. (In Press.) 

Moore, E. C. S. New Tables for the Complete Solution of Ganguillet and 
Kutt Ts Formula.8vo, 


Morecroft, J. H., and Hehre, F. W. Short Course in Electrical Testing. 

8vo, 

Moreing, C. A., and Neal, T. New General and Mining Telegraph Code. 


8vo, 

Morgan, A. P. Wireless Telegraph Apparatus for Amateurs.i2mo, 

Moses, A. J. The Characters of Crystals.8vo, 

-and Parsons, C. L. Elements of Mineralogy.Ovo, 

Moss, S.A. Elements cf Gas Engine Design.(Science Series No.i2i.)i6mo, 

-The Lay-out of Corliss Valve Gears. (Science Series No. 119.)i6mo, 

Mulford, A. C. Boundaries and Landmarks.i2mo, 

Midlin, J. P. Modem Moulding and Pattern-making.i2mo, 


19 

*4 50 
*3 00 


*3 50 
*4 00 
*4 50 

*1 50 

o 50 
*1 00 
2 50 
*1 25 

1 00 

1 50 
1 50 


5 00 
10 00 

*2 50 

*1 00 
*4 00 
*3 00 

*3 00 

*1 50 
*2 50 

*2 00 
*1 00 


*5 co 

*1 50 

*5 00 
*1 50 
*2 00 
*2 50 

o 50 
O 50 
*1 00 
2 50 





































20 D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 

Munby, A. E. Chemistry and Physics of Building Materials. (West¬ 
minster Series.).8vo, *2 oo 

Murphy, J. G. Practical Mining...i6mo, i oo 

Murphy, W. S. Textile Industries. Eight Volumes. *20 00 

‘Sold separately, each, *3 00 

Murray, J. A. Soils and Manures. (Westminster Series.).8vo, *2 00 

Naquet, A. Legal Chemistry.i2mo, 2 00 

Nasmith, J. The Student’s Cotton Spinning.8vo, 3 co 

-Recent Cotton Mill Construction.i2mo, 2 00 

Neave, G. B., and Heilbron, I. M. Identification of Organic Compounds. 

i2mo, *1 25 

Neilson, R. M. Aeroplane Patents. 8vo, *2 00 

Nerz, F. Searchlights. Trans, by C. Rodgers.8vo, *3 00 

Neuberger, H., and Noalhat, H. Technology of Petroleum. Trans, by 

J. G. McIntosh.8vo, *10 00 

Newall, J. W. Drawing, Sizing and Cutting Bevel-gears.8vo, 1 50 

Nicol, G. Ship Construction and Calculations.8vo, *450 

Nipher, F. E. Theory of Magnetic Measurements.i2mo, 1 00 

Nisbet, H. Grammar of Textile Design.8vo, *3 00 

Nolan, H. The Telescope. ’(Science Series No. 51.).i6mo, 050 

Noll, A. How to Wire Buildings.izmo, 1 50 

North, H. B. Laboratory Experiments in General Chemistry.i2mo, *1 co 

Nugent, E. Treatise on Optics.nmo, 1 50 

O’Connor, H. The Gas Engineer’s Pocketbook.i2mo, leather, 3 50 

-Petrol Air Gas.i2mo, *0 75 

Ohm, G. S., and Lockwood, T. D. Galvanic Circuit. Translated by 

William Francis. (Science Series No. 102.).i6mo, o 50 

Olsen, J. C. Text-book of Quantitative Chemical Analysis.8vo, *4 00 

Olsson, A. Motor Control, in Turret Turning and Gun Elevating. (U. S. 

Navy Electrical Series, No. 1.).i2mo, paper, *0 50 

Ormsby, M. T. M. Surveying.i2mo, 1 50 

Oudin, M. A. Standard Polyphase Apparatus and Systems.8vo, *3 00 

Owen, D. Recent Physical Research.8vo, *1 50 

Pakes, W. C. C., and Nankivell, A. T. The Science of Hygiene . .8vo, *1 75 

Palaz, A. Industrial Photometry. Trans, by G. W. Patterson, Jr. . 8vo, *4 00 

Pamely, C. Colliery Manager’s Handbook.8vo, *10 00 

Parker, P. A. M. The Control of Water.8vo, *5 00 

Parr, G. D. A. Electrical Engineering Measuring Instruments... .8vo, *3 50 

Parry, E. J. Chemistry of Essential Oils and Artificial Perfumes.. .8vo, *5 00 

-Foods and Drugs. Two Volumes.8vo, 

Vol. I. Chemical and Microscopical Analysis of Foods and Drugs. *7 50 

Vol. II. Sale of Food and Drugs Act. *3 00 

-and Coste, J. H. Chemistry of Pigments.8vo, *4 50 

Parry, L. A. Risk and Dangers of Various Occupations.8vo, *3 00 

Parshall, H. F., and Hobart, H. M. Armature Windings.4to, *7 50 

-Electric Railway Engineering.4to, *10 00 

•-and Parry, E. Electrical Equipment of Tramways. . {In Press.) 








































D. VAN NOSTRAND CO.’S SHORT TITLE CAT 4 LOG 21 

Parsons, S. J. Malleable Cast Iron.Svo, * 2 50 

Partington, J. R. Higher Mathematics for Chemical Students.. 12010, *2 00 

-Textbook of Thermodynamics.8vo, *4 00 

Passmore, A. C. Technical Terms Used in Architecture.3vo, *3 50 

Patched, W. H. Electric Power in Mines.8vo, *4 00 

Paterson, G. W. L. Wiring Calculations.i2mo, *2 00 

Patterson, D. The Color Printing of Carpet Yarns.8vo, *3 50 

-Color Matching on Textiles.8vo, *3 00 

-The Science of Color Mixing.8vo, *3 00 

Paulding, C. P. Condensation of Steam in Covered and Bare Pipes. .8vo, *2 00 

Transmission of Heat through Cold-storage Insulation.i2mo, *1 00 

Payne, D. W. Iron Founders’ Handbook. (In Press.) 

Peddie, R. A. Engineering and Metallurgical Books.i2mo, *1 50 

Peirce, B. System of Analytic Mechanics.4to, 10 00 

Pendred, V. The Railway Locomotive. (Westminster Series.).8vo, *200 

Perkin, F. M. Practical Methods of Inorganic Chemistry.i2mo, *1 00 

Perrigo, 0 . E. Change Gear Devices.8vo, 1 00 

Perrine, F. A. C. Conductors for Electrical Distribution.8vo, *3 50 

Perry, J. Applied Mechanics.8vo, *2 50 

Petit, G. White Lead and Zinc White Paints.8vo, *1 50 

Petit, R. How to Build an Aeroplane. Trans, by T. O’B. Hubbard, and 

J. H. Ledeboer.8vo, *1 50 

Pettit, Lieut. J. S. Graphic Processes. (Science Series No. 76.)... i6mo, o 53 
Philbrick, P. H. Beams and Girders. (Science Series No. 88.).. .i6mo, 

Phillips, J. Engineering Chemistry.8vo, *4 50 

-Gold Assaying.8vo, *2 50 

-Dangerous Goods.8vo, 3 50 

Phin, J. Seven Follies of Science.i2mo, *1 25 

Pickworth, C. N. The Indicator Handbook. Two Volumes. . i2mo, each, 1 50 

-Logarithms for Beginners.12mo. boards, o 50 

-The Slide Rule.i2tno, 1 00 

* 

Plattner’s Manual of Blow-pipe Analysis. Eighth Edition, revised. Trans. 

by H. B. Cornwall.8vo, *4 00 

Plympton, G. W. The Aneroid Barometer. (Science Series No. 35.) i6mo, o 50 

-How to become an Engineer, (Science Series No. 100.).i6mo, o 50 

-Van Nostrand’s Table Book. (Science Series No. 104.).i6mo, o 50 

Pochet, M. L. Steam Injectors. Translated from the French. (Science 

Series No. 29.).,.i6mo, o 50 

Packet Logarithms to Four Places. (Science Series No. 65.).i6mo, o 50 

leather, 1 00 

Polleyn, F. Dressings and Finishings for Textile Fabrics.8vo, *3 00 

Pope, F. G. Organic Chemistry.12010, *2 25 

Pope, F. L. Modern Practice of the Electric Telegraph.8vo, 1 50 

Popple well, W. C. Elementary Treatise on Heat and Heat Engines. . 12 mo, *3 00 

-Prevention of Smoke.8vo, *3 50 

-Strength of Materials.8vo, *1 75 

Porritt, B. D. The Chemistry of Rubber. (Chemical Monographs, 

No. 3.).iamo, *075 

Porter, J. R. Helicopter Flying Machine.12010, *1 25 

Potter, T. Concre'e.8vo, *3 0# 














































22 


D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Potts, U. E. Chemistry of the Rubber Industry. (Outlines of Indus¬ 
trial Chemistry).8vo, *2 00 

Practical Compounding of Oils, Tallow and Grease.8vo, *3 50 

Practical Iron Founding.12010, 1 50 

Pratt, K. Boiler Draught.nmo, *1 25 

Pray, T., Jr. Twenty Years with the Indicator.8vo, 2 50 

-Steam Tables and Engine Constant.8vo, 2 00 

Preece, W. H. Electric Lamps.. N . . . . ( In Press.) 

Prelini, C. Earth and Rock Excavation.8vo, *3 00 

-Graphical Determination of Earth Slopes.8vo, *2 00 

-Tunneling. New Edition. 8vo, *3 00 

-Dredging. A Practical Treatise.8vo, *3 00 

Prescott, A. B. Organic Analysis.8vo, 5 co 

Prescott, A. B., and Johnson, 0 . C. Qualitative Chemical Analysis. . .8vo, *3 50 

Prescott, A. B., and Sullivan, E. C. First Book in Qualitative Chemistry. 

i2mo, *1 50 

Prideaux, E. B. R. Problems in Physical Chemistry.8vo, *2 00 

Pritchard, 0 . G. The Manufacture of Electric-light Carbons. .8vo, paper, *0 60 

Pullen, W. W. F. Application of Graphic Methods to the Design of 

Structures.i2mo, *2 50 

-Injectors: Theory, Construction and Working.i2mo, *1 50 

Pulsifer, W. H. Notes for a History of Lead. . .8vo, 4 00 

Purchase, W. R. Masonry.i2mo, *3 00 

Putsch, A. Gas and Coal-dust Firing.8vo, *3 00 

Pynchon, T. R. Introduction to Chemical Physics.8vo, 3 00 

Rafter G. W. Mechanics of Ventilation. (Science Series No. 33.). i6mo, o 50 

-Potable Water. (Science Series No. 103.).i6mo, o 50 

-Treatment of Septic Sewage. (Science Series No. n 3 .) . .. i6mo, o 50 

Rafter, G. W., and Baker, M. N. Sewage Disposal in the United States. 

4to, *6 00 

Raikes, H. P. Sewage Disposal Works.8vo, *4 00 

Randall, P. M. Quartz Operator’s Handbook.i2mo, 2 00 

Randau, P. Enamels and Enamelling.8vo, *4 00 

Rankine, W. J. M. Applied Mechanics.8vo, 5 00 

-Civil Engineering.8vo, 6 50 

-Machinery and Millwork. 8vo, 5 00 

-The Steam-engine and Other Prime Movers.8vo, 5 00 

— Useful Rules and Tables.8vo, 4 00 

Tankine, W. J. M., and Bamber, E. F. A Mechanical Text-book.. .. 8vo, 3 50 
Raphael, F. C. Localization of Faults in Electric Light and Power Mains. 

Svo, *3 00 

Rasch, E. Electric Arc Phenomena. Trans, by K. Tornberg.8vo, *2 00 

Rathbone, R. L. B. Simple Jewellery.8vo, *2 00 

Rateau, A. Flow of Steam through Nozzles and Orifices. Trans, by H. 

B. Brydon.8vo *1 50 

Rausenberger, F. The Theory of the Recoil of Guns.8vo, *4 50 

Rautenstrauch, W. Notes on the Elements of Machine Design.8vo, boards, *1 50 

Rautenstrauch, W., and Williams, J. T. Machine Drafting and Empirical 
Design. 




































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 23 


<* 

Part I. Machine Drafting.g VOj 25 

Part II. Empirical Design.(7n Preparation.) 

Raymond, E. B. Alternating Current Engineering.i2mo, *2 50 

Rayner, H. Silk Throwing and Waste Silk Spinning.8vo, *2 50 

Recipes for the Color, Paint, Varnish, Oil, Soap and Drysaltery Trades.8vo, *3 50 
Recipes for Flint Glass Making.-.i2mo, *4 50 

Redfern, J. B., and Savin, J. Bells, Telephones (Installation Manuals 

Series.).i6mo, *0 50 

Redgrove, H. S. Experimental Mensuration.i2mo, *1 25 

Redwood, B. Petroleum. (Science Series No. 92.).i6mo, o 50 

Reed, S. Turbines Applied to Marine Propulsion. *5 00 

Reed’s Engineers’Handbook.8vo, *5 00 

Key to the Nineteenth Edition of Reed’s Engineers’ Handbook. .8vo, *3 00 

-Useful Hints to Sea-going Engineers.i2mo, 1 50 

-Marine Boilers. I2 mo, 200 

■ Guide to the Use of the Slide Valve.i2mo, *1 60 

Reinhardt, C. W. Lettering for Draftsmen, Engineers, and Students. 


oblong 4to, boards, 1 00 

-The Technic of Mechanical Drafting.oblong 4to, boards, *1 00 

Reiser, F. Hardening and Tempering of Steel. Trans, by A. Morris and 

H. Robson.12013, *2 50 

Reiser, N. Faults in the Manufacture of Woolen Goods. Trans, by A. 

Morris and H. Robson.8vo, *2 50 

-Spinning and Weaving Calculations.8vo, *5 00 

Renwick, W. G. Marble and Marble Working.8vo, 5 00 

Reynolds, O., and Idell, F. E. Triple Expansion Engines. (Science 

Series No. 99.).i6mo, o 50 

Rhead, G. F. Simple Structural Woodwork.i2mo, *1 00 

Rhodes, H. J. Art of Lithography.8vo, 3 50 

Rice, J. M., and Johnson, W. W. A New Method of Obtaining the Differ¬ 
ential of Functions.12110, o 50 

Richards, W. A. Forging of Iron and Steel. (In Press.) 


Richards, W. A., and North, H. B. Manual of Cement Testing.... i2mo, *1 50 


Richardson, J. The Modern Steam Engine.8vo, *3 50 

Richardson, S. S. Magnetism and Electricity.i2mo, *2 00 

Rideal, S. Glue and Glue Testing.8vo, *4 00 

Rimmer, E. J. Boiler Explosions, Collapses and Mishaps.8vo, *1 75 

Rings, F. Concrete in Theory and Practice.i2mo, *2 50 

-Reinforced Concrete Bridges.4to, *5 00 

Ripper, W. Course of Instruction in Machine Drawing.folio, *600 

Roberts, F. C. Figure of the Earth. (Science Series No. 79.).i6mo, o 50 

Roberts, J., Jr. Laboratory Work in Electrical Engineering.8vo, *2 00 

Robertson, L. S. Water-tube Boilers.8vo, 2 00 

Robinson, J. B. Architectural Composition.8vo, *2 50 

Robinson, S. W. Practical Treatise on the Teeth of Wheels. (Science 

Series No. 24.)..i6mo, o 5c 

-Railroad Economics. (Science Series No. 59.).i6mo, o 53 

■-Wrought Iron Bridge Members. (Science Series No. 60.).i6mo, o 50 

Robson, J. H. Machine Drawing and Sketching.8vo, *1 50 

Roebling, J. A. Long and Short Span Railway Bridges.folio, 25 oo 














































24 


D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Rogers, A. A Laboratory Guide of Industrial Chemistry.i2mo, *i 50 

Rogers, A., and Aubert, A. B. Industrial Chemistry.8vo, *5 oa 

Rogers, F. Magnetism of Iron Vessels. (Science Series No. 30.). i6mo, o 5o 

Rohland, P. Colloidal and Crystalloidal State of Matter. Trans, by 

W. J. Britland and H. E. Potts.12mo, *1 25 

Rollins, W. Notes on X-Light. 8 vo, *5 00 

Rollinson, C. Alphabets.Oblong, i2mo, *1 00 

Rose, J. The Pattern-makers’ Assistant.8vo, 2 50 

-Key to Engines and Engine-running.i2mo, 2 50 

Rose, T. K. The Precious Metals. (Westminster Series.).8vo, *2 00 

Rosenhain, W. Glass Manufacture. (Westminster Series.).8vo, *200 

Ross, W. A. Blowpipe in Chemistry and Metallurgy.i2mo, *2 00 

Roth. Physical Chemistry.8vo, *2 00 

Rouillion, L. The Economics of Manual Training. 8vo, 2 00 

Rowan, F. J. Practical Physics of the Modern Steam-boiler.8vo, *3 00 

-and Idell, F. E. Boiler Incrustation and Corrosion. (Science 

Series No. 27.).i6mo, 0 50 

Roxburgh, W. General Foundry Practice.8vo, *3 50 

Ruhmer, E. Wireless Telephony. Trans, by J. Erskine-Murray. .8vo, *3 50 

Russell, A. Theory of Electric Cables and Networks.8vo, *3 00 

Sabine, R. History and Progress of the Electric Telegraph.i2mo, 1 25 

Saeltzer, A. Treatise on Acoustics.i2mo, 1 00 

Sanford, P. G. Nitro-explosives.:.8vo, *4 00 

Saunders, C. H. Handbook of Practical Mechanics.i6mo, 1 00 

leather, 1 25 

Saunnier, C. Watchmaker’s Handbook.i2mo, 3 00 

Sayers, H. M. Brakes for Tram Cars.8vo, *1 25 

Scheele, C. W. Chemical Essays.8vo, *2 00 

Scheithauer, W. Shale Oils and Tars.8vo, *3 5o 

Schellen, H. Magneto-electric and Dynamo-electric Machines ... .8vo, 5 oo 

Scherer, R. Casein. Trans, by C. Salter.8vo, *3 00 

Schidrowitz, P. Rubber, Its Production and Industrial Uses.8vo, *5 00 

Schindler, K. Iron and Steel Construction Works.i2mo, *1 25 

Schmall, C. N. First Course in Analytic Geometry, Plane and Solid. 

i2mo, half leather, *1 75 

Schmall, C. N., and Shack, S. M. Elements of Plane Geometry.. . i2mo, *1 25 

Schmeer, L. Flow of Water.8vo, *3 or 

Schumann, F. A Manual of Heating and Ventilation. .. .i2mo, leather, 1 50 

Schwarz, E. H. L. Causal Geology.8vo, *2 50 

Schweizer, V. Distillation of Resins.8vo, *3 50 

Scott, W. W. Qualitative Analysis. A Laboratory Manual.8vo, *1 50 

Scribner, J. M. Engineers’ and Mechanics’ Companion. .i6mo, leather, 1 50 

Scudder, H.j Electrical Conductivity and Ionization Constants of 

Organic Compounds.8vo, *3 00 

Searle, A. B. Modern Brickraaking.8vo, *5 00 

-Cement, Concrete and Bricks.8vo, *3 00 

Searle, G. M. “Sumners’ Method.” Condensed and Improved. 

(Science Series No. 124.).i6mo, o 50 

Seaton, A. E. Manual of Marine Engineering.8vo 8 00 








































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Seaton, A. E., and Rounthwaite, H. M. Pocket-book of Marine Engi¬ 


neering.i6mo, leather, 

Seeligmann, T., Torrilhon, G. L., and Falconnet, H. India Rubber and 

Gutta Percha. Trans, by J. G. McIntosh.8vo, 

Seidell, A. Solubilities of Inorganic and Organic Substances.8vo, 

Sellew, W. H. Steel Rails. 4 to, 

Senter, G. Outlines of Physical Chemistry.i2mo, 

-Text-book of Inorganic Chemistry.i2mo, 

Sever, G. F. Electric Engineering Experiments.8vo, boards, 

Sever, G. F., and Townsend, F. Laboratory and Factory Tests in Elec¬ 
trical Engineering.8vo, 

Sewall, C. H. Wireless Telegraphy.8vo, 

-Lessons in Telegraphy.i2mo, 

Sewell, T. Elements of Electrical Engineering.8vo, 

-The Construction of Dynamos....8vo, 

Sexton, A. H. Fuel and Refractory Materials.i2mo, 

-Chemistry of the Materials of Engineering.i2mo, 

-Alloys (Non-Ferrous).8vo, 

-The Metallurgy of Iron and Steel. 8vo, 

Seymour, A. Practical Lithography.8vo, 

-Modern Printing Inks...8vo, 


Shaw, Henry S. H. Mechanical Integrators. (Science Series No. 83.) 


i6mo, 

Shaw, S. History of the Staffordshire Potteries.8vo, 

-Chemistry of Compounds Used in Porcelain Manufacture. .. .8vo, 

Shaw, W. N. Forecasting Weather.8vo, 

Sheldon, S., and Hausmann, E. Direct Current Machines.i2mo, 

-Alternating Current Machines.i2mo, 

Sheldpn, S., and Hausmann, E. Electric Traction and Transmission 

Engineering.i2mo, 

Sheriff, F. F. Oil Merchants’ Manual.i2mo, 

Shields, J. E. Notes on Engineering Construction.i2mo, 

Shreve, S. H. Strength of Bridges and Roofs.8vo, 

Shunk, W. F. The Field Engineer.i2mo, morocco, 

Simmons, W. H., and Appleton, H. A. Handbook of Soap Manufacture, 

8vo, 

Simmons, W. H., and Mitchell, C. A. Edible Fats and Oils.8vo, 

Simms, F. W. The Principles and Practice of Levelling.8vo, 


-Practical Tunneling.8vo, 

Simpson, G. The Naval Constructor.i2mo, morocco, 

Simpson, W. Foundations.8vo. (In Press.) 


Sinclair, A. Development of the Locomotive Engine.. .8vo, half leather, 
-Twentieth Century Locomotive.8vo, half leather, 

Sindall, R. W., and Bacon, W. N. The Testing of Wood Pulp.8vo, 

Sindall, R. W. Manufacture of Paper. (Westminster Series.). .. .8vo, 


Sloane, T. O’C. Elementary Electrical Calculations.i2mo, 

Smallwood, J. C. Mechanical Laboratory Methods. ...i2mo, leather, 


Smith, C. A. M. Handbook of Testing, MATERIALS.8vo, 

Smith, C. A. M., and Warren, A. G. New Steam Tables ..8vo, 


25 


3 00 

*5 00 
*3 00 
*12 50 
*1 7.5 
** 75 
*1 00 

*2 50 
*2 00 
: T 00 
*3 00 
*3 00 
*2 50 
*2 50 
*3 00 

*6 50 
*2 50 
*2 00 

o 50 

2 00 
*5 00 
*3 50 
*2 50 
*2 50 

*2 50 
*3 50 

1 50 

3 50 

2 50 

*3 00 
*3 00 
2 50 
7 50 
*5 00 

5 00 
*5 00 

*2 50 
*2 00 

*2 00 
*2 50 

*2 50 
*1 25 















































26 D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Smith, C. F. Practical Alternating Currents and Testing.8vo, *2 50 

-Practical Testing of Dynamos and Motors.8vo, *2 00 

Smith, F. E. Handbook of General Instruction for Mechanics . . . i2mo, 1 50 
Smith, H. G. Minerals and the Microscope. 

Smith, J. C. Manufacture of Paint.8vo, *3 oc 

-Paint and Painting Defects. 

Smith, R. H. Principles of Machine Work.nmo, *3 00 

-Elements of Machine Work..i2mo, *2 00 

Smith, W. Chemistry of Hat Manufacturing.i2mo, *3 00 

Snell, A. T. Electric Motive Power.8vo, *4 00 

Snow, W. G. Pocketbook of Steam Heating and Ventilation. (In Press.) 

Snow, W. G., and Nolan, T. Ventilation of Buildings. (Science Series 

No. 5.).i6mo, o 50 

Soddy, F. Radioactivity.8vx>, *3 00 

Solomon, M. Electric Lamps. (Westminster Series.).8vo, *2 00 

Sothern, J. W. The Marine Steam Turbine.8vo, *5 00 

-Verbal Notes and Sketches for Marine Engineers.8vo, *5 00 

Southcombe, J. E. Chemistry of the Oil Industries. (Outlines of In¬ 
dustrial Chemistry.).8vo, *3 00 

Soxhlet, D. H. Dyeing and Staining Marble. Trans, by A. Morris and 

H. Robson. 8vo, *2 50 

Spang, H. W. A Practical Treatise on Lightning Protection.i2mo, 1 00 

Spangenburg, L. Fatigue of Metals. Translated by S. H. Shreve. 

(Science Series No. 23.).i6mo, 0 50 

Specht, G. J., Hardy, A. S., McMaster, J. B., and Walling. Topographical 

Surveying. (Science Series No. 72.).i6mo, o 50 

Speyers, C. L. Text-book of Physical Chemistry.8vo, *2 25 . 

Sprague, E. H. Hydraulics.i2mo, 1 25* 

Stahl, A. W. Transmission of Power. (Science Series No. 28.) . i6mo, 

Stahl, A. W., and Woods, A. T. Elementary Mechanism.12.no, *2 00 

Staley, C., and Pierson, G. S. The Separate System of Sewerage.. .8/0, *3 00 

Standage, H. C. Leatherworkers’ Manual.8vo, *3 50 

-Sealing Waxes, Wafers, and Other Adhesives.8vo, *2 00 

-Agglutinants of all Kinds for all Purposes.12mo, *350 

Stanley, H. Practical Applied Physics. (In Press.) 

Stansbie, J. H. Iron and Steel. (Westminster Series.).8vo, *2 00 

Steadman, F. M. Unit Photography and Actinometry. (In Press.) 

Stecher, G. E. Cork. Its Origin and Industrial Uses.i2mo, 1 00 

Steinman, D. B. Suspension Bridges and Cantilevers. (Science Series 

No. 127.). o 50 

Stevens, H. P. Paper Mill Chemist..i6mo, *2 50 

Stevens, J. S. Precision of Measurements. (In Press.) 

Stevenson, J. L. Blast-Furnace Calculations.121110, leather, *2 00 

Stewart, A. Modern Polyphase Machinery.i2mo, *2 00 

Stewart, G. Modern Steam Traps.i2mo, *1 25 

Stiles, A. Tables for Field Engineers.i2mo, 1 00 

Stillman, P. Steam-engine Indicator.i2mo, 1 00 

Stodola, A. Steam Turbines. Trans, by L. C. Loewenstein... ... .8vo, *5 00 

Stone, H. The Timbers of Commerce.8vo, 3 50 

Stone, Gen. R. New Roads and Road Laws.i2mo, 1 00 













































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Stopes, M. Ancient Plants.8vo, * 

-The Study of Plant Life.8vo, * 

Stumpf, Prof. Una-Flow of Steam Engine.4to, * 

Sudborough, J. J., and James, T. C. Practical Organic Chemistry.. nmo, * 

Suffling, E. R. Treatise on the Art of Glass Painting.8vo, * 

Swan, K. Patents, Designs and Trade Marks. (Westminster Series.). 

8 vo, * 

Swinburne, J., Wordingham, C. H., and Martin, T. C. Electric Currents. 

(Science Series No. 109.).i6mo, 

Swoope, C. W. Lessons in Practical Electricity.nmo, * 


Tailfer, L. Bleaching Linen and Cotton Yarn and Fabrics.8vo, * 

Tate, J. S. Surcharged and Different Forms of Retaining-walls. (Science 

Series No. 7.).i6mo, 

Taylor, E. N. Small Water Supplies.nmo, * 

Templeton, W. Practical Mechanic’s Workshop Companion. 

i2mo, morocco, 

Terry, H. L. India Rubber and its Manufacture. (Westminster Series.) 

8vo, * 

Thayer, H. R. Structural Design. 8vo. 

Vol. I. Elements of Structural Design. * 

Vol. II. Design of Simple Structures.( 7 n Preparation.) 

Vol. III. Design of Advanced Structures. (In Preparation.) 

Thiess, J. B., and Joy, G. A. Toll Telephone Practice.8vo, * 

Thom, C., and Jones, W. H. Telegraphic Connections.. . oblong, nmo, 

Thomas, C. W. Paper-makers’ Handbook. (In Press.) 

Thompson, A. B. Oil Fields of Russia. 4 t°» 4 

-Petroleum Mining and Oil Field Development.8vo, * 

Thompson, S. P. Dynamo Electric Machines. (Science Series No. 75.) 

i6mo, 

Thompson, W. P. Handbook of Patent Law of All Countries.i6mo, 

Thomson, G. S. Milk and Cream Testing.i2mo, * 

-Modern Sanitary Engineering, House Drainage, etc.8vo, * 

Thornley, T. Cotton Combing Machines.8vo, * 

--Cotton Waste.8vo, 

-Cotton Spinning. 8vo. 

First Year. 

Second Year... 

Third Year. 

Thurso, J. W. Modern Turbine Practice.8vo, 

Tidy, C. Meymott. Treatment of Sewage. (Science Series No. 94.) i6mo, 
Tillmans, J. Water Purification and Sewage Disposal. Trans, by 

Hugh S. Taylor. 8v0 > 

Tenney, E. H. Test Methods for Steam Power Plants- (In Press.) 

Tinney, W. H. Gold-mining Machinery.8vo, 

Titherley, A. W. Laboratory Course of Organic Chemistry.8vo, 

Toch, M. Chemistry and Technology of Mixed Paints.8vo, 

_Materials for Permanent Painting.i2mo, 

_Chemistry and Technology of Mixed Paints. (In two volumes.) 

(In Press.) 


27 

2 00 

2 00 

3 50 

2 00 

3 50 

2 00 

o 50 
2 00 

5 00 

o 50 
2 00 

2 00 

2 00 

2 00 


3 50 
1 50 

7 5° 
5 00 

0 So 
1 53 
‘i 75 
‘3 00 
*3 00 
'3 00 

“1 50 

"2 50 
"2 50 
*4 00 
o 50 

*2 00 

*3 00 
*2 00 
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28 D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Todd, J., and Whall, W. B. Practical Seamanship.8vo, *750 

Tonge, J. Coal. (Westminster Series.).8vo, *2 00 

Townsend, F. Alternating Current Engineering.8vo, boards, *0 75 

Townsend, J. Ionization of Gases by Collision.8vo, *1 25 

Transactions of the American Institute of Chemical Engineers, 8vo. 

Vol. I. 1908. *6 00 

Vol. II. 1909.•. *6 00 

Vol. III. 1910. *6 00 

Vol. IV. 1911. *6 00 

Vol. V. 1912. *6 00 

Traverse Tables. (Science Series No. 115.).i6mo, 050 

morocco, 1 00 

Treiber, E. Foundry Machinery. Trans, by C. Salter.i2mo, 1 25 


Trinks, W., and Housum, C. Shaft Governors. (Science Series No. 122.) 

i6mo, o 50 

Trowbridge, W. P. Turbine Wheels. (Science Series No. 44.).. i6mo, 050 

Tucker, J. H. A Manual of Sugar Analysis.8vo, 3 50 

Tunner, P. A. Treatise on Roll-turning. Trans, by J. B. Pearse. 

8vo, text and folio atlas, 10 00 

Turnbull, Jr., J., and Robinson, S. W. A Treatise on the Compound 

Steam-engine. (Science Series No. 8.).i6mo, 

Turrill, S. M. Elementary Course in Perspective.i2mo, *125 


Underhill, C. R. Solenoids, Electromagnets and Electromagnetic Wind¬ 


ings.i2mo, *2 00 

Underwood, N., and Sullivan, T. V. Chemistry and Technology of 

Printing Inks..'. (In Press.) 

Urquhart, J. W. Electric Light Fitting.i2mo, 200 

-Electro-plating..i2mo, 2 00 

-Electrotyping.i2mo, 2 00 

-Electric Ship Lighting. i2mo, 3 00 

Usborne, P. O. G. Design of Simple Steel Bridges.8vo, *4 00 

Vacher, F. Food Inspector’s Handbook. 

Van Nostrand’s Chemical Annual. Third issue 1913... .leather, i2mo, *2 5c 

-Year Book of Mechanical Engineering Data. (In Press.) 

Van Wagenen, T. F. Manual of Hydraulic Mining.i6mo, 1 00 

Vega, Baron Von. Logarithmic Tables.8vo, cloth, 2 00 

half morroco, 2 50 

Vincent, C. Ammonia and its Compounds. Trans, by M. J. Salter. 8vo, *2 00 

Volk, C. Haulage and Winding Appliances.8vo, *4 00 

Von Georgievics, G. Chemical Technology of Textile Fibres. Trans. 

by C. Salter.8vo, *4 5o 

-Chemistry of Dyestuffs. Trans, by C. Salter.,.8vo, *450 

Vose, G. L. Graphic Method for Solving Certain Questions in Arithmetic 

and Algebra (Science Series No. 16.).i6mo, o 50 

Vosmaer, A. Ozone. (In Press.) 


Wabner, R. Ventilation in Mines. Trans, by C. Salter.8vo, *4 50 

Wade, E. J. Secondary Batteries.8vo, *4 00 



































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'Wadmore, T. M. Elementary Chemical Theory.i2mo, *1 50 

Wadsworth, C. Primary Battery Ignition.i2mo, *050 

Wagner, E. Preserving Fruits, Vegetables, and Meat.i2mo, *250 

Waldram, P. J. Principles of Structural Mechanics.i2mo, *300 

Walker, F. Aerial Navigation.8vo, 2 00 

-Dynamo Building. (Science Series No. 98.).i6mo, o so 

Walker, F. Electric Lighting for Marine Engineers.8vo, 2 00 

Walker, J. Organic Chemistry for Students of Medicine.8vo, *2 50 

Walker, S. F. Steam Boilers, Engines and Turbines.8vo, 3 00 

-Refrigeration, Heating and Ventilation on Shipboard.i2mo, *2 00 

-Electricity in Mining.8vo, *3 50 

Wallis-Tayler, A. J. Bearings and Lubrication.8vo, *1 50 

-Aerial or Wire Ropeways.8vo, *3 00 

-Motor Cars.8vo, 1 80 

-Motor Vehicles for Business Purposes.8vo, 3 50 

Wallis-Tayler, A. J. Pocket Book of Refrigeration and Ice Making. i2mo, 1 50 

--Refrigeration, Cold Storage and Ice-Making.8vo, *4 50 

-Sugar Machinery.i2mo, *2 00 

Wanklyn, J. A. Water Analysis.12010, 2 00 

Wansbrough, W. D. The A B C of the Differential Calculus.12010, *1 50 

-Slide Valves.12010, *2 00 

Wariog, Jr., G. E. Sanitary Conditions. (Science Series No. 31.) .i6mo, o 50 

-Sewerage and Land Drainage. *6 00 

Waring, Jr., G. E. Modern Methods of Sewage Disposal.12010, 2 00 

-How to Drain a House.12010, 1 25 

Waroes, A. R. Coal Tar Distillation.8vo, *2 50 

Warren, F. D. Handbook on Reinforced Concrete.i2mo, *2 50 

Watkins, A. Photography. (Westminster Series.).8vo, *200 

Watson, E. P. Small Engines and Boilers.12010, 1 25 

Watt, A. Electro-plating and Electro-refining of Metals.8vo, *4 50 

-Electro-metallurgy.12010, 1 00 

-The Art of Soap Making.8vo, 3 00 

-Leather Manufacture. 8v0 > *4 00 

-Paper-Making. 8v0 > 3 00 

Weale, J. Dictionary of Terms Used in Architecture.12010, 2 50 

Weale’s Scientific and Technical Series. (Complete list sent on appli¬ 
cation.) 

Weather and Weather Instruments.12010, 1 00 

paper, o 50 

Webb, H. L. Guide to the Testing of Insulated Wires and Cables. 12010, 1 00 

Webber, W. H. Y. Town Gas. (Westminster Series.).8vo, *200 

Weisbach, J. A Manual of Theoretical Mechanics.8vo, *6 00 

sheep, *7 50 

Weisbach, J., and Herrmann, G. Mechanics of Air Machinery... .8vo, *3 75 

Welch, W. Correct Lettering. (In Press.) 

Weston, E. B. Loss of Head Due to Friction of Water in Pipes. .12010, *1 50 

Weymouth, F. M. Drum Armatures and Commutators.8vo, *3 00 

Wheatley, 0 . Ornamental Cement Work. (In Press.) 

Wheeler, J. B. Art of War.. 1 75 

-Field Fortifications.. 1 75 























































30 


D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Whipple, S. An Elementary and Practical Treatise on Bridge Building 
White, A. T. Toothed Gearing. .. 


Wilcox, R. M. Cantilever Bridges. (Science Series No. 25.). 

Wilda, H. Steam Turbines. Trans, by C. Salter. 

-Cranes and Hoists. Trans, by C. Salter. 


Williamson, R. S. 


8vo, 

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Wilson, F. J., and Heilbron, I. M. Chemical Theory and Calculations. 

i2mo, 

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Wimperis, H. E. Internal Combustion Engine.8vo, *3 00 

-Application of Power to Road Transport.i2mo, *1 50 

-Primer of Internal Combustion Engine.i2mo, *1 00 

Winchell, N. H., and A. N. Elements of Optical Mineralogy.8vo, *3 50 

Winkler, C., and Lunge, G. Handbook of Technical Gas-Analysis. .8vo, 4 00 

Winslow, A. Stadia Surveying. (Science Series No. 77.).i6mo, o 50 

Wisser, Lieut. J. P. Explosive Materials. (Science Series No. 70.) 

i6mo, o 50 

Wisser, Lieut. J. P. Modern Gun Cotton. (Science Series No. 89.). i6mo, 050 
Wood, De V. Luminiferous Aether. (Science Series No. 85)...i6mo, o 50 
Wood, J. K. Chemistry of Dyeing. (Chemical Monographs No. 2.) 

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Worden, E. C. The Nitrocellulose Industry. Two Volumes.8vo, 

-Cellulose Acetate.8vo, (In Press.) 

Wren, H. Organometallic Compounds of Zinc and Magnesium. (Chem¬ 
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Wright, A. C. Analysis of Oils and Allied Substances.8vo, 

-Simple Method for Testing Painters’ Materials.8vo, 

Wright, F. W. Design of a Condensing Plant.i2mo, *1 50 


10 00 


75 
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Wright, H. E. Handy Book for Brewers.8vo, 

Wright, J. Testing, Fault Finding, etc., for Wiremen. (Installation 


"5 00 


Young, J. E. Electrical Testing for Telegraph Engineers.8vo, 


Zimmer, G. F. Mechanical Handling of Material.4to, *10 00 

Zipser, J. Textile Raw Materials. Trans, by C. Salter. ..,.8vo, 

Zur Nedden, F. Engineering Workshop Machines and Processes. Trans, 
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